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Starting from the modelling requirements of the early design phase of the product development, the paper will show a possible strategy to overcome some limitations of current CAS/CAD systems. In fact, the styling stage involves both technical knowledge and fuzzy and dynamic aspects, which have to be taken into account for a proper management. The paper focuses on high-level modelling tools developed to deform surfaces with semantic (aesthetic) constraints, i.e. the crucial design elements for the stylist. Furthermore, the communication among the other actors of the design process is consequently facilitated. [ABSTRACT FROM AUTHOR]

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multilevel Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O(ϵ−2) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all one-dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the two-dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the multilevel Monte Carlo give a substantial reduction in the computation cost. [ABSTRACT FROM AUTHOR]

This paper is meant to be the continuation of the previous work [1] where a coupled ODE/PDE method for the simulation of semiconductor devices was introduced. From a strictly mathematical viewpoint, analytical results on coupled PDE/ODE systems (as arising in integrated circuit simulation) can be found in [2]. In particular, in the present paper, we investigate numerically new algorithms of Domain Decomposition type for the simulation of circuits containing distributed devices (Sect. 2) as well as semiconductors in which some part is modeled with lumped parameters (Sect. 3). The results presented here have been investigated in the seminal work [3], while a more extended analysis is ongoing [4]. [ABSTRACT FROM AUTHOR]

In this paper we discuss upscaling of immiscible multiphase and miscible multicomponent flow and transport in heterogeneous porous media. The discussion presented in the paper summarizes the results of in Upscaled Modeling in Multiphase Flow Applications by Ginting et al. (2004) and in Upscaling of Multiphase and Multicomponent Flow by Ginting et al. (2006). Perturbation approaches are used to upscale the transport equation that has hyperbolic nature. Our numerical results show that these upscaling techniques give an improvement over the existing upscaled models which ignore the subgrid terms. [ABSTRACT FROM AUTHOR]

The success in the use of lattice-Boltzmann methods for the simulation of laminar .ows has prompted the interest in extending the technique for the simulation of turbulent flows. In this paper, a square cylinder at Re = 21400 is used to investigate the suitability of lattice-Boltzmann methods to solve turbulent unsteady problems with open boundary conditions. Numerical simulations are performed with a single-relaxation-time lattice-Boltzmann method and with a large-eddy simulation turbulence model. These simulations present several not-fully-resolved issues for lattice-Boltzmann methods, which are briefly discussed in this paper. Specifically, we propose a filtered-density open-boundary condition for fluid-flow simulations with the lattice-Boltzmann equation. This filter modification of inflow boundary condition is shown to improve simulations of unsteady flows at high Reynolds numbers, in terms of calculation stability and speed, and quality of the results. [ABSTRACT FROM AUTHOR]

This paper presents a finite element method for solving the resonance line transfer problem in moving media. The algorithm is capable of dealing with three spatial dimensions, using hierarchically structured grids which are locally refined by means of duality-based a posteriori error estimates. Application of the method to coherent isotropic scattering and complete redistribution gives a result of matrix structure which is discussed in the paper. The solution is obtained by way of an iterative procedure, which solves a succession of quasi-monochromatic radiative transfer problems. It is therefore immediately evident that any simulation of the extended frequency-dependent model requires a solution strategy for the elementary monochromatic transfer problem, which is fast as well as accurate. The present implementation is applicable to arbitrary model configurations with optical depths up to 103-104. Additionally, a combination of a discontinuous finite element method with a superior preconditioning method is presented, which is designed to overcome the extremely poor convergence properties of the linear solver for optically thick and highly scattering media. The contents of this article is as follows: IntroductionOverview: numerical methodsMonochromatic 3D radiative transferPolychromatic 3D line transferTest calculationsApplicationsMulti-model preconditioningConclusion [ABSTRACT FROM AUTHOR]

In this paper, new natural element approximations are proposed, in order to address issues associated with incompressibility as well as to increase the accuracy in the Natural Element Method (NEM). The NEM exhibits attractive features such as interpolant shape functions or auto-adaptive domain of influence, which alleviates some of the most common difficulties in meshless methods. Nevertheless, the shape functions can only reproduce linear polynomials, and in contrast to moving least squares methods, it is not easy to define interpolations with arbitrary approximation consistency. In order to treat mechanical models involving incompressible media in the framework of mixed formulations, the associated functional approximations must satisfy the well known inf-sup, or LBB condition. The first proposed approach constructs richer NEM approximation schemes by means of bubbles associated with the topological entities of the underlying Delaunay tessellation, allowing to pass the LBB and to remove pressure oscillations in the incompressible limit. Despite of its simplicity, this approach does not construct approximation with higher order consistency. The second part of the paper deals with a discussion on the construction of second-order accurate NEM approximations. For this purpose, two techniques are investigated : (a) the enrichment in the MLS framework of the bubbles with higher-order polynomials and (b) the use of a new Hermite-NEM formulation. [ABSTRACT FROM AUTHOR]

In this paper we present the application of the meshfree method of finite spheres to the solution of thin and thick plates composed of isotropic as well as functionally graded materials. For the solution of such problems it is observed that using Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper a new technique, presented in [26, 21], in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline preprocessing step, is shown to provide significant reduction of computational time without sacrificing accuracy. [ABSTRACT FROM AUTHOR]

In the past few years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several areas of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and have been shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present contribution follows the lines of a series of recent publications by the authors on DDM. In these papers, the authors developed a unified theory of primal and dual methods and presented a family of DDM that were shown to be more efficient than previous methods. The present paper extends this work, presenting a new family of related DDM, thus enriching the theory of the relations between primal and dual methods. [ABSTRACT FROM AUTHOR]

Recent progress has been made to more robustly handle the increased complexity of high-order schemes by focusing on the local nature of the discretization. This locality is particularly true for many Discontinuous Galerkin formulations and is the focus of this paper. The contributions of this paper are twofold. First, novel observations regarding various flux representations in the discontinuous Galerkin formulation are highlighted in the context of overlapping Schwarz methods. Second, we conduct additional experiments using high-order elements for the indefinite Helmholtz equation to expose the impact of overlap. [ABSTRACT FROM AUTHOR]

The parareal algorithm is a method to solve time dependent problems parallel in time: it approximates parts of the solution later in time simultaneously to parts of the solution earlier in time. In this paper the relation of the parareal algorithm to space-time multigrid and multiple shooting methods is first briefly discussed. The focus of the paper is on some new convergence results that show superlinear convergence of the algorithm when used on bounded time intervals, and linear convergence for unbounded intervals. [ABSTRACT FROM AUTHOR]

A typical problem in engineering is to find a numerical solution to a partial differential equation (or a coupled set thereof), given a number of boundary conditions, and the usual approach of solving the problem starts by discretizing the domain into elementary volumes. In this paper, we focus on mesh generation suitable for the solution of field problems in arbitrary VLSI structures. We assume that the problem cannot be easily reduced to a lower dimensionality by exploiting symmetry or regularity, so that the problem-domain is intrinsically threedimensional. Also, we assume that the selected numerical technique (e.g., the finite element method) requires a three-dimensional discretization (as opposed to a surface-discretization). Surveys on mesh generation are given in [2] and [5]. The mesh generator described in this paper is based on techniques from the Delaunay-based mesh generation literature. The main benefit of these techniques is that the quality of the resulting meshes can be guaranteed, and, equally important, that the meshes are still small enough to be practically useful. An additional advantage is that computation of the mesh is efficient in practice. In general, mesh computation is much faster than solving the subsequent numerical problems. An example mesh generated by our implementation is shown in Figure 1. [ABSTRACT FROM AUTHOR]

In nonlinear electromagnetic field computations, one is not only faced with large jumps of material coefficients across material interfaces but also with high variation in these coefficients even inside homogeneous materials due to the nonlinearity. The radiation condition can conveniently be taken into account by a coupled boundary integral and domain integral variational formulation. The coupled finite and boundary element discretization leads to large-scale nonlinear algebraic systems. In this paper we propose special inexact Newton methods where the Jacobi systems arising in every step of the Newton method are solved by a special preconditioned finite and boundary element tearing and interconnecting solver. The numerical experiments show that the preconditioner proposed in the paper can handle large jumps in the coefficients across the material interfaces as well as high variation in these coef- ficients on the subdomains. Furthermore, the convergence does not deteriorate if many inner subdomains touch the unbounded exterior subdomain. [ABSTRACT FROM AUTHOR]

The paper describes the application of the Newton method in conjunction with the Finite Integration Technique. Even on orthogonal grid pairs, the material matrices become nondiagonal and lead to higher algorithmic complexity. A uni-directional version of these matrices provides a computationally inexpensive alternative. The paper compares and discusses the two algorithms' order of convergence and their computational complexity. [ABSTRACT FROM AUTHOR]

This paper summarizes the recent circuit-simulation activities [Roo04]-[Sil06] at Helsinki University of Technology (TKK), Circuit Theory Laboratory (CTL). This paper is mostly based on the results of the national projects Advanced Radio Frequency SImulation and Modeling (ARFSIM 2002-2003) [Roo04], MOdeling and Simulation for Advanced Integrated Circuits and Systems (MOSAICS 2004-2005), and Accurate Models Aim for Zero Errors (AMAZE 2006-2008). All these projects have been funded by the National Technology Agency of Finland, Nokia Corporation, and AWR-APLAC Corporation; the annual volume at TKK CTL has been 4.0-5.5 man years. In these projects, APLAC circuit simulation and design tool [A06] has been used as a common platform for the circuit analysis and modeling methods developed. [ABSTRACT FROM AUTHOR]

The design of microwave and millimeter wave devices requires more and more accurate synthesis procedures to satisfy the increasingly stringent specifications of modern communication systems [1]. Most of the available synthesis techniques are based on models that do not conveniently describe the physical behavior of circuits. The goal of the present paper is to calculate the scattering matrix for the case of single and cascaded strip gratings. The strip gratings allow a complete transmission of certain frequencies and a complete reflection at other frequencies and, then, exists a simple type of frequency selective surface [2]. A wide variety of filter characteristics can be obtained by cascading multiple layers of frequencies-selective surfaces. In this paper, a new method for scattered matrix analysis is presented. This method is based on Floquet harmonics analysis. [ABSTRACT FROM AUTHOR]

In this paper we give an introduction to modelling the natural gas value chain including production, transportation, processing, contracts, and markets. The presentation gives insight in the complexity of planning in the natural gas supply chain and how optimization can help decision makers in a natural gas company coordinate the different activities. We present an integrated view from the perspective of an upstream company. The paper starts with decribing how to model natural gas transportation and storage, and at the end we present a stochastic portfolio optimization model for the natural gas value chain in a liberalized market. [ABSTRACT FROM AUTHOR]

The paper has two main themes: The first theme is to give the reader an introduction to modern methods for systems of conservation laws. To this end, we start by introducing two classical schemes, the Lax-Friedrichs scheme and the Lax-Wendroff scheme. Using a simple example, we show how these two schemes fail to give accurate approximations to solutions containing discontinuities. We then introduce a general class of semi-discrete finite-volume schemes that are designed to produce accurate resolution of both smooth and nonsmooth parts of the solution. Using this special class we wish to introduce the reader to the basic principles used to design modern high-resolution schemes. As examples of systems of conservation laws, we consider the shallow-water equations for water waves and the Euler equations for the dynamics of an ideal gas. The second theme in the paper is how programmable graphics processor units (GPUs or graphics cards) can be used to efficiently compute numerical solutions of these systems. In contrast to instruction driven micro-processors (CPUs), GPUs subscribe to the data-stream-based computing paradigm and have been optimised for high throughput of large data streams. Most modern numerical methods for hyperbolic conservation laws are explicit schemes defined over a grid, in which the unknowns at each grid point or in each grid cell can be updated independently of the others. Therefore such methods are particularly attractive for implementation using data-stream-based processing. [ABSTRACT FROM AUTHOR]

Using graphics hardware for general-purpose computations (GPGPU) has for selected applications shown a performance increase of more than one order of magnitude compared to traditional CPU implementations. The intent of this paper is to give an introduction to the use of graphics hardware as a computational resource. Understanding the architecture of graphics hardware is essential to comprehend GPGPU-programming. This paper first addresses the fixed functionality graphics pipeline, and then explains the architecture and programming model of programmable graphics hardware. As the CPU is instruction driven, while a graphics processing unit (GPU) is data stream driven, a good CPU algorithm is not necessarily well suited for GPU implementation. We will illustrate this with some commonly used GPU algorithms. The paper winds up with examples of GPGPU-research at SINTEF within simulation, visualization, image processing, and geometry processing. [ABSTRACT FROM AUTHOR]

This paper describes a hybrid LES/CAA approach for the numerical prediction of airframe and combustion noise. In the hybrid method first a Large-Eddy Simulation (LES) of the flow field containing the acoustic source region is carried out from which then the acoustic sources are extracted. These are then used in the second computational Aeroacoustics (CAA) step in which the acoustic field is determined by solving linear acoustic perturbation equations. For the application of the CAA method to a unconfined turbulent flame, an extension of the method to reacting flow fields is presented. The LES method is applied to a turbulent flow over an airfoil with a deflected flap at a Reynolds number of Re = 106. The comparison of the numerical results with the experimental data shows a good agreement which shows that the main characteristics of the flow field are well resolved by the LES. However, it is also shown that a zonal LES which concentrates of the trailing edge region on a refined local mesh leads to a further improvement of the accuracy. In the second part of the paper, the CAA method with the extension to reacting flows is explained by an application to a non-premixed turbulent flame. The monopole nature of the combustion noise is clearly verified, which demonstrates the capability of the hybrid LES/CAA method for noise prediction in reacting flows. [ABSTRACT FROM AUTHOR]

In this paper we address various efficiency aspects of finite element (FE) simulations on vector computers. Especially for the numerical simulation of large scale Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems efficiency and robustness of the algorithms are two key requirements. In the first part of this paper a straightforward concept is described to increase the performance of the integration of finite elements in arbitrary, unstructured meshes by allowing for vectorization. In addition the effect of different programming languages and different array management techniques on the performance will be investigated. Besides the element calculation, the solution of the linear system of equations takes a considerable part of computation time. Using the jagged diagonal format (JAD) for the sparse matrix, the average vector length can be increased. Block oriented computation schemes lead to considerably less indirect addressing and at the same time packaging more instructions. Thus, the overall performance of the iterative solver can be improved. The last part discusses the input and output facility of parallel scientific software. Next to efficiency the crucial requirements for the IO subsystem in a parallel setting are scalability, flexibility and long term reliability. [ABSTRACT FROM AUTHOR]

The paper is concerned with functional approach to the a posteriori error control for approximate solutions of differential equations. Functional a posteriori estimates are derived by purely functional methods using the analysis of variational problems or integral identities. They are intended to give computable minorants and majorants for various measures of the difference between exact solutions and their conforming approximations. Functional estimates contain no mesh dependent constants and provide guaranteed lower and upper bounds of errors. In this paper, the major attention is paid on a posteriori estimates in terms of local norms or locally based linear functionals. It is shown that for linear elliptic and parabolic problems functional estimates in global (energy) norms imply a posteriori estimates in terms of local quantities. [ABSTRACT FROM AUTHOR]

The increasing complexity of models for prediction of the native spatial structure of RNA molecules requires visualization methods that help to analyze and understand the models and their predictions. This paper improves the visualization method for sequences of barrier trees previously published by the authors. The barrier trees of these sequences are rough topological simplifications of changing folding landscapes — energy landscapes in which kinetic folding takes place. The folding landscapes themselves are generated for RNA molecules where the number of nucleotides increases. Successive landscapes are thus correlated and so are the corresponding barrier trees. The landscape sequence is visualized by an animation of a barrier tree that changes with time. The animation is created by an adaption of the foresight layout with tolerance algorithm for dynamic graph layout problems. Since it is very general, the main ideas for the adaption are presented: construction and layout of a supergraph, and how to build the final animation from its layout. Our previous suggestions for heuristics lead to visually unpleasing results for some datasets and, generally, suffered from a poor usage of available screen space. We will present some new heuristics that improve the readability of the final animation. [ABSTRACT FROM AUTHOR]

Based on the results of an interdisciplinary research project the paper addresses the embedding of knowledge about the function of different parts/structures of a macro molecule (protein, DNA, RNA) directly into the 3D model of this molecule. Thereby the 3D visualization becomes an important user interface component when accessing domain-specific knowledge — similar to a web browser enabling its users to access various kinds of information. In the prototype implementation — named BioBrowser — various information related to bio-research is managed by a database using a fine-grain access control. This also supports restricting the access to parts of the material based on the user privileges. The database is supplied by a SOAP web service so that it is possible (after identifying yourself by a login procedure of course) to query, to change, or to add some information remotely by just using the 3D model of the molecule. All these actions are performed on sub structures of the molecules. These can be selected either by an easy query language or by just picking them in th 3D model with the mouse. [ABSTRACT FROM AUTHOR]

The bioelectric activity that takes place throughout the human body enables the action of muscles and the transmission of information in nerves. A variety of imaging modalities have therefore been developed to assess this activity. In particular, electrocardiography for the heart and electrocardiography and magnetoencephalography for the brain permit to measure non-invasively the resulting electric signal. Beyond their obvious clinical applications these techniques also open the door to a computational reconstruction of the physiological activity at the origin of this signal through the numerical solution of so-called inverse problems. In this case as well as in basic bioengineering research effective postprocessing tools are necessary to facilitate the interpretation of measured and simulated bioelectric data and permit to derive anatomical and functional insight from it. In contrast to scalar quantities for which effective depictions generally exist and are routinely used, the vector-valued nature of this information bears specific challenges that are insufficiently addressed by the visualization tools typically available to biomedical practitioners. This paper reports on the application of advanced vector visualization techniques to the postprocessing analysis of bioelectric fields as they arise in cardiovascular and inverse source reconstruction research. Our work demonstrates the ability of the corresponding visual representations to improve the interpretation of the data and support new insight into the underlying physiology. [ABSTRACT FROM AUTHOR]

In this paper we present the framework of our reconstruction and visualization system for planar cross sectional data. Three-dimensional reconstructions are used to analyze the patterns and functions of dying (apoptotic) and dividing (mitotic) cells in the early developing nervous system. Reconstructions are built-up from high resolution scanned, routinely stained histological serial sections (section thickness = 1 μm), which provide optimal conditions to identify individual cellular events in complete embryos. We propose new sophisticated filter algorithms to preprocess images for subsequent contour detection. Fast active contour methods with enhanced interaction functionality and a new memory saving approach can be applied on the pre-filtered images in order to semiautomatically extract inner contours of the embryonic brain and outer contours of the surface ectoderm. We present a novel heuristic reconstruction algorithm, which is based on contour and chain matching, and which was designed to provide good results very fast in the majority of cases. Special cases are solved by additional interaction. After optional postprocessing steps, surfaces of the embryo as well as cellular events are simultaneously visualized. [ABSTRACT FROM AUTHOR]

This paper deals with a coupled system of non-linear elliptic differential equations arising in electrodeposition modelling process. We show the existence and uniqueness of the solution. A numerical algorithm to compute an approximation of the weak solution is described. We introduce a domain decomposition method to take in account the anisotropy of the solution. We show the domain decomposition method convergence. A numerical example is presented and commented. [ABSTRACT FROM AUTHOR]

State estimation is necessary in diagnosing anomalies inWater Demand Systems (WDS). In this paper we present a neural network performing such a task. State estimation is performed by using optimization, which tries to reconcile all the available information. Quantification of the uncertainty of the input data (telemetry measures and demand predictions) can be achieved by means of robust estate estimation. Using a mathematical model of the network, fuzzy estimated states for anomalous states of the network can be obtained. They are used to train a neural network capable of assessing WDS anomalies associated with particular sets of measurements. [ABSTRACT FROM AUTHOR]

Thin-film flows occur in a variety of physical contexts including, for example, industry, biology and nature, and have been the subject of considerable theoretical research. (See, for example, the review by Oron, Davis and Bankoff [4].) In particular, there are several practically important situations in which an external airflow has a significant effect on the behaviour of a film of fluid, and consequently there has been considerable theoretical and numerical work done to try to understand better the various flows that can occur. (See, for example, the studies by King and Tuck [2] and Villegas-Díaz, Power and Riley [6].) The flow of a rivulet on a planar substrate subject to a shear stress at its free surface has been investigated by several authors, notably Myers, Liang and Wetton [3], Saber and El-Genk [5], and Wilson and Duffy [9]. All of these works concern a non-perfectly wetting fluid; the flow of a rivulet of a perfectly wetting fluid in the absence of a shear stress at its free surface has been treated by Alekseenko, Geshev and Kuibin [1], and by Wilson and Duffy [7,8]. In the present short paper we use the lubrication approximation to obtain a complete description of the steady unidirectional flow of a thin rivulet of a perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal shear stress at its free surface. [ABSTRACT FROM AUTHOR]

The evaporation of liquid droplets is of fundamental importance to industry, with a vast number of applications including ink-jet printing, spray cooling and DNA mapping, and has been the subject of considerable theoretical and experimental research in recent years. Significant recent papers include those by Deegan [1], Deegan et al. [2], Hu and Larson [3], Poulard et al. [4], Sultan et al. [5], and Shahidzadeh-Bonn et al. [6]. [ABSTRACT FROM AUTHOR]

This paper introduces the principles of creating the web-tool on differential equations. It can be used to support European Master Program for Mathematics in Industry. Such a Program is working already on the leading partner universities of ECMI and now the use of e-study as an innovational step is being discussed. [ABSTRACT FROM AUTHOR]

In this paper we will show an industrial application of a new framework, called LaTEX2WeB, which translates LaTEX material into an interactive Web-based document. The more important characteristic of LaTEX2WeB is the possibility of integrating, in the Web-based document, external programs produced in every languages. We exploited LaTEX2WeB to create an interactive Web-based manual, which illustrates a new software for the multiobjective optimization applied to the parameter extraction in circuit design. Thanks to LaTEX2WeB it was possible to simulate the algorithms written in C, C++, and FORTRAN, used in the multiobjective optimization software. [ABSTRACT FROM AUTHOR]

In this paper we consider the recovery of ellipsoidal 3D shapes with piecewise constant coefficients in Diffuse Optical Tomography (DOT). We use an adjoint scheme for calculating gradients for the shape parameters defining the unknown ellipsoids, and a Newton-type optimisation process for the minimization of a least squares data misfit functional. A boundary integral formulation is used for the forward modelling. An advantage of the proposed method is the implicit regularisation effect arising from the reduced dimensionality of the inverse problem. Results of a numerical experiment in 3D are shown which demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]

In this paper we demonstrate model order reduction of a nonlinear academic model of a diode chain. Two reduction methods, which are suitable for nonlinear differential algebraic equation systems are used, the trajectory piecewise linear approach and the proper orthogonal decomposition with missing point estimation. [ABSTRACT FROM AUTHOR]

The general question which will make the object of this paper is the homogenization of some nonlinear problems arising in the modelling of thermal diffusion in a two-component composite. We shall consider, at the microscale, a periodic structure formed by two materials with different thermal properties. We shall deal with two situations: in the first one, we assume that we have some nonlinear sources acting in both components and that at the interface between our two materials the temperature and the flux are continuous, while in the second problem we shall address here, we assume that the flux is still continuous, but depends in a nonlinear way on the jump of the temperature field. In both cases, since the characteristic sizes of these two components are small compared with the macroscopic length-scale of the flow domain, we can apply an homogenization procedure. [ABSTRACT FROM AUTHOR]

The correct simulation of industrial plants firing pulverized fuels (pf: coal, biomass, etc.) by means of commercial CFD codes relies on a number of submodels for the various processes, including, e.g. heat transfer (radiation, conduction through deposits, etc.) and particle combustion. The latter is of major importance in the design of the combustion chamber and the selection of the mills or, conversely, regarding the feasibility of burning a new fuel in an existing boiler. In the last decade, the introduction of new, internationally traded coals and alternative fuels into the power market has motivated renewed interest in the experimental and theoretical characterization of the combustion of these fuels. Regarding experimentation, it is generally accepted that the ‘reactivity' of a fuel can not be determined in desktop analytical instruments; instead, drop tube furnaces or entrained flow reactors (EFR) must be used in order to reproduce the high temperature, high heating rate conditions found in a real pf combustion chamber [1]. Several alternative experimental procedures have been developed in the past and are still used (see, e.g. [2, 3]). On the other hand, two general approaches are used in the literature to model pulverized coal/biomass char combustion: one intends to characterize the evolution of the pores inside the burning particle, and considers both internal and external diffusion, whereas the kinetics for the basic homogeneous and heterogeneous reactions are taken from low temperature analysis or fundamental knowledge of the chemistry involved (e.g. [4]); the other one, followed here, makes use of an apparent kinetics based on the outer particle surface, and includes external diffusion [5]. In the latter case, two parameters governing an Arrhenius-like kinetics are the main unknowns to be determined from the experiments performed in an EFR. The aim of this paper is to discuss some aspects of the mathematical procedure for the determination of those parameters. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to contribute to the mathematical modelling of the combustion of coal particles in pulverised coal furnaces, and also to propose an algorithm for its numerical solution. The mathematical model includes two coupled phases: the solid phase, for the coal particles, where a Lagrangian description is used and an Eulerian description for the gas phase, where the effects of the combustion of coal particles are homogenised. [ABSTRACT FROM AUTHOR]

This paper is concerned with a fascinating phenomenon in boundary layer transition, namely, three-dimensional disturbances undergo rapid amplification despite that they have smaller linear growth rates than two-dimensional ones. Physical mechanisms are sought by considering two types of nonlinear interactions between oblique and planar instability modes. The first is the well-known subharmonic resonance. The relevant mathematical theory and its main predictions are briefly summarised. This mechanism, however, operates only among a very restrictive set of modes, and hence is unable to explain the broadband nature of the amplifying disturbances observed in experiments. The second mechanism involves the interaction between a planar and a pair of oblique Tollmien—Schlichting (T—S) waves which are phase-locked in that they travel with (nearly) the same phase speed. It is a more general type of interaction than subharmonic resonance since no further restriction is imposed on the frequencies. Yet similar to subharmonic resonance, this interaction also leads to super-exponential growth of the oblique modes, while the planar mode remains to follow linear stability theory. The dominant planar mode therefore plays the role of a catalyst, the implications of which for the eN-method and for transition control are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with mathematical modelling and numerical simulation of induction heating furnaces for axisymmetric geometries. The mathematical model presented consists in a coupled thermo-magneto-hydrodynamic problem with phase change. We propose a finite element method and an iterative algorithm to solve the equations. Some numerical results for an industrial furnace used for silicon purification are shown. [ABSTRACT FROM AUTHOR]

The mathematical modeling of swirling flames is a difficult task due to the intense coupling between turbulent transport processes and chemical kinetics in particular for instationary processes like the combustion induced vortex breakdown. In this paper a mathematical model to describe the turbulencechemistry interaction is presented. The described method consists of two parts. Chemical kinetics are taken into account with reduced chemical reaction mechanisms, which have been developed using the ILDM-Method ("Intrinsic Low-Dimensional Manifold"). The turbulence-chemistry interaction is described by solving the joint probability density function (PDF) of velocity and scalars. Simulations of test cases with simple geometries verify the developed model. [ABSTRACT FROM AUTHOR]

This paper addresses the algorithmic and implementation issues associated with fluid structure interaction simulations, specially on vector architecture. Firstly, the fluid structure coupling algorithm is presented and then a newly developed parallel sparse linear solver is introduced and its performance discussed. [ABSTRACT FROM AUTHOR]

Biomechanical simulations are an important field of application for high performance computing due to the complexity and largeness of involved problems. This paper is concerned with coupled problems in the human respiratory system with emphasis on mechanical ventilation. In this context we focus on the modeling aspects of pulmonary alveoli and the lower airways. Our alveolar model is based on artificially generated random geometries and takes into account realistic tissue behavior as well as interfacial phenomena. On the part of the structural solver a smoothed aggregation algebraic multigrid method is used. For the first four generations of the bronchial tree, a geometry based on human computer tomography scans obtained from in-vivo experiments is employed. With the help of fluid-structure interaction simulations, flow patterns and airway wall stresses for normal breathing and mechanical ventilation of the healthy and diseased lung are investigated. [ABSTRACT FROM AUTHOR]

In this paper we report on a non-overlapping and an overlapping domain decomposition method as preconditioners for the boundary element approximation of an indefinite hypersingular integral equation on a surface. The equation arises from an integral reformulation of the Neumann screen problem with the Helmholtz equation in the exterior of a screen in ℝ3. [ABSTRACT FROM AUTHOR]

An efficient implementation of the Schwarz method is used to solve the 2D linear system of shallow-water equations (SWEs) on the sphere with an overset grid system named Yin-Yang. In this paper the convergence of optimized Schwarz method for solving an elliptic problem is increased by substructuring the algorithm in terms of interface unknowns. In this work we show, by numerical tests, that the use of the Yin-Yang grid avoids the "poles problems" resulting from the global latitude-longitude mesh convergence in the polar regions. [ABSTRACT FROM AUTHOR]

Two parallel and scalable multilevel preconditioners for the Bidomain system in computational electrocardiology are introduced and studied. The Bidomain system, consisting of two degenerate parabolic reaction-diffusion equations coupled with a stiff system of several ordinary differential equations, generates very ill-conditioned discrete systems when discretized with semi-implicit methods in time and finite elements in space. The multilevel preconditioners presented in this paper attain the best performance to date, both in terms of convergence rate and solution time and outperform the simpler one-level preconditioners previously introduced. Parallel numerical results, using the PETSc library and run on Linux Clusters, show the scalability of the proposed preconditioners and their efficiency on largescale simulations of a complete cardiac cycle. [ABSTRACT FROM AUTHOR]

In the context of fluid-structure interactions, there are several natural starting points for domain decomposition. First, the decomposition into the fluid and the structure domain, second, the further decomposition of those domains into subdomains for parallelisation, and, third, the decomposition of the solver grid into finer and coarser levels for multilevel approaches. In this paper, we focus on the efficient implementation of the first two types of domain decomposition. The underlying concepts offer a kind of framework that can be ‘filled' with variable content on the part of the discretization, the actual equation solver, and interpolations and projections for the inter-code communication. According to this pursuit of flexibility, modularity, and reusability, we restrict to partitioned approaches regarding the decomposition into fluid and structure domain, that is we use existing stand-alone fluid and structure solvers for the coupled fluid-structure simulation. The essential tools we use to achieve efficiency are space-partitioning and space-filling curves. Space-partitioning grids — quad- and octree grids are the most famous representations — are cartesian grids arising from a recursive local refinement procedure starting from a very coarse discretization of the domain. See Fig. 1 for examples. Such grids and the associated trees are widely used for example in computer graphics, grid generation, as computational grids etc. (compare [3]). They allow for the development of very efficient algorithms due to their strict structure and their local recursivity. [ABSTRACT FROM AUTHOR]

In this paper we present a FETI-DP type algorithm for solving the system of algebraic equations arising from the mortar finite element discretization of a fourth order problem on a nonconforming mesh. A conforming reduced Hsieh-Clough-Tocher macro element is used locally in the subdomains. We present new FETI-DP discrete problems and later introduce new parallel preconditioners for two cases: where there are no crosspoints in the coarse division of subdomains and in the general case. [ABSTRACT FROM AUTHOR]

It is necessary to set a computational domain appropriately for the numerical simulation of wave propagation phenomena in unbounded region. There are several approaches for this problem. In 1994, J.-P. Bérenger introduced the technique of Perfectly Matched Layer (PML). It is said that PML technique gives the best performance for Finite Difference Time Domain (FDTD) method in unbounded region. Some researchers expanded this idea into the linearized Euler equation and acoustic wave equation. In this paper, we consider some mathematical and numerical problem of PML technique, and propose a new discretization scheme that is better than the original scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of solution verification and accuracy assessment for computing complex Partial Differential Equation (PDE) model. Our main target applications are bio-heat transfer and blood flow simulation problems. However our long term goal is to provide a postprocessing package that can be attached to any existing numerical simulation package, for example widely used commercial codes such as ADINA, Ansys, Fluent, Star-CD etc., and provide an a posteriori error estimate to their simulation. [ABSTRACT FROM AUTHOR]