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The electric potential is an essential quantity for the confinement process of tokamak plasmas, with important impact on the performances of fusion reactors. Understanding its evolution in the peripheral region – the part of the plasma interacting with the wall of the device – is of crucial importance, since it governs the boundary conditions for the burning core plasma. The aim of the present paper is to study numerically the evolution of the electric potential in this peripheral plasma region. In particular, we are interested in introducing an efficient Asymptotic-Preserving (AP) numerical scheme capable to cope with the strong anisotropy of the problem as well as the non-linear boundary conditions, and this with acceptable computational costs. This work constitutes the numerical follow-up of the more mathematical paper by C. Negulescu, A. Nouri, Ph. Ghendrih, Y. Sarazin, Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics . [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe a Matlab toolbox, called μ -diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in μ -diff are based on the Fourier series expansions of the four basic integral operators arising in scattering theory. Based on these expressions, an efficient spectrally accurate finite-dimensional solution of multiple scattering problems can be simply obtained for complex media even when many scatterers are considered as well as large frequencies. The solution of the global linear system to solve can use either direct solvers or preconditioned iterative Krylov subspace solvers for block Toeplitz matrices. Based on this approach, this paper explains how the code is built and organized. Some complete numerical examples of applications (direct and inverse scattering) are provided to show that μ -diff is a flexible, efficient and robust toolbox for solving some complex multiple scattering problems. Program summary Program title: μ -diff Catalogue identifier: AEWH_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEWH_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 13,718 No. of bytes in distributed program, including test data, etc.: 1,466,301 Distribution format: tar.gz Programming language: Matlab. Computer: PC, Mac. Operating system: Windows, Mac OS, Linux. Has the code been vectorized or parallelized?: Yes RAM: 2000 Megabytes Classification: 4.6, 10, 18. Nature of problem: Modeling and simulation of two-dimensional multiple wave scattering by large clusters of circular cylinders for any frequency. The program is well-designed to manage highly accurate solutions for deterministic or random media, with various boundary conditions and physics properties of the scatterers. Pre- and post-processing facilities are designed specifically for these problems. Solution method: We use spectral Fourier approximation schemes and direct or iterative Krylov subspace methods. Running time: From a few seconds for simple problems to a few minutes for more complex situations on a medium computer. [ABSTRACT FROM AUTHOR]

This paper introduces a new publicly available numerical library for cosmology, C osmo++. The library has been designed using object-oriented programming techniques, and fully implemented in C++. C osmo++ introduces a unified interface for using most of the frequently used numerical methods in cosmology. Most of the features are implemented in C osmo++ itself, while a part of the functionality is implemented by linking to other publicly available libraries. The most important features of the library are Cosmic Microwave Background anisotropies power spectrum and transfer function calculations, likelihood calculations, parameter space sampling tools, sky map simulations, and mask apodization. C osmo++ also includes a few mathematical tools that are frequently used in numerical research in cosmology and beyond. A few simple examples are included in C osmo++ to help the user understand the key features. The library has been fully tested, and we describe some of the important tests in this paper. C osmo++ is publicly available at http://cosmo.grigoraslanyan.com . [ABSTRACT FROM AUTHOR]

Abstract: Focusing on the local geometric properties of the shockpeakon for the Degasperis–Procesi equation, a multi-symplectic method for the quasi-Degasperis–Procesi equation is proposed to reveal the jump discontinuity of the shockpeakon for the Degasperis–Procesi equation numerically in this paper. The main contribution of this paper lies in the following: (1) the uniform multi-symplectic structure of the b-family equation is constructed; (2) the stable jump discontinuity of the shockpeakon for the Degasperis–Procesi equation is reproduced by simulating the peakon–antipeakon collision process of the quasi-Degasperis–Procesi equation. First, the multi-symplectic structure and several local conservation laws are presented for the b-family equation with two exceptions ( and ). And then, the Preissman Box multi-symplectic scheme for the multi-symplectic structure is constructed and the mathematical proofs for the discrete local conservation laws of the multi-symplectic structure are given. Finally, the numerical experiments on the peakon–antipeakon collision of the quasi-Degasperis–Procesi equation are reported to investigate the jump discontinuity of shockpeakon of the Degasperis–Procesi equation. From the numerical results, it can be concluded that the peakon–antipeakon collision of the quasi-Degasperis–Procesi equation can be simulated well by the multi-symplectic method and the simulation results can reveal the jump discontinuity of shockpeakon of the Degasperis–Procesi equation approximately. [Copyright &y& Elsevier]

Abstract: In the Projector Augmented Wave (PAW) method developed by Blöchl (1994), a PAW data file is needed for each element, taking the role of the pseudopotential file used with the norm-conserving or ultrasoft formalisms. In this paper, we review methods for generating PAW data files and for evaluating their accuracy, transferability, and numerical efficiency in simulations of bulk solids. We have developed a new set of PAW atomic data files for most of the stable elements in the periodic table. These files are provided in a standard XML format for use in any PAW electronic structure code. The new dataset performs well as measured by the “ ” evaluation criterion introduced by Lejaeghere et al. (2014), and also performs well in a modified evaluation scheme proposed in the present paper. [Copyright &y& Elsevier]

In electrical engineering and physics, Maxwell's equations play a very important role and have a variety of applications. In this paper, we propose and analyse a novel class of time domain conservative schemes in rectangular coordinate to solve Maxwell's equations with periodic boundary conditions. This class of methods is explicit and easy to implement with low computational cost and memory storage. The error estimates presented in this paper demonstrate that the numerical solutions obtained by this class of conservative schemes can achieve arbitrarily high-order accuracy. The discrete divergences in numerical experiments motivate us to show that the conservative scheme is divergence-free by the rigorous numerical analysis, which is of great importance in the sense of geometric numerical integration. The discrete energy monitors give light to the statement that the conservative scheme can keep the linear relationship among some qualitative features of the underlying Maxwell's equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a Fourier spectral method for spatial variables and three fast and efficient explicit time stepping methods for the numerical solution of two-dimensional (2D) nonlinear partial differential equations (PDEs) including sine-Gordon and molecular beam epitaxy (MBE) models. We discretize the original PDEs with discrete Fourier transform in space and then apply some fourth-order time stepping schemes such as Runge–Kutta integrating factor (IFRK), Runge–Kutta exponential time differencing (ETDRK) and ETDRK method with improved accuracy (ETDRKB), to the resulting systems of ordinary differential equations (ODEs). With regard to stiffness and nonlinearities of the models, in this approach we take advantage of using the fast Fourier transform in combination with explicit fourth-order time stepping methods and expect to get a better accuracy and CPU time in comparison with other reported spatial discretizations and implicit time stepping schemes in literature. Comparing the numerical solutions with analytical solutions and also some reported results in the literature demonstrates the effectiveness of the proposed schemes. We will also show that the schemes of this paper exhibit the conservation of energy for both PDEs. [Copyright &y& Elsevier]

Abstract: The current paper reports on the implementation of a numerical solver on the Graphic Processing Units (GPUs) to model reactive gas mixtures with detailed chemical kinetics. The solver incorporates high-order finite volume methods for solving the fluid dynamical equations coupled with stiff source terms. The chemical kinetics are solved implicitly via an operator-splitting method. We explored different approaches in implementing a fast kinetics solver on the GPU. The detail of the implementation is discussed in the paper. The solver is tested with two high-order shock capturing schemes: MP5 (Suresh and Huynh, 1997) [9] and ADERWENO (Titarev and Toro, 2005) [10]. Considering only the fluid dynamics calculation, the speed-up factors obtained are 30 for the MP5 scheme and 55 for ADERWENO scheme. For the fully-coupled solver, the performance gain depended on the size of the reaction mechanism. Two different examples of chemistry were explored. The first mechanism consisted of 9 species and 38 reactions, resulting in a speed-up factor up to 35. The second, larger mechanism, consisted of 36 species and 308 reactions, resulting in a speed-up factor of up to 40. [Copyright &y& Elsevier]

Abstract: In this paper, four alternating direction implicit (ADI) schemes are presented for solving two-dimensional cubic nonlinear Schrödinger equations. Firstly, we give a Crank–Nicolson ADI scheme and a linearized ADI scheme both with accuracy , with the same method, use fourth-order Padé compact difference approximation for the spatial discretization; two HOC-ADI schemes with accuracy are given. The two linearized ADI schemes apply extrapolation technique to the real coefficient of the nonlinear term to avoid iterating to solve. Unconditionally stable character is verified by linear Fourier analysis. The solution procedure consists of a number of tridiagonal matrix equations which make the computation cost effective. Numerical experiments are conducted to demonstrate the efficiency and accuracy, and linearized ADI schemes show less computational cost. All schemes given in this paper also can be used for two-dimensional linear Schrödinger equations. [Copyright &y& Elsevier]

The generation of direct current electricity using solid oxide fuel cells (SOFCs) involves several interplaying transport phenomena. Their simulation is crucial for the design and optimization of reliable and competitive equipment, and for the eventual market deployment of this technology. An open-source library for the computational modeling of mass-transport phenomena in SOFCs is presented in this article. It includes several multicomponent mass-transport models (i.e. Fickian, Stefan–Maxwell and Dusty Gas Model), which can be applied both within porous media and in porosity-free domains, and several diffusivity models for gases. The library has been developed for its use with OpenFOAM®, a widespread open-source code for fluid and continuum mechanics. The library can be used to model any fluid flow configuration involving multicomponent transport phenomena and it is validated in this paper against the analytical solution of one-dimensional test cases. In addition, it is applied for the simulation of a real SOFC and further validated using experimental data. Program summary: Program title: multiSpeciesTransportModels Catalogue identifier: AEKB_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKB_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 18 140 No. of bytes in distributed program, including test data, etc.: 64 285 Distribution format: tar.gz Programming language:: C++ Computer: Any x86 (the instructions reported in the paper consider only the 64 bit case for the sake of simplicity) Operating system: Generic Linux (the instructions reported in the paper consider only the open-source Ubuntu distribution for the sake of simplicity) Classification: 12 External routines: OpenFOAM® (version 1.6-ext) (http://www.extend-project.de) Nature of problem: This software provides a library of models for the simulation of the steady state mass and momentum transport in a multi-species gas mixture, possibly in a porous medium. The software is particularly designed to be used as the mass-transport library for the modeling of solid oxide fuel cells (SOFC). When supplemented with other sub-models, such as thermal and charge-transport ones, it allows the prediction of the cell polarization curve and hence the cell performance. Solution method: Standard finite volume method (FVM) is used for solving all the conservation equations. The pressure-velocity coupling is solved using the SIMPLE algorithm (possibly adding a porous drag term if required). The mass transport can be calculated using different alternative models, namely Fick, Maxwell–Stefan or dusty gas model. The code adopts a segregated method to solve the resulting linear system of equations. The different regions of the SOFC, namely gas channels, electrodes and electrolyte, are solved independently, and coupled through boundary conditions. Restrictions: When extremely large species fluxes are considered, current implementation of the Neumann and Robin boundary conditions do not avoid negative values of molar and/or mass fractions, which finally end up with numerical instability. However this never happened in the documented runs. Eventually these boundary conditions could be reformulated to become more robust. Running time: From seconds to hours depending on the mesh size and number of species. For example, on a 64 bit machine with Intel Core Duo T8300 and 3 GBytes of RAM, the provided test run requires less than 1 second. [ABSTRACT FROM AUTHOR]

Abstract Many PDEs can be recast into the general multi-symplectic formulation possessing three local conservation laws. We devote the present paper to some systematic methods, which hold the discrete versions of the local conservation laws respectively, for the general multi-symplectic PDEs. For the original problem subjected to appropriate boundary conditions, the proposed methods are globally conservative. The proposed methods are successfully applied to many one-dimensional and multi-dimensional Hamiltonian PDEs, such as KdV equation, G–P equation, Maxwell's equations and so on. Numerical experiments are carried out to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the solitary wave solutions of the two-dimensional regularized long-wave equation which is arising in the investigation of the Rossby waves in rotating flows and the drift waves in plasmas. The main idea behind the numerical solution is to use a combination of boundary knot method and the analog equation method. The boundary knot method is a meshless boundary-type radial basis function collocation technique. In contrast with the method of fundamental solution, the boundary knot method uses the non-singular general solution instead of the singular fundamental solution to obtain the homogeneous solution. Similar to method of fundamental solution, the radial basis function is employed to approximate the particular solution via the dual reciprocity principle. In the current paper, we applied the idea of analog equation method. According to the analog equation method, the nonlinear governing operator is replaced by an equivalent nonhomogeneous linear one with known fundamental solution and under the same boundary conditions. Furthermore, in order to show the efficiency and accuracy of the proposed method, the present work is compared with finite difference scheme. The new method is analyzed for the local truncation error and the conservation properties. The results of several numerical experiments are given for both the single and double-soliton waves. [Copyright &y& Elsevier]

Abstract: In a previous paper we proposed a model to study the dynamics of opinion formation in human societies by a co-evolution process involving two distinct time scales of fast transaction and slower network evolution dynamics. In the transaction dynamics we take into account short range interactions as discussions between individuals and long range interactions to describe the attitude to the overall mood of society. The latter is handled by a uniformly distributed parameter α, assigned randomly to each individual, as quenched personal bias. The network evolution dynamics is realised by rewiring the societal network due to state variable changes as a result of transaction dynamics. The main consequence of this complex dynamics is that communities emerge in the social network for a range of values in the ratio between time scales. In this paper we focus our attention on the attitude parameter α and its influence on the conformation of opinion and the size of the resulting communities. We present numerical studies and extract interesting features of the model that can be interpreted in terms of social behaviour. [Copyright &y& Elsevier]

Abstract: For the general multidimensional perturbed oscillators with , the order conditions for the ARKN methods are presented by X. Wu et al. [Order conditions for ARKN methods solving oscillatory systems, Comput. Phys. Comm. 180 (2009) 2250–2257]. These methods integrate exactly the multidimensional unperturbed oscillators and are highly efficient when the perturbing function is small. In this paper, we are concerned with the analysis of the concrete multidimensional ARKN methods based on the order conditions for the multidimensional ARKN methods. We extent the matrix K to a general case, in which K is not required to be symmetric. Numerical experiments demonstrate that the novel multidimensional ARKN methods presented in this paper are more efficient compared with some well-know RKN methods in the scientific literature. [ABSTRACT FROM AUTHOR]

Abstract: A new nonlinear gyro-kinetic flux tube code (GKW) for the simulation of micro instabilities and turbulence in magnetic confinement plasmas is presented in this paper. The code incorporates all physics effects that can be expected from a state of the art gyro-kinetic simulation code in the local limit: kinetic electrons, electromagnetic effects, collisions, full general geometry with a coupling to a MHD equilibrium code, and shearing. In addition the physics of plasma rotation has been implemented through a formulation of the gyro-kinetic equation in the co-moving system. The gyro-kinetic model is five-dimensional and requires a massive parallel approach. GKW has been parallelised using MPI and scales well up to 8192+ cores. The paper presents the set of equations solved, the numerical methods, the code structure, and the essential benchmarks. Program summary: Program title: GKW Catalogue identifier: AEES_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEES_v1_0.html Program obtainable from: CPC Program Library, Queen''s University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 29 998 No. of bytes in distributed program, including test data, etc.: 206 943 Distribution format: tar.gz Programming language: Fortran 95 Computer: Not computer specific Operating system: Any for which a Fortran 95 compiler is available Has the code been vectorised or parallelised?: Yes. The program can efficiently utilise 8192+ processors, depending on problem and available computer. 128 processors is reasonable for a typical nonlinear kinetic run on the latest x86-64 machines. RAM: for a linear run; 25 GB for typical nonlinear kinetic run (30 million grid points) Classification: 19.8, 19.9, 19.11 External routines: None required, although the functionality of the program is somewhat limited without a MPI implementation (preferably MPI-2) and the FFTW3 library. Nature of problem: Five-dimensional gyro-kinetic Vlasov equation in general flux tube tokamak geometry with kinetic electrons, electro-magnetic effects and collisions Solution method: Pseudo-spectral and finite difference with explicit time integration Additional comments: The MHD equilibrium code CHEASE [1] is used for the general geometry calculations. This code has been developed in CRPP Lausanne and is not distributed together with GKW, but can be downloaded separately. The geometry module of GKW is based on the version 7.1 of CHEASE, which includes the output for Hamada coordinates. Running time: (On recent x86-64 hardware) ∼10 minutes for a short linear problem; 48 hours for typical nonlinear kinetic run. References: [1] H. Lütjens, A. Bondeson, O. Sauter, Comput. Phys. Comm. 97 (1996) 219, http://cpc.cs.qub.ac.uk/summaries/ADDH_v1_0.html. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss several improvements of a substructuring Domain Decomposition Method (DDM) devoted to Electromagnetic computations, based on the Boundary Element Method (BEM) and the Finite Element Method (FEM). This computation procedure is applied to the analysis of antenna performance on board vehicles as well as Radar Cross Section (RCS). The benefits of the subdomain Computational Electromagnetic Method are mainly the ability to deal with collaborative studies involving several companies, and the reduction of the computation costs by one or more orders of magnitude, especially in the context of parametric studies. Furthermore, this paper proposes a Spectral Basis Function (SBF) defined on fictitious surfaces surrounding equipment, to deal with both the computation of antenna far field patterns and RCS in a multi-domain mode. By masking the complexity of the equipment (wires, thin surfaces, materials, supply network, weapons) the external domain of the vehicle can be closed so that the Combined Field Integral Equation (CFIE) can be used, which is better conditioned than the Electric Field Integral Equation (EFIE). This calculation procedure leads to a faster convergence when using iterative Multi Level Fast Multiple Algorithms (MLFMA). The accuracy and efficiency of this technique is assessed by performing the computation of the diffraction and radiation of several test-objects in a multi-domain way cross compared with reference integral equation results. [Copyright &y& Elsevier]

In this paper we investigate the connection between closed Newton–Cotes, trigonometrically-fitted differential methods and symplectic integrators. From the literature we can see that several one step symplectic integrators have been obtained based on symplectic geometry. However, the investigation of multistep symplectic integrators is very poor. The well-known open Newton–Cotes differential methods presented as multilayer symplectic integrators by Zhu et al. [W. Zhu, X. Zhao, Y. Tang, Journal of Chem. Phys. 104 (1996) 2275]. The construction of multistep symplectic integrators based on the open Newton–Cotes integration methods is investigated by Chiou and Wu [J.C. Chiou, S.D. Wu, J. Chem. Phys. 107 (1997) 6894]. In this paper we investigate the closed Newton–Cotes formulae and we write them as symplectic multilayer structures. After this we construct trigonometrically-fitted symplectic methods which are based on the closed Newton–Cotes formulae. We apply the symplectic schemes in order to solve Hamilton''s equations of motion which are linear in position and momentum. We observe that the Hamiltonian energy of the system remains almost constant as integration proceeds. [Copyright &y& Elsevier]

Abstract: In some recent papers Li, Voskoboynikov, Lee, Sze and Tretyak suggested an iterative scheme for computing the electronic states of quantum dots and quantum rings taking into account an electron effective mass which depends on the position and electron energy level. In this paper we prove that this method converges globally and linearly in an alternating way, i.e. yielding lower and upper bounds of a predetermined energy level in turn. Moreover, taking advantage of the Rayleigh functional of the governing nonlinear eigenproblem, we propose a variant which converges even quadratically thereby reducing the computational cost substantially. Two examples of finite element models of quantum dots of different shapes demonstrate the efficiency of the method. [Copyright &y& Elsevier]

A FORTRAN program is presented which solves a system of nonlinear simultaneous equations using the continuous analog of Newton's method (CANM). The user has the option of either to provide a subroutine which calculates the Jacobian matrix or allow the program to calculate it by a forward-difference approximation. Five iterative schemes using different algorithms of determining adaptive step size of the CANM process are implemented in the program.: Program summaryTitle of program: CANMCatalogue number: ADSNProgram summary URL: http://cpc.cs.qub.ac.uk/summaries/ADSNProgram available from: CPC Program Library, Queen's University of Belfast, Northern IrelandLicensing provisions: noneComputer for which the program is designed and others on which it has been tested:Computers: IBM RS/6000 Model 320H, SGI Origin2000, SGI Octane, HP 9000/755, Intel Pentium IV PCInstallation: Department of Chemistry, University of Toronto, Toronto, CanadaOperating systems under which the program has been tested: IRIX64 6.1, 6.4 and 6.5, AIX 3.4, HP-UX 9.01, Linux 2.4.7Programming language used: FORTRAN 90Memory required to execute with typical data: depends on the number of nonlinear equations in a system. Test run requires 80 KBNo. of bits in distributed program including test data, etc.: 15283Distribution format: tar gz formatNo. of lines in distributed program, including test data, etc.: 1794Peripherals used: line printer, scratch disc storeExternal subprograms used: DGECO and DGESL [1]Keywords: nonlinear equations, Newton's method, continuous analog of Newton's method, continuous parameter, evolutionary differential equation, Euler's methodNature of physical problem: System of nonlinear simultaneous equations Fi(x1,x2,…,xn)=0, 1&les;i&les;n, is numerically solved. It can be written in vector form as F(X)=0, X∈Rn, where F :Rn→Rn is a twice continuously differentiable function with domain and range in n-dimensional Euclidean space. The solutions of such systems of equations are often the last step in the solution of practical problems arising in physics and engineering. The purpose of this paper is to present the iterative procedure for finding zeroes of a system of n nonlinear equations in n variables using the continuous analog of Newton's method (CANM).Method of solution: A system of n nonlinear simultaneous equations is solved by the iterative CANM procedure [2–4]. In this approach, the solution of a system F(X)=0 is reduced to a solution of evolutionary differential equation d/dtF(X(t))=−F(X(t)), X(0)=X0, with respect to an additional continuous parameter t, 0&les;t<∞. The resulting Cauchy problem is solved by Euler's method with variable step length τ. This iterative procedure with step τ specified in different ways [5,6], yields a variety of iterative Newton schemes that are frequently superior to the classical scheme.Restrictions on the complexity of the problem: The computer memory requirements depend on the number of nonlinear simultaneous equations to be solved. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long write-up and program listing for details). The user must also supply subroutine FCN which evaluates the nonlinear functions. The user has the option of either to provide a subroutine JAC which calculates the Jacobian matrix or allow the program to calculate it by the forward-difference approximation.Typical Running time: The running time depends critically upon the number of nonlinear equations to be solved. The test run which accompanies this paper took 0.06 s on the SGI Origin 2000.References[1]J.J. Dongarra, J.R. Bunch, C.B. Moler, G.W. Stewart, LINPACK Users' Guide, SIAM, Philadelphia, 1979. These routines are freely available from the NETLIB at http://www.netlib.org/linpack/index.html.[2]M.K. Gavurin, Izv. Vyssh. Uchebn. Zaved. Mat. 5 (1958) 18; M.K. Gavurin, Math. Rev. 25 (1958) 1380; M.K. Gavurin, Uspekhi Mat. Nauk 12 (1957) 173.[3]E.P. Zhidkov, G.I. Makarenko, I.V. Puzynin, Fiz. E&grave;lementar. Chastits i Atom. Yadra 4 (1973) 53; Sov. J. Part. Nucl. 4 (1973) 53.[4]V.S. Melezhik, I.V. Puzynin, T.P. Puzynina, L.N. Somov, J. Comput. Phys. 54 (1984) 221.[5]V.V. Ermakov, N.N. Kalitkin, Zh. Vychisl. Mat. Mat. Fiz. 21 (1981) 491.[6]T. Zhanlav, I.V. Puzynin, Comput. Math. Math. Phys. 32 (1992) 729. [Copyright &y& Elsevier]

In the paper, gridless particle techniques are presented in order to solve problems involving electrostatic, collisionless plasmas. The method makes use of computational particles having the shape of spherical shells or of rings, and can be used to study cases in which the plasma has spherical or axial symmetry, respectively. As a computational grid is absent, the technique is particularly suitable when the plasma occupies a rapidly changing space region. [ABSTRACT FROM AUTHOR]

In this paper, we consider a phase-field model for dendritic growth in a two-dimensional cavity flow and propose a computationally efficient numerical method for solving the model. The crystal is fixed in the space and cannot be convected in most of the previous studies, instead the supercooled melt flows around the crystal, which is hard to be realized in the real world experimental setting. Applying advection to the crystal equation, we have problems such as deformation of crystal shape and ambiguity of the crystal orientation for the anisotropy. To resolve these difficulties, we present a phase-field method by using a moving overset grid for the dendritic growth in a cavity flow. Numerical results show that the proposed method can predict the crystal growth under flow. [ABSTRACT FROM AUTHOR]

The approach used for computation of the convecting face fluxes and the cell face velocities results in different underlying numerical algorithms in finite volume collocated grid solvers for the incompressible Navier–Stokes equations. In this study, the effect of the following five numerical algorithms on the numerical dissipation rate and on the temporal consistency of a selection of Runge–Kutta schemes is analysed: (1) the original algorithm of Rhie and Chow (1983), (2) the standard OpenFOAM method, (3) the algorithm used by Vuorinen et al. (2014), (4) the Kazemi-Kamyab et al. (2015) method, and (5) the D'Alessandro et al. (2018) approach. The last three algorithms refer to recent implementations of low dissipative numerical methods in OpenFOAM®. No new computational methods are presented in this paper. Instead, the main scientific contributions of this paper are: (1) the systematic assessment of the effect of the considered five numerical approaches on the numerical dissipation rate and on the temporal consistency of the selected Runge–Kutta schemes within one unified framework which we have implemented in OpenFOAM, and (2) the application of the method of Komen et al. (2017) in order to quantify the numerical dissipation rate introduced by three of the five numerical methods in quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow. In addition, we explain the effects of the introduced numerical dissipation on the observed trends in the corresponding numerical results. As one of the major conclusions, we found that the pressure error, which is introduced due to the application of a compact stencil in the pressure Poisson equation, causes a reduction of the order of accuracy of the temporal schemes for the test cases in this study. Consequently, application of higher order temporal schemes is not useful from an accuracy point of view, and the application of a second order temporal scheme appears to be sufficient. [ABSTRACT FROM AUTHOR]

We consider the relativistic Vlasov–Maxwell (RVM) equations in the limit when the light velocity c goes to infinity. In this regime, the RVM system converges towards the Vlasov–Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell’s equations in order to damp the higher and higher frequencies present in the numerical solution. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem. [ABSTRACT FROM AUTHOR]

Calculating strong-field, momentum-resolved photoelectron spectra (PES) from numerical solutions of the time-dependent Schrödinger equation (TDSE) is a very demanding task due to the large spatial excursions and drifts of electrons in intense laser fields. The time-dependent surface flux (t-SURFF) method for the calculation of PES [Tao and Scrinzi (2012)] allows to keep the numerical grid much smaller than the space over which the wavefunction would be spread at the end of the laser pulse. We present an implementation of the t-SURFF method in the well established TDSE-solver Qprop [Bauer and Koval (2006)]. Qprop efficiently propagates wavefunctions for single-active electron systems with spherically symmetric binding potentials in classical, linearly (along z ) or elliptically (in the x y -plane) polarized laser fields in dipole approximation. Its combination with t-SURFF makes the simulation of PES feasible in cases where it is just too expensive to keep the entire wavefunction on the numerical grid, e.g., in the long-wavelength or long-pulse regime. Program summary Program title: Qprop Catalogue identifier: ADXB_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXB_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 12458 No. of bytes in distributed program, including test data, etc.: 86258 Distribution format: at.gz Programming language: C++. Computer: x86_64. Operating system: Linux. RAM: The memory requirements for calculating PES are determined by the maximum ℓ in the spherical harmonics expansion of the wave function and the number of momentum (or energy) values for which the PES are to be calculated. The example with the largest memory demand ( large-clubs ) uses approximately 6GB of RAM. The size of the numerical representation of a wavefunction during propagation is modest for the examples included (53 MB for the large-club example). Number of processors used: The evaluation of the PES can be distributed over up to N k MPI processes ( N k is the number of momentum values). Catalogue identifier of previous version: ADXB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 174(2006)396 Classification: 2.5. External routines: GNU Scientific Library, Open MPI (optional), BOOST (optional) Does the new version supersede the previous version?: For TDDFT calculations the previous version should be used. Nature of problem: When atoms are ionized by intense laser fields electrons may escape with large momenta (especially when rescattering is involved). This translates to a rapidly spreading wavefunction in numerical simulations of these systems thus rendering the calculation of PES very costly for increasing wave lengths and peak intensities. Solution method: The TDSE is solved by propagating the wavefunction using a Crank–Nicolson propagator. The wavefunction is represented by an expansion in spherical harmonics. In order to reduce the requirements with respect to the grid size the t-SURFF method is used to calculate PES. Reasons for new version: Using the window operator method to calculate PES is increasingly costly with increasing ponderomotive energies and pulse durations. The new version of Qprop provides an implementation of the t-SURFF method which allows the use of much smaller numerical grids. Summary of revisions: An implementation of the t-SURFF method and examples for calculating PES are provided in the new release. Restrictions: The dipole approximation for the laser interaction has to be applicable. t-SURFF is only implemented for velocity gauge. Furthermore a finite cutoff for long range binding potentials has to be used in the implemented t-SURFF method. Additional comments: For additional information see www.qprop.de Running time: Depends strongly on the laser interaction studied. The examples given in this paper have run times from a few minutes to 12.5 hours. [ABSTRACT FROM AUTHOR]

Mitigation of soot emissions from combustion devices is a global concern. For example, recent EURO 6 regulations for vehicles have placed stringent limits on soot emissions. In order to allow design engineers to achieve the goal of reduced soot emissions, they must have the tools to so. Due to the complex nature of soot formation, which includes growth and oxidation, detailed numerical models are required to gain fundamental insights into the mechanisms of soot formation. A detailed description of the CoFlame FORTRAN code which models sooting laminar coflow diffusion flames is given. The code solves axial and radial velocity, temperature, species conservation, and soot aggregate and primary particle number density equations. The sectional particle dynamics model includes nucleation, PAH condensation and HACA surface growth, surface oxidation, coagulation, fragmentation, particle diffusion, and thermophoresis. The code utilizes a distributed memory parallelization scheme with strip-domain decomposition. The public release of the CoFlame code, which has been refined in terms of coding structure, to the research community accompanies this paper. CoFlame is validated against experimental data for reattachment length in an axi-symmetric pipe with a sudden expansion, and ethylene–air and methane–air diffusion flames for multiple soot morphological parameters and gas-phase species. Finally, the parallel performance and computational costs of the code is investigated. Program summary Program title: CoFlame Catalogue identifier: AFAU_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFAU_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 94964 No. of bytes in distributed program, including test data, etc.: 6242986 Distribution format: tar.gz Programming language: Fortran 90, MPI. (Requires an Intel compiler). Computer: Workstations. Operating system: Linux. RAM: From 16 GB to over 1000 GB depending on size of system being simulated Classification: 22. Nature of problem: Soot formation in laminar diffusion flames with detailed description of thermodynamics, kinetic, and transport data Solution method: Finite volume method utilizing the pseudo-transient SIMPLE algorithm and locally coupled chemistry solver Additional comments: The code was specifically developed for modeling soot formation in laminar diffusion flames Running time: From hours to a month depending on the complexity of the chemical mechanism and the disparity between the initial guess and the final solution. [ABSTRACT FROM AUTHOR]

This paper describes the functionality and usage of bal , a C/C++ library with a Python front-end for the brute-force analysis of continuous-time dynamical systems described by ordinary differential equations (ODEs). bal provides an easy-to-use wrapper for the efficient numerical integration of ODEs and, by detecting intersections of the trajectory with appropriate Poincaré sections, allows to classify the asymptotic trajectory of a dynamical system for bifurcation analysis. Some examples of application are discussed, concerning two-dimensional bifurcation diagrams, Lyapunov exponents and finite-time Lyapunov exponents, basins of attraction, simulation of switching ODE systems, and integration with AUTO, a software package for continuation analysis. Program summary Program title: BAL (Library) Catalogue identifier: AEYY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYY_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 65256 No. of bytes in distributed program, including test data, etc.: 438133 Distribution format: tar.gz Programming language: C/C++, Python. Computer: PCs and Workstations. Operating system: Any Unix based system such as Linux and Mac OSX. RAM: Variable, depending on the number of dimensions of the dynamical system and duration of the simulation. Classification: 4.3, 4.12. External routines: CVODE, Boost, HDF5 Nature of problem: The numerical analysis of continuous-time nonlinear dynamical systems often requires the computation of a large number of solutions of the system, for varying parameter sets, and the subsequent classification of the steady state solution. Solution method: This library provides a convenient interface to the library CVODE for the integration of sets of differential equations and at the same time implements all the machinery required for integrating and classifying the behaviour of the system for varying parameter sets and initial conditions. A high-level Python interface makes the usage of the library amenable also to users who are not familiar with the C/C++ programming languages. [ABSTRACT FROM AUTHOR]

In this paper, an improved weakly compressible smoothed particle hydrodynamics (SPH) method is proposed to simulate transient free surface flows of viscous and viscoelastic fluids. The improved SPH algorithm includes the implementation of (i) the mixed symmetric correction of kernel gradient to improve the accuracy and stability of traditional SPH method and (ii) the Rusanov flux in the continuity equation for improving the computation of pressure distributions in the dynamics of liquids. To assess the effectiveness of the improved SPH algorithm, a number of numerical examples including the stretching of an initially circular water drop, dam breaking flow against a vertical wall, the impact of viscous and viscoelastic fluid drop with a rigid wall, and the extrudate swell of viscoelastic fluid have been presented and compared with available numerical and experimental data in literature. The convergent behavior of the improved SPH algorithm has also been studied by using different number of particles. All numerical results demonstrate that the improved SPH algorithm proposed here is capable of modeling free surface flows of viscous and viscoelastic fluids accurately and stably, and even more important, also computing an accurate and little oscillatory pressure field. [ABSTRACT FROM AUTHOR]

Numerical kinetic models of plasma turbulence require careful treatment of conserved quantities. In the collisionless limit, numerical dissipation can impact entropy in a non-controlled manner. In this paper, the impact of the error in entropy conservation is investigated. In a simulation of ion-acoustic turbulence, a large error ( 15 % ) in entropy conservation is found. Surprisingly, this error is independent of the numerical method, scheme, or number of grid points. Adding a collision operator resolves this issue, but only if the collision frequency is large enough that it modifies the qualitative time evolution of observables, such as electric field amplitude, anomalous resistivity, or phase-space structures. [ABSTRACT FROM AUTHOR]

In this paper we present a novel Lattice Boltzmann model for immiscible fluids with soluble surfactants adsorbing at the interface with improved numerical and extended physical properties. The numerical improvements are based on the use of an analytical representation of a regularized delta-function in the surface free energy functional for the surfactant. Furthermore, the physics of the system have been extended to differential solubility of the surfactant combined with the use of Frumkin sorption behaviour. This enables the scheme to approach more realistic systems like foams and emulsions. This novel scheme is much superior in numerical stability than our previous scheme, based on a squared gradient approximation. Furthermore, we have observed the phenomenon of interface broadening under certain conditions. This phenomenon limits the surface pressure to about 30% of the capillary pressure of a bare droplet. It remains to be investigated whether this interface broadening reflects some physical effect, as has been observed for proteins. [ABSTRACT FROM AUTHOR]

Functionally-fitted methods generalize collocation techniques to integrate exactly a chosen set of linearly independent functions. In this paper, we propose a new type of functionally-fitted block methods for initial value problems of second order ordinary differential equations. The basic theory for the proposed methods is established. First, we present a sufficient condition for the existence of the functionally-fitted block methods. We then obtain some basic characteristics of the methods by Taylor series expansions, and show that the r -point functionally-fitted block method is convergent of order at least r for second order ordinary differential equations. Numerical experiments are conducted to demonstrate the validity and efficiency of the functionally-fitted block methods by comparison with some existing numerical methods. [ABSTRACT FROM AUTHOR]

This paper analyzes the convergence of the numerical solution of a set of equations which contains Poisson and current continuity equations required to simulate organic solar cells under illumination and bias applied. Due to the strong nonlinearity, choosing appropriate initial guesses is a key parameter in obtaining the convergence. To establish such initial guesses, we analyzed the behavior of electrostatic potential, and electron and hole concentration profiles along the active layer as a function of generation rate of photo-induced e–h pairs, charge mobility and thickness. Based on these results, we propose simple functions to obtain the starting values for reaching the solution in an optimized number of iterations. By using this approach, the convergence can be successfully achieved for a wide range of physical parameters such as generation rate of photo-induced e–h pairs, charge mobility, and thickness. For an organic solar cell with an active layer thickness of around 120 nm, the results show that the solution at equilibrium condition, under illumination without bias applied, and under illumination with bias applied requires around 7, 9 and 5 iterations, respectively. Although the analysis was carried out using physical parameters of one of the most studied material pair: P3HT and PCBM, our proposal can be used for arbitrary organic semiconductor. [ABSTRACT FROM AUTHOR]

In its most widespread, classical formulation, the Nernst–Planck–Poisson system for ion transport in electrolytes fails to take into account finite ion sizes. As a consequence, it predicts unphysically high ion concentrations near electrode surfaces. Historical and recent approaches to an appropriate modification of the model are able to fix this problem. Several appropriate formulations are compared in this paper. The resulting equations are reformulated using absolute activities as basic variables describing the species amounts. This reformulation allows to introduce a straightforward generalisation of the Scharfetter–Gummel finite volume discretisation scheme for drift–diffusion equations. It is shown that it is thermodynamically consistent in the sense that the solution of the corresponding discretised generalised Poisson–Boltzmann system describing the thermodynamical equilibrium is a stationary state of the discretised time-dependent generalised Nernst–Planck system. Numerical examples demonstrate the improved physical correctness of the generalised models and the feasibility of the numerical approach. [ABSTRACT FROM AUTHOR]

The spatial volume occupied by an atom depends on its electronic density. Although this density can only be evaluated exactly for hydrogen-like atoms, there are many excellent algorithms and packages to calculate it numerically for other materials. Three-dimensional visualization of charge density is challenging, especially when several molecular/atomic levels are intertwined in space. In this paper, we explore several approaches to this, including the extension of an anaglyphic stereo visualization application based on the AViz package for hydrogen atoms and simple molecules to larger structures such as nanotubes. We will describe motivations and potential applications of these tools for answering interesting physical questions about nanotube properties. [ABSTRACT FROM AUTHOR]

The commonly used second order Finite-Difference Time-Domain (FDTD) scheme for electromagnetic solvers in Particle-In-Cell codes produces fast solvers that scale well in parallel, but suffers from anomalous numerical effects resulting from discretization, such as numerical dispersion. High order schemes are therefore seen as the remedy for reducing the discretization errors. In the modeling of various applications, an open boundary is necessary for simulating vacuum extending beyond the computational box, for which algorithms based on–or derived from–Bérenger’s Perfectly Matched Layers (PML) have demonstrated high efficiency over a wide range of wavelength and angle of incidence. The amount of numerical reflection of PMLs has been studied numerically and analytically for low order stencils but not systematically at higher order, nor for the pseudo-spectral scheme. In this paper, we extend the theoretical and numerical analysis of the coefficient of reflection of PML layers to solvers of any order of accuracy. Results show that the PML efficiency is preserved at any order, including at the infinite order limit that is attained by the pseudo-spectral formulation. [ABSTRACT FROM AUTHOR]

OpenSMOKE++ is a general framework for numerical simulations of reacting systems with detailed kinetic mechanisms, including thousands of chemical species and reactions. The framework is entirely written in object-oriented C++ and can be easily extended and customized by the user for specific systems, without having to modify the core functionality of the program. The OpenSMOKE++ framework can handle simulations of ideal chemical reactors (plug-flow, batch, and jet stirred reactors), shock-tubes, rapid compression machines, and can be easily incorporated into multi-dimensional CFD codes for the modeling of reacting flows. OpenSMOKE++ provides useful numerical tools such as the sensitivity and rate of production analyses, needed to recognize the main chemical paths and to interpret the numerical results from a kinetic point of view. Since simulations involving large kinetic mechanisms are very time consuming, OpenSMOKE++ adopts advanced numerical techniques able to reduce the computational cost, without sacrificing the accuracy and the robustness of the calculations. In the present paper we give a detailed description of the framework features, the numerical models available, and the implementation of the code. The possibility of coupling the OpenSMOKE++ functionality with existing numerical codes is discussed. The computational performances of the framework are presented, and the capabilities of OpenSMOKE++ in terms of integration of stiff ODE systems are discussed and analyzed with special emphasis. Some examples demonstrating the ability of the OpenSMOKE++ framework to successfully manage large kinetic mechanisms are eventually presented. Program summary Program title: OpenSMOKE++ Catalogue identifier: AEVY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVY_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 146353 No. of bytes in distributed program, including test data, etc.: 4890534 Distribution format: tar.gz Programming language: C++. Computer: Any computer that can run a C++ Compiler. Operating system: Tested on Microsoft Windows 7, Ubuntu 14.4. RAM: From a few Mb to several Gb depending on the size of the system being simulated. Classification: 22. External routines: Eigen, Boost C++ Libraries, RapidXML Nature of problem: Evolution of reacting gas mixtures with detailed description of thermodynamic, kinetic and transport data. Solution method: Stiff systems of Ordinary differential Equations, whose solution is obtained using methods based on the Backward Differentiation Formulas (BDF) (LU factorization of dense matrices is required). Additional comments: The code was specifically conceived for managing homogeneous, reacting mixtures including thousands of species and reactions. Running time: Problem-dependent, from seconds (small kinetics) to hours [ABSTRACT FROM AUTHOR]

In this paper the numerical integration of non conservative perturbations of differential systems that possess a first integral, as for example slowly dissipative Hamiltonian systems, is considered. Numerical methods that are able to reproduce appropriately the evolution of the first integral are proposed. These algorithms are based on a combination of standard numerical integration methods and certain projection techniques. Some conditions under which known conservative methods reproduce that desirable evolution in the invariant are analysed. Finally, some numerical experiments in which we compare the behaviour of the new proposed methods, the averaged vector field method AVF proposed by Quispel and McLaren and standard RK methods of orders 3 and 5 are presented. The results confirm the theory and show a good qualitative and quantitative performance of the new projection methods. [ABSTRACT FROM AUTHOR]

We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low’s Lagrangian or on a Hamiltonian with a non-canonical Poisson bracket. The useful property of this variational principle is that it allows independent transformations of particle coordinates and velocities, i.e., transformations in particle phase space. With such transformations, a finite degree-of-freedom drift-kinetic action is obtained through time-averaging of the finite degree-of-freedom fully-kinetic action. Variation of the drift-kinetic Lagrangian density leads to a self-consistent, macro-particles and fields numerical model. Since the computational particles utilize only guiding center coordinates and velocities, there is a large computational advantage in the time integration part of the algorithm. Numerical comparison between the time-averaged fully-kinetic and drift-kinetic charge and current, deposited on a computational grid, offers insight into the range of validity of the model. Being based on a variational principle, the algorithm respects the energy conserving property of the underlying continuous system. The development in this paper serves to further emphasize the advantages of using variational approaches in plasma particle simulations. [ABSTRACT FROM AUTHOR]

This paper studies a periodic one-dimensional exclusion process constituted by multiple diffusive channels and a common driven part. We have performed mean field analysis for the phase diagram, the density profiles, and the currents, which is in good agreement with the Monte Carlo simulations. In particular, in the special case that the diffusive channels are identical, the phase boundaries have been derived explicitly. It is shown that, in the driven part, the low density–high density region and the low density region shrink and will finally vanish with the increase of the number of diffusive channels. On the other hand, the high density region and the low density–high density region vanish if the total number of particles keeps constant. Numerical examples indicate that these features might be extended to a general case in which the diffusive channels are not identical. [ABSTRACT FROM AUTHOR]

In this paper, a new linearized high-order compact difference method is presented for numerical simulation of three dimensional (3D) Allen-Cahn equation with three kinds of boundary conditions. The method, which is based on the Crank-Nicholson/Adams-Bashforth scheme combined with the Douglas-Gunn ADI method, is second order accurate in time and fourth order accurate in space and energy degradation. The main advantages of this method is that the nonlinear penalty term f(u)f(u) is linear and an extra stabilizing term is added to alleviate the stability constraint while maintaining accuracy and simplicity. Numerical experiments are given to demonstrate the validity and applicability of the new method. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present a new major release of the program FIESTA (Feynman Integral Evaluation by a Sector decomposiTion Approach). This version presents features like cluster-parallelization, new asymptotic expansion algorithms, calculations in physical regions, new sector-decomposition strategies, as well as multiple speed, memory, and stability improvements. Program summary: Program title: FIESTA 3 Catalogue identifier: AECP_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECP_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 109631 No. of bytes in distributed program, including test data, etc.: 6777017 Distribution format: tar.gz Programming language: Wolfram Mathematica 7.0 or higher, C++. Computer: From a desktop PC to a supercomputer. Operating system: Unix, Linux, Mac OS X. Has the code been vectorized or parallelized?: Yes. Number of processors used: from 1 processor up to loading a supercomputer (tests were performed up to 1024 cores) RAM: Depends on the complexity of the problem Catalogue identifier of previous version: AECP_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 790 Classification: 4.4, 4.12, 5, 6.5. External routines: Wolfram Mathematica [1], KyotoCabinet [2], Cuba [3], QHull [4] Does the new version supercede the previous version?: Yes. Some obsolete options were removed as being superseded by better approaches. Nature of problem: The sector decomposition approach to evaluating Feynman integrals falls apart into the sector decomposition itself, where one has to minimize the number of sectors; the pole resolution and epsilon expansion; and the numerical integration of the resulting expression. Moreover, in cases where the integrand is complex, one has to perform a contour deformation. Solution method: The program has a number of sector decomposition strategies. One of the most important features is the ability to perform a contour deformation, as well as the so-called pre-resolution in the case of integrals at the threshold. Everything except the integration is performed in Wolfram Mathematica [1] (required version is 7.0 or higher). This part of the calculation is parallelizable with the use of shared memory. The database is stored on hard disk with the use of the KyotoCabinet [2] database engine. The integration part of the algorithm, which can be performed on a cluster, is written in c++ and does not need Wolfram Mathematica. For integration we use the Cuba library package [3]. Reasons for new version: Application of FIESTA to physical values (complex integration) as well as the cluster-parallelization. Summary of revisions: FIESTA 3 is an absolutely new version with multiple new features such as [•] integration in physical regions [•] new asymptotic expansion methods [•] MPI-parallelization [•] multiple speed and memory improvements [•] total reconstruction: the integrator is completely separated and can be used by other programs Restrictions: The complexity of the problem is mostly restricted by the CPU time required to perform the integration and obtain a proper precision. Running time: Depends on the complexity of the problem. References: [[1]] http://www.wolfram.com/mathematica/, commercial algebraic software; [[2]] http://fallabs.com/kyotocabinet/, open source; [[3]] http://www.feynarts.de/cuba/, open source; [[4]] http://www.qhull.org, open source. [ABSTRACT FROM AUTHOR]

Abstract: Based on B-series theory, the order conditions of the multidimensional ARKN methods are presented for the general multi-frequency and multidimensional oscillatory second-order initial value problems by Wu et al. (2009). These multidimensional ARKN methods exactly integrate the multi-frequency and multidimensional unperturbed oscillators. In this paper, we pay attention to the analysis of the concrete multidimensional ARKN methods for the general multi-frequency oscillatory second-order initial value problems whose right-hand side functions depend on both and (the class of physical problems which fall within its scope is broader). Numerical experiments are carried out to show that the new multidimensional ARKN methods are more efficient compared with some well-known methods for dealing with the oscillatory problems in the scientific literature. [Copyright &y& Elsevier]

Abstract: In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU–GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix–vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed. [Copyright &y& Elsevier]

Abstract: In order to resolve the three dimensional Schrödinger equation, we report in this paper a method providing sufficient accuracy, stability and flexibility with respect to the size and shape of the quantum dot. This numerical method, already used in the two-dimensional case, is based on a suitable combination of coordinate transformation and the finite difference method. It provides an efficient and simple approach for the energy and wavefunction calculations of quantum nanostructures. The proposed method is used to investigate the electron and hole energy levels as well as their wave functions in InAs/GaAs strained and unstrained quantum dots with the aim to attain the 1.55 μm wavelength with realistic dot size. The optical transition energies and the oscillator strengths are also studied. The obtained results are in agreement with several previous works. [Copyright &y& Elsevier]

Abstract: The fast Fourier transform (FFT) is undoubtedly an essential primitive that has been applied in various fields of science and engineering. In this paper, we present a decomposition method for the parallelization of multi-dimensional FFTs with the smallest communication amounts for all ranges of the number of processes compared to previously proposed methods. This is achieved by two distinguishing features: adaptive decomposition and transpose order awareness. In the proposed method, the FFT data is decomposed based on a row-wise basis that maps the multi-dimensional data into one-dimensional data, and translates the corresponding coordinates from multi-dimensions into one dimension so that the one-dimensional data can be divided and allocated equally to the processes using a block distribution. As a result and different from previous works that have the dimensions of decomposition pre-defined, our method can adaptively decompose the FFT data on the lowest possible dimensions depending on the number of processes. In addition, this row-wise decomposition provides plenty of alternatives in data transpose, and different transpose order results in different amounts of communication. We identify the best transpose orders with the smallest communication amounts for the 3-D, 4-D, and 5-D FFTs by analyzing all possible cases. We also develop a general parallel software package for the most popular 3-D FFT based on our method using the 2-D domain decomposition. Numerical results show good performance and scaling properties of our implementation in comparison with other parallel packages. Given both communication efficiency and scalability, our method is promising in the development of highly efficient parallel packages for the FFT. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new weighted essentially non-oscillatory (WENO) procedure for solving hyperbolic conservation laws, on uniform meshes. The new scheme combines essentially non-oscillatory (ENO) reconstructions together with monotone upwind schemes for scalar conservation laws’ interpolants. In a one-dimensional context, first, we obtain an optimum polynomial on a five-cells stencil. This optimum polynomial is fifth-order accurate in regions of smoothness. Next, we modify a third-order ENO polynomial by choosing an additional point inside the stencil in order to obtain the highest accuracy when combined with the Harten–Osher reconstruction–evolution method limiter. Then, we consider the optimum polynomial as a symmetric and convex combination of four polynomials with ideal weights. After that, following the methodology of the classic WENO procedure, we calculate non-oscillatory weights with the ideal weights. Also, the numerical solution is advanced in time by means of the linear multi-step total variation bounded ( ) technique. Numerical examples on both scalar and gas dynamics problems confirm that the new scheme is non-oscillatory and yields sharp results when solving profiles with discontinuities. Comparing the new scheme with high-order WENO schemes shows that our method reduces smearing near shocks and corners, and in some cases it is more accurate near discontinuities. Finally, the new method is extended to multi-dimensional problems by a dimension-by-dimension approach. Several multi-dimensional examples are performed to show that our method remains non-oscillatory while giving good resolution of discontinuities. [Copyright &y& Elsevier]

Abstract: This paper investigates a class of algorithms for numerical integration of a function in dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations: the first is to subtract the histogram approximation, whose integral we may easily evaluate explicitly, from the function and integrate the difference using Monte Carlo; the second is to modify the bin parameters in order to make the variance of the Monte Carlo estimate of the integral the same for all bins. This allows us to use Student’s -test as a trigger for rebinning, which we claim is more stable than the test that is commonly used for this purpose. We provide a program that we have used to study the algorithm for the case where the histogram is represented as a product of one-dimensional histograms. We discuss the assumptions and approximations made, as well as giving a pedagogical discussion of the myriad ways in which the results of any such Monte Carlo integration program can be misleading. [Copyright &y& Elsevier]

Abstract: In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation (NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well as other applications, and discuss their dynamical properties ranging from time reversible, time transverse invariant, mass and energy conservation, and dispersion relation to soliton solutions. Then, we review and compare different numerical methods for solving the NLSE/GPE including finite difference time domain methods and time-splitting spectral method, and discuss different absorbing boundary conditions. In addition, these numerical methods are extended to the NLSE/GPE with damping terms and/or an angular momentum rotation term as well as coupled NLSEs/GPEs. Finally, applications to simulate a quantized vortex lattice dynamics in a rotating BEC are reported. [Copyright &y& Elsevier]

Abstract: In this paper, we numerically investigate the ground-state structure and dynamics of atomic–molecular Bose–Einstein condensates at zero temperature, which are modeled by coupled Gross–Pitaevskii equations (GPEs). To get the ground state, we evolve a gradient flow with discrete normalization numerically. To study the dynamics, we employ an efficient numerical method—the time-splitting Fourier pseudospectral method for solving the coupled GPEs. The proposed numerical methods have been numerically tested and employed in studying the mechanism on how an atomic condensate can be converted into an atomic–molecular mixture or a pure molecular condensate from an atomic condensate either in equilibrium or dynamically. [Copyright &y& Elsevier]

Abstract: This paper provides a technique to investigate the solutions of generalized nonlinear singular Lane–Emden equations of first and second kinds by using a Haar wavelet quasi-linearization approach. The Lane–Emden equation is widely studied and is treated as a challenging equation in the theory of stellar structure for the gravitational potential of a self gravitating, spherically symmetric polytropic fluid which models the thermal behavior of a spherical cloud of gas acting under the mutual attraction of its molecules and subject to the classical laws of thermodynamics. The proposed method is based on the quasi-linearization approximation and replacement of an unknown function through a truncated series of Haar wavelet series of the function. The method is shown to be very reliable and easy to capture the solutions of generalized nonlinear singular Lane–Emden equations. The applicability of the method is shown by numerical tests on various cases of the generalized Lane–Emden equation and solutions are also reported in the neighborhood of a singular point. [Copyright &y& Elsevier]

Abstract: This paper proposes a technique, based on the Inexact Shift–Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented results of numerical experiments confirm the technique can be effectively applied to challenging, large-scale problems characterized by very dense spectra, such as resonant cavities with spatial dimensions which are large with respect to wavelengths of the resonating electromagnetic fields. It is also shown that the proposed scheme based on inexact linear solves delivers superior performance, as compared to methods which rely on exact linear solves, indicating tremendous potential of the ‘inexact solve’ concept. Finally, the scheme which generates an extended projection basis is found to provide a cost-efficient alternative to classical deflation schemes when several eigenvalues are computed. [Copyright &y& Elsevier]