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Quantum dynamics, typically expressed in the form of a time-dependent Schrödinger equation with a Hermitian Hamiltonian, is a natural application for quantum computing. However, when simulating quantum dynamics that involves the emission of electrons, it is necessary to use artificial boundary conditions (ABCs) to confine the computation within a fixed domain. The introduction of ABCs alters the Hamiltonian structure of the dynamics, and existing quantum algorithms cannot be directly applied since the evolution is no longer unitary. The current paper utilizes a recently introduced Schrödingerization method that converts non-Hermitian dynamics into a Schrödinger form for the artificial boundary problems [S. Jin, N. Liu, and Y. Yu, Quantum Simulation of Partial Differential Equations via Schrödingerisation, preprint, arXiv:2212.13969, 2022], [S. Jin, N. Liu, and Y. Yu, Phys. Rev. A, 108 (2023), 032603]. We implement this method for three types of ABCs, including the complex absorbing potential technique, perfectly matched layer methods, and Dirichlet-to-Neumann approach. We analyze the query complexity of these algorithms and perform numerical experiments to demonstrate the validity of this approach. This helps to bridge the gap between available quantum algorithms and computational models for quantum dynamics in unbounded domains. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast high order method for the time-fractional diffusion equation on unbounded spatial domains. The proposed numerical method is a combination of a time-stepping scheme and spectral method for the spatial discretization. First, we reformulate the unbounded domain problem into a bounded domain problem by introducing suitable artificial boundary conditions. Then the time fractional derivatives involved in the equation and the artificial boundary condition are discretized using the so-called L2 formula and sum-of-exponentials (SOE) approximation. The former has been a popular formula for discretization of the Caputo fractional derivative, while the latter is a computational cost reducing technique frequently employed in recent years for convolution integrals. The spatial discretization makes use of the standard Legendre spectral method. The stability and the accuracy of the full discrete problem are analyzed. Our obtained theoretical results include a rigorous proof of the convergence order for both uniform mesh and graded mesh, and a stability proof for the uniform mesh. Finally, several numerical examples are provided to validate the theoretical results and to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A novel finite element scheme is derived to evaluate the transient dynamic response of a multi-layered saturated porous half-space due to obliquely incident P or SV wave. The system consists of N − 1 layers with different thickness and properties that overlay on a saturated half-space from which the wave is input. Biot theory is utilized to describe the mechanism of saturated poroelastic media. In this method finite computational area is truncated from the infinite domain by a horizontal artifitial boundary introduced in the underlying half-space. Wave inputting effects and absorbing boundary condition at the bounday are derived. The spatial problem is then transformed approximatedly into a one-dimensional problem based on the Snell's law. The transient 1-D problem is descritized spacially by means of FEM and solved by the standard time intergration algorithm. Numerical examples show that the proposed 1-D finite element artificial boundary method can provide accurate results for seismic performance of saturated layerd half-space under obliquely incident waves with low values of permeability or frequency content. The method is applied in site response analysis of Hong Kong-Zhuhai-Macao immersed tunnel project. By comparison with the analytical solutions, it is demonstrated for geotechnic earthquake engineering problems, site response solutions with satisfactory accuracy can be achieved by the proposed method. [ABSTRACT FROM AUTHOR]

The novel concept of a functionally graded three-phase composite structure is derived from the urgent need to improve the mechanical properties of traditional two-phase composite structures in aviation. In this paper, we study the free vibrations of a new functionally graded three-phase composite cylindrical shell reinforced synergistically with graphene platelets and carbon fibers. We calculate the equivalent elastic properties of the new three-phase composite cylindrical shell using the Halpin-Tsai and Mori-Tanaka models. The governing equations of this three-phase composite cylindrical shell are derived by using first-order shear deformation theory and Hamilton's principle. We obtain the natural frequencies and mode shapes of the new functionally graded three-phase composite cylindrical shell under artificial boundary conditions. By comparing the results of this paper with the numerical results of finite element software, the calculation method is verified. The effects of the boundary spring stiffness, GPL mass fraction, GPL functionally graded distributions, carbon fiber content, and the carbon fiber layup angle on the free vibrations of the functionally graded three-phase composite cylindrical shell are analyzed in depth. The conclusions provide a certain guiding significance for the future application of this new three-phase composite structure in the aerospace and engineering fields. [ABSTRACT FROM AUTHOR]

In this article, the Carrera Unified Formulation and full Green–Lagrange nonlinear relations are employed to investigate the postbuckling behavior of laminated composite panels subjected to in-plane shear and combined loadings. The layerwise refined plate models are implemented by the efficient Lagrange expansion functions through the laminate thickness. An artificial surrounding area is assumed to model shear conditions. The accuracy of the presented model is validated based on the available literature. Then, the effects of stiffeners on the nonlinear response of panels are evaluated, and comprehensive assessments are provided for the equilibrium curves and stress distributions. [ABSTRACT FROM AUTHOR]

The novel concept of a functionally graded three-phase composite structure is derived from the urgent need to improve the mechanical properties of traditional two-phase composite structures in aviation. In this paper, we study the free vibrations of a new functionally graded three-phase composite cylindrical shell reinforced synergistically with graphene platelets and carbon fibers. We calculate the equivalent elastic properties of the new three-phase composite cylindrical shell using the Halpin-Tsai and Mori-Tanaka models. The governing equations of this three-phase composite cylindrical shell are derived by using first-order shear deformation theory and Hamilton’s principle. We obtain the natural frequencies and mode shapes of the new functionally graded three-phase composite cylindrical shell under artificial boundary conditions. By comparing the results of this paper with the numerical results of finite element software, the calculation method is verified. The effects of the boundary spring stiffness, GPL mass fraction, GPL functionally graded distributions, carbon fiber content, and the carbon fiber layup angle on the free vibrations of the functionally graded three-phase composite cylindrical shell are analyzed in depth. The conclusions provide a certain guiding significance for the future application of this new three-phase composite structure in the aerospace and engineering fields.

We consider the linearized and nonlinear systems describing the motion of incompressible flow around a rotating and translating rigid body Ɗ in the exterior domain Ω = ℝ3 \ Ɗ, where Ɗ ⊂ ℝ3 is open and bounded, with Lipschitz boundary. We derive the L∞-estimates for the pressure and investigate the leading term for the velocity and its gradient. Moreover, we show that the velocity essentially behaves near the infinity as a constant times the first column of the fundamental solution of the Oseen system. Finally, we consider the Oseen problem in a bounded domain ΩR := BR ∩ Ω under certain artificial boundary conditions on the truncating boundary ∂BR, and then we compare this solution with the solution in the exterior domain Ω to get the truncation error estimate.

The paper deals with the steady Navier–Stokes problem, describing a flow of a viscous incompressible fluid through a spatially periodic profile cascade. Using the reduction to one spatial period Ω, the problem is formulated by means of boundary conditions of three types: the conditions of periodicity on curves Γ0 and Γ1, the Dirichlet boundary conditions on Γin and ΓP, and an artificial boundary condition on Γout (see Figure 1). For "small data," we consider the so‐called "do nothing" boundary condition on Γout and prove the existence and uniqueness of a weak and strong solution in the Lr–framework. For "large data," we consider an appropriately modified "do nothing" condition on Γout and prove the existence of a weak and strong solution. [ABSTRACT FROM AUTHOR]

In this paper, we derive the exact artificial boundary conditions for one-dimensional reaction-diffusion-advection equation on an unbounded domain. By employing the Laplace transform, we reduce the original unbound domain problem into a bounded domain problem. The exact artificial boundary conditions are given by Caputo-tempered fractional derivatives in the reduced initial-boundary value problem. We show that the reduced initial-boundary value problem is stable with the exact artificial boundary conditions. We design a finite difference scheme for the reduced finite domain problem. To save the computational cost, we developed a fast algorithm to solve Caputo-tempered derivatives arise in the boundary conditions. We prove that the present difference schemes are uniquely solvable and unconditionally stable in the energy norm. Finally, we demonstrate the effectiveness of the proposed methods by some numerical examples. [ABSTRACT FROM AUTHOR]

This paper aims to solve numerically the linearized Korteweg-de Vries equation. We begin by deriving suitable boundary conditions then approximate them using finite difference method. The methodology of derivation, used in this paper, yields to Non-Standard Boundary Conditions (NSBC) that perfectly absorb wave reflections at the boundary. In addition, these NSBC are exact and local in time and space for non necessarily supported initial data and source terms. We finish with numerical examples that show the absorbing quality of these boundary conditions. Further comparisons are made using standard boundary conditions like, Dirichlet, Neumann and a variant of absorbing boundary conditions called discrete artificial ones. [ABSTRACT FROM AUTHOR]

We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain R3∖D¯, where D⊂R3 is open and bounded, with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we consider the linearized problem in a truncation domain DR:=BR∖D¯ of the exterior domain R3∖D¯ under certain artificial boundary conditions on the truncating boundary ∂BR, and then compare this solution with the solution in the exterior domain R3∖D¯ to get the truncation error estimate. [ABSTRACT FROM AUTHOR]

In this paper, we introduce artificial boundary conditions for the linearized Green-- Naghdi system of equations. The derivation of such continuous (respectively, discrete) boundary conditions includes the inversion of Laplace transform (respectively, \scrZ -transform) and these boundary conditions are in turn nonlocal in time. In the case of continuous boundary conditions, the inversion is done explicitly. We consider two spatial discretizations of the initial system either on a staggered or on a collocated grid, both of interest from the practical point of view. We use a Crank--Nicolson time discretization. The proposed numerical scheme with the staggered grid permits explicit \scrZ - transform inversion, whereas the collocated grid discretization does not. A stable numerical procedure is proposed for this latter inversion. We test numerically the accuracy of the described method with standard Gaussian initial data and wave packet initial data which are more convenient to explore the dispersive properties of the initial set of equations. We used our transparent boundary conditions to solve numerically the problem of injecting propagating (planar) waves in a computational domain. [ABSTRACT FROM AUTHOR]

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Abstract The numerical solution of the logarithmic Schrödinger equation on unbounded domains is considered in this paper. It is difficult to develop numerical methods for the logarithmic Schrödinger equation on unbounded domains, due to the blow up of the logarithmic nonlinearity and the unboundedness of the physical domain. Thus, a regularized version of the logarithmic Schrödinger equation on unbounded domains with a small regularization parameter is developed. Then, the local artificial boundary conditions for the regularized logarithmic Schrödinger equation are designed by applying the unified approach, which based on the idea of well-known operator splitting method. The regularized logarithmic Schrödinger equation defined on unbounded domains is reduced to an initial boundary value problem on the bounded computational domain, which can be solved by the finite difference method. The convergence and the stability of the reduced problem are analyzed by introducing some auxiliary variables. In order to choose the optimal absorb parameter in the local artificial boundary conditions, an adaptive algorithm is presented. Numerical results are reported to verify the accuracy and effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider the valuation of swing options with the possibility of incorporating spikes in the underlying electricity price. This kind of contracts are modelled as path dependent options with multiple exercise rights. From the mathematical point of view the valuation of these products is posed as a sequence of free boundary problems where two consecutive exercise rights are separated by a time period. Due to the presence of jumps, the complementarity problems are associated with a partial-integro differential operator. In order to solve the pricing problem, we propose appropriate numerical methods based on a Crank–Nicolson semi-Lagrangian method for the time discretization of the differential part of the operator, jointly with the explicit treatment of the integral term by using the Adams–Bashforth scheme and combined with biquadratic Lagrange finite elements for space discretization. In addition, we use an augmented Lagrangian active set method to cope with the early exercise feature. Moreover, we employ appropriate artificial boundary conditions to treat the unbounded domain numerically. Finally, we present some numerical results in order to illustrate the proper behaviour of the numerical schemes. [ABSTRACT FROM AUTHOR]

In this article, we present a numerical framework based on continuum models for the fluid dynamics and the CO2 gas distribution in the alveolar sacs of the human lung during expiration and inspiration, including the gas exchange to the cardiovascular system. We include the expansion and contraction of the geometry by means of the Arbitrary Lagrangian-Eulerian (ALE) method. For discretisation, we use equal-order finite elements in combination with pressure-stabilisation techniques based on local projections or interior penalties. We derive formulations for both techniques that are suitable on arbitrarily anisotropic meshes. These formulations are novel within the ALE method. Moreover, we investigate the effect of different boundary conditions, that vary between inspiration and expiration. We present numerical results on a simplified two-dimensional alveolar sac geometry and investigate the influence of the pressure stabilisations as well as the boundary conditions. [ABSTRACT FROM AUTHOR]

The method of artificial boundary conditions provides a way of significantly expanding the amount of useable data for performing model update or damage detection. It accomplishes this by artificially applying boundary conditions directly to the measured frequency response functions, which can then be curve fit to obtain the modal parameters. A critical task in the application of this method is the selection of modes from a large available set of candidate modes generated by the application of various artificial boundary conditions. An orthogonal projection procedure is used to select modes from which to build a composite sensitivity matrix of minimum condition number for update and damage detection. Both simulation and experiment are used to investigate this method. The experimental study makes use of two beams, identical except for damage installed in one beam. Issues regarding the number and type of artificial boundary conditions, the synthesis of boundary conditions, and test frequency resolution are studied. Both the simulation and the experiment reveal that model updating and damage detection can be accomplished with high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a finite difference method for the nonlinear Schrödinger equations on unbounded domain by using artificial boundary conditions. Two artificial boundary conditions are introduced to restrict the original Schrödinger equations on an unbounded domain into an initial–boundary value problem with a bounded domain. Then, a finite difference scheme for the reduced problem is proposed. The important feature of the proposed scheme is that an extrapolation operator is introduced to treat the nonlinear term while the scheme keeps unconditionally stable and does not introduce any oscillations at the artificial boundaries. The proposed scheme with the discrete artificial boundary conditions is rigorously analyzed to yield the unconditional stability and the scheme is also proved to be convergent. Numerical examples are given to show the performance of our scheme. [ABSTRACT FROM AUTHOR]

A new transparent artificial boundary condition for the two-dimensional (vertical) (2DV) free surface water wave propagation modelled using the meshless Radial-Basis-Function Collocation Method (RBFCM) as boundary-only solution is derived. The two-way artificial boundary condition (2wABC) works as pure incidence, pure radiation and as combined incidence/radiation BC. In this work the 2wABC is applied to harmonic linear water waves; its performance is tested against the analytical solution for wave propagation over horizontal sea bottom, standing and partially standing wave as well as wave interference of waves with different periods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new family of infinitely smooth and “nearly” locally supported radial basis functions (RBFs), derived from the general solution of a heat equation arising from the American option pricing problem. These basis functions are expressed in terms of “the repeated integrals of the complementary error function” and provide highly efficient tools to solve the free boundary partial differential equation resulting from the related option pricing model. We introduce an integral operator with a function-dependent lower limit which is employed as a basic tool to prove the radial positive definiteness of the proposed basis functions and could be of independent interest in the RBF theory. We then show that using the introduced functions as expansion bases in the context of an RBF-based meshless collocation scheme, we could exactly impose the transparent boundary condition accompanying the heat equation. We prove that the condition numbers of the resulting collocation matrices are orders of magnitude less than those arising from other popular RBF families used in current literature. Some other properties of these bases such as their Fourier transforms as well as some useful representations in terms of positive Borel measures will also be discussed. [ABSTRACT FROM AUTHOR]

A fast and accurate numerical scheme is presented for the computation of the time fractional Schrödinger equation on an unbounded domain. The main idea consists of two parts. First, we use artifi- cial boundary methods to equivalently reformulate the unbounded problem into an initial-boundary value (IBV) problem. Second, we present two numerical schemes for the IBV problem: a direct scheme and a fast scheme. The direct scheme stands for the direct discretization of the Caputo fractional derivative by using the L1-formula. The fast scheme means that the sum-of-exponentials approximation is used to speed up the evaluation of the Caputo fractional derivative. The resulting fast algorithm significantly reduces the storage requirement and the overall computational cost compared to the direct scheme. Furthermore, the corresponding stability analysis and error estimates of two schemes are established, and numerical examples are given to verify the performance of our approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg–de Vries (KDV) and Benjamin–Bona–Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z -transform of an holomorphic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data. [ABSTRACT FROM AUTHOR]

We consider the derivation of continuous and fully discrete artificial boundary conditions for the linearized Korteweg-de Vries equation. We show that we can obtain them for any constant velocities and any dispersion. The discrete artificial boundary conditions are provided for two different numerical schemes. In both continuous and discrete case, the boundary conditions are nonlocal with respect to time variable. We propose fast evaluations of discrete convolutions. We present various numerical tests which show the effectiveness of the artificial boundary conditions.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1455-1484, 2016 [ABSTRACT FROM AUTHOR]

This article deals with artificial boundaries which you encounter when a large spatial domain is confined to a smaller computational domain. Such an artificial boundary condition should not preferably interact with the fluid at all. Standard boundary conditions, e.g., a pressure or velocity condition, result in unphysical reflections. So far, existing artificial boundary conditions for the lattice Boltzmann method (LBM) are transferred from macroscopic formulations. In this work we propose novel discrete artificial boundary conditions (ABCs) which are tailored on the LBM’s mesoscopic level. They are derived directly for the chosen LBM with the aim of higher accuracy. We describe the idea of discrete ABCs in a three velocity (D1Q3) model governing the Navier–Stokes equations in one dimension. Numerical results finally demonstrate the superiority of our new boundary condition in terms of accuracy compared to previously used ABCs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the equations of linear elasticity in an exterior domain. We exhibit artificial boundary conditions on a circle, which lead to a non-coercive second order boundary value problem. In the particular case of an axisymmetric geometry, explicit computations can be performed in Fourier series proving the well-posedness except for a countable set of parameters. A perturbation argument allows us to consider near-circular domains. We complete the analysis by some numerical simulations. [ABSTRACT FROM AUTHOR]

We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann map is proposed and mathematically analyzed via a non-selfadjoint spectral problem: under general assumptions we show convergence of the solution to an eddy current problem involving a truncated Dirichlet-to-Neumann map to the solution on the entire, unbounded axisymmetric domain as the truncation parameter tends to infinity. Under stronger assumptions on the physical parameters of the eddy current problem, convergence rates are shown. We further validate our theoretical results through numerical experiments for a realistic physical setting inspired by eddy current probes of nuclear reactor core tubes. [ABSTRACT FROM AUTHOR]

We consider the numerical solution of the time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain. Introduce an artificial boundary and find the exact and approximate artificial boundary conditions for the given problem, which lead to a bounded computational domain. Using the exact or approximating boundary conditions on the artificial boundary, the original problem is reduced to an initial–boundary-value problem on the bounded computational domain which is respectively equivalent to or approximates the original problem. A finite difference method is used to solve the reduced problems on the bounded computational domain. The numerical results demonstrate that the method given in this paper is effective and feasible. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of construction of non-reflecting boundary condition for certain second-order nonlinear dispersive equations. It is shown that using the concept of microlocality it is possible to relax the requirement of compact support of the initial data. The method is demonstrated for a class of initial data such that outside the computational domain it behaves like a continuous-wave. The generalization is detailed for two existing schemes in the framework of pseudo-differential calculus, namely, Szeftel's method (Szeftel (2006) [1]) and gauge transformation strategy (Antoine et al. (2006) [2]). Efficient numerical implementation is discussed and a comparative performance analysis is presented. The paper also briefly surveys the possibility of extension of the method to higher-dimensional PDEs. [Copyright &y& Elsevier]

Abstract: When using a lattice Boltzmann method on an unbounded (or very large) domain one has to confine this spatial domain to a computational domain. This is realized by introducing so-called artificial boundary conditions. Until recently, characteristic boundary conditions for the Euler equations were considered and adapted to the lattice Boltzmann method. In this work we propose novel discrete artificial boundary conditions which are derived directly for the chosen lattice Boltzmann model, i.e., on the discrete level. They represent the first exact artificial boundary conditions for lattice Boltzmann methods. Doing so, we avoid any detour of considering continuous equations and obtain boundary conditions that are perfectly adapted to the chosen numerical scheme. We illustrate the idea for a one dimensional, two velocity (D1Q2) lattice Boltzmann method and show how the computational efficiency can be increased by a finite memory approach. Analytical investigations and numerical results finally demonstrate the advantages of our new boundary condition compared to previously used artificial boundary conditions. [Copyright &y& Elsevier]

Abstract: The method of difference potentials generalizes the method of Calderon’s operators from PDEs to arbitrary difference equations and systems. It offers several key advantages, such as the capability of handling boundaries/interfaces that are not aligned with the discretization grid, variable coefficients, and nonstandard boundary conditions. In doing so, the complexity of the algorithm remains comparable to that of an ordinary finite difference scheme on a regular structured grid. Previously, we have applied the method of difference potentials to solving several variable coefficient interior Helmholtz problems with fourth and sixth order accuracy. We have employed compact finite difference schemes as a core discretization methodology. Those schemes enable high order accuracy on narrow stencils and hence require only as many boundary conditions as needed for the underlying differential equation itself. Numerical experiments corroborate the high order accuracy of our method for variable coefficients, regular grids, and non-conforming boundaries. In the current paper, we extend the previously developed methodology to exterior problems. We present a complete theoretical analysis of the algorithm, as well as the results of a series of numerical simulations. Specifically, we study the scattering of time-harmonic waves about smooth shapes, subject to various boundary conditions. We also solve the transmission/scattering problems, in which not only do the waves scatter off a given shape but also propagate through the interface and travel across the heterogeneous medium inside. In all the cases, our methodology guarantees high order accuracy for regular grids and non-conforming boundaries and interfaces. [Copyright &y& Elsevier]

Abstract: In this paper, for a class of fractional sub-diffusion equations on a space unbounded domain, firstly, exact artificial boundary conditions, which involve the time-fractional derivatives, are derived using the Laplace transform technique. Then the original problem on the space unbounded domain is reduced to the initial-boundary value problem on a space bounded domain. Secondly, an efficient finite difference approximation for the reduced initial-boundary problem on the space bounded domain is constructed. Different from the method of order reduction used in [37] for the fractional sub-diffusion equations on a space half-infinite domain, the presented difference scheme, which is more simple than that in the previous work, is developed using the direct discretization method, i.e. the approximate method of considering the governing equations at mesh points directly. The stability and convergence of the scheme with numerical accuracy are proved by means of discrete energy method and Sobolev imbedding inequality, where γ is the order of time-fractional derivative in the governing equation, τ and h are the temporal stepsize and spatial stepsize, respectively. Thirdly, a compact difference scheme for the case of is derived with the truncation errors of fourth-order accuracy for interior points and third-order accuracy for boundary points, respectively. Then the global convergence order of the compact difference scheme is proved. Finally, numerical experiments are used to verify the numerical accuracy and the efficiency of the obtained schemes. [Copyright &y& Elsevier]

Abstract: While many successful absorbing boundary conditions (ABCs) are developed to simulate wave propagation into unbounded domains, most of them ignore the effect of interior discretization and result in spurious reflections at the artificial boundary. We tackle this problem by developing ABCs directly for the discretized wave equation. Specifically, we show that the discrete system (mesh) can be stretched in a non-trivial way to preserve the discrete impedance at the interface. Similar to the perfectly matched layers (PML) for continuous wave equation, the stretch is designed to introduce dissipation in the exterior, resulting in a PML-type ABC for discrete media. The paper includes detailed formulation of the new discrete ABC, along with the illustration of its effectiveness over continuous ABCs with the help of error analysis and numerical experiments. For time-harmonic problems, the improvement over continuous ABCs is achieved without any computational overhead, leading to the conclusion that the discrete ABCs should be used in lieu of continuous ABCs. [Copyright &y& Elsevier]

Abstract: Sensitivity-based model error localization and damage detection is hindered by the relative differences in modal sensitivity magnitude among updating parameters. The method of artificial boundary conditions is shown to directly address this limitation, resulting in the increase of the number of updating parameters at which errors can be accurately localized. Using a single set of FRF data collected from a modal test, the artificial boundary conditions (ABC) method identifies experimentally the natural frequencies of a structure under test for a variety of different boundary conditions, without having to physically apply the boundary conditions, hence the term “artificial”. The parameter-specific optimal ABC sets applied to the finite element model will produce increased sensitivities in the updating parameter, yielding accurate error localization and damage detection solutions. A method is developed for identifying the parameter-specific optimal ABC sets for updating or damage detection, and is based on the QR decomposition with column pivoting. Updating solution residuals, such as magnitude error and false error location, are shown to be minimized when the updating parameter set is limited to those corresponding to the QR pivot columns. The existence of an optimal ABC set for a given updating parameter is shown to be dependent on the number of modes used, and hence the method developed provides a systematic determination of the minimum number of modes required for localization in a given updating parameter. These various concepts are demonstrated on a simple model with simulated test data. [Copyright &y& Elsevier]

Abstract: We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods. [Copyright &y& Elsevier]