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107
A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations
, 2005
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Multilevel preconditioners constructed from inversebased ILUs
, 2004
"... This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few of strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the Incomplete LU factorization resulting from dropping small entries in Gaussian elimination prod ..."
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Cited by 23 (8 self)
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This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few of strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the Incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. As a consequence a few strategies are developed whose goal is to achieve this feature. A number of “templates” for enabling implementations of these factorizations are presented. Numerical experiments show that the resulting ILUs offer a good compromise between robustness and efficiency.
BLOCK KRYLOV SPACE METHODS FOR LINEAR SYSTEMS WITH Multiple Righthand Sides: An Introduction
, 2006
"... In a number of applications in scientific computing and engineering one has to solve huge sparse linear systems of equations with several righthand sides that are given at once. Block Krylov space solvers are iterative methods that are especially designed for such problems and have ..."
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Cited by 20 (0 self)
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In a number of applications in scientific computing and engineering one has to solve huge sparse linear systems of equations with several righthand sides that are given at once. Block Krylov space solvers are iterative methods that are especially designed for such problems and have
Fast dynamic simulation of multibody systems using impulses
 In Virtual Reality Interactions and Physical Simulations (VRIPhys
, 2006
"... A dynamic simulation method for multibody systems is presented in this paper. The special feature of this method is that it satisfies all given constraints by computing impulses. In each simulation step the joint states after the step are predicted. In order to obtain valid states after the simulat ..."
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Cited by 8 (4 self)
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A dynamic simulation method for multibody systems is presented in this paper. The special feature of this method is that it satisfies all given constraints by computing impulses. In each simulation step the joint states after the step are predicted. In order to obtain valid states after the simulation step, impulses are computed and applied to the connected bodies. Since a valid joint state is targeted exactly, there is no drift as the simulation proceeds in time and so no additional stabilisation is required. In previous approaches the impulses for a multibody system were computed iteratively. Since dependencies between joints were not taken into account, the simulation of complex models was slow. A novel method is presented that uses a system of linear equations to describe these dependencies. By solving this typically sparse system the required impulses are determined. This method allows a very fast simulation of complex multibody systems. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation 1.
D.: Parallel simulation of inextensible cloth
 In Virtual Reality Interactions and Physical Simulations (VRIPhys
, 2008
"... This paper presents an efficient simulation method for parallel cloth simulation. The presented method uses an impulsebased approach for the simulation. Cloth simulation has many application areas like computer animation, computer games or virtual reality. Simulation methods often make the assumpti ..."
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Cited by 7 (6 self)
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This paper presents an efficient simulation method for parallel cloth simulation. The presented method uses an impulsebased approach for the simulation. Cloth simulation has many application areas like computer animation, computer games or virtual reality. Simulation methods often make the assumption that cloth is an elastic material. In this way the simulation can be performed very efficiently by using spring forces. These methods disregard the fact that many textiles cannot be stretched significantly. The simulation of inextensible textiles with methods based on spring forces leads to stiff differential equations which cause a loss of performance. In contrast to that, in this paper a method is presented that simulates cloth by using impulses. The mesh of a cloth model is subdivided into strips of constraints. The impulses for each strip can be computed in linear time. The strips that have no common particle are independent from each other and can be solved in parallel. The impulsebased method allows the realistic simulation of inextensible textiles in realtime. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation 1.
An Algorithm for the Fast Solution of Symmetric Linear Complementarity Problems
, 2008
"... This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improveme ..."
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Cited by 4 (1 self)
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This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe [19] that combines projected GaussSeidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely illconditioned problems. Numerical tests indicate that the approach is more efficient than interiorpoint and gradient projection methods on some physical simulation problems that arise in computer game scenarios.
JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices
, 2007
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A KRYLOV METHOD FOR THE DELAY EIGENVALUE PROBLEM
"... Abstract. The Arnoldi method is currently a very popular algorithm to solve largescale eigenvalue problems. The main goal of this paper is to generalize the Arnoldi method to the characteristic equation of a delaydifferential equation (DDE), here called a delay eigenvalue problem (DEP). The DDE ca ..."
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Cited by 4 (4 self)
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Abstract. The Arnoldi method is currently a very popular algorithm to solve largescale eigenvalue problems. The main goal of this paper is to generalize the Arnoldi method to the characteristic equation of a delaydifferential equation (DDE), here called a delay eigenvalue problem (DEP). The DDE can equivalently be expressed with a linear infinite dimensional operator whose eigenvalues are the solutions to the DEP. We derive a new method by applying the Arnoldi method to the generalized eigenvalue problem (GEP) associated with a spectral discretization of the operator and by exploiting the structure. The result is a scheme where we expand a subspace not only in the traditional way done in the Arnoldi method. The subspace vectors are also expanded with one block of rows in each iteration. More importantly, the structure is such that if the Arnoldi method is started in an appropriate way, it has the (somewhat remarkable) property that it is in a sense independent of the number of discretization points. It is mathematically equivalent to an Arnoldi method with an infinite matrix, corresponding to the limit where we have an infinite number of discretization points. We also show an equivalence with the Arnoldi method in an operator setting. It turns out that with an appropriately defined operator over a space equipped with scalar product with respect to which Chebyshev polynomials are orthonormal, the vectors in the Arnoldi iteration can be interpreted as the coefficients in a Chebyshev expansion of a function. The presented method yields the same Hessenberg matrix as the Arnoldi method applied to the operator. 1. Introduction. Consider
Domain decomposition method for Maxwell’s equations: Scattering off periodic structures
, 2006
"... We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer metho ..."
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Cited by 4 (0 self)
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We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multilayer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.