Multifrontal parallel distributed symmetric and unsymmetric solvers

Amestoy, Patrick; Duff, Iain S.; L’Excellent, Jean-Yves

doi:10.1016/s0045-7825(99)00242-x

Cited by 809 publications

(558 citation statements)

References 12 publications

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“…This partitioner intensively uses subroutines provided by METIS [38]. The factorization of each sub-matrices is performed thanks to a direct sparse solver [9,10] and stored during the resolution of the interface problem. The interface problem uses a crude GMRES method without any preconditioner.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The efficiency of the method mainly depends on the ability of inverting the associated global sparse linear system. This type of problem is strongly dimension dependent and, if in 2D, the use of direct solvers like [9][10][11][12] is obvious (a typical scattering problem with 10 6 unknowns is solved in few dozen of seconds on a classical PC), the resolution of the linear system arising from the discretization of 3D configurations with a direct solver is much more tricky, time and memory consuming.…”

Section: Introductionmentioning

confidence: 99%

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Scattered Field Computation With an Extended Feti-Dpem2 Method

Voznyuk¹,

Tortel²,

Litman³

2013

PIER

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Abstract-Due to the increasing number of applications in engineering design and optimization, more and more attention has been paid to full-wave simulations based on computational electromagnetics. In particular, the finite-element method (FEM) is well suited for problems involving inhomogeneous and arbitrary shaped objects. Unfortunately, solving large-scale electromagnetic problems with FEM may be time consuming. A numerical scheme, called the dual-primal finite element tearing and interconnecting method (FETI-DPEM2), distinguishes itself through the partioning on the computation domain into non-overlapping subdomains where incomplete solutions of the electrical field are evaluated independently. Next, all the subdomains are "glued" together using a modified Robin-type transmission condition along each common internal interface, apart from the corner points where a simple Neumann-type boundary condition is imposed. We propose an extension of the FETI-DPEM2 method where we impose a Robin type boundary conditions at each interface point, even at the corner points. We have implemented this Extended FETI-DPEM2 method in a bidimensional configuration while computing the field scattered by a set of heterogeneous, eventually anistropic, scatterers. The results presented here will assert the efficiency of the proposed method with respect to the classical FETI-DPEM2 method, whatever the mesh partition is arbitrary defined.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scattered Field Computation With an Extended Feti-Dpem2 Method

Voznyuk¹,

Tortel²,

Litman³

2013

PIER

View full text Add to dashboard Cite

show abstract

“…Additionally, we set the constant γ appearing in the interior penalty parameter σ defined by (3.6) equal to 10. The resulting system of nonlinear equations is solved by a damped Newton method; for each inner (linear) iteration, we employ the Multifrontal Massively Parallel Solver (MUMPS); see Amestoy et al (2000Amestoy et al ( , 2001Amestoy et al ( , 2006. The hp-adaptive meshes are constructed by first marking the elements for refinement/derefinement according to the size of the local error indicators η K ; this is achieved via a fixed fraction strategy where the refinement and derefinement fractions are set to 25% and 5%, respectively.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows

Congreve

Houston

Süli³

et al. 2013

IMA Journal of Numerical Analysis

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In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ R d , d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

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“…The internal forces are computed by solving non-linear equations for each finite element. The computing time and costs for these steps are negligible compared to solving linear system (6). The stiffness matrix, K , is symmetric and positive definite for elastic, constrained systems; hence, ∀u = 0 : u T K u > 0 and all eigenvalues of K are positive.…”

Section: Problem Definition: Composite Materialsmentioning

confidence: 99%

“…An important advantage of direct solution methods is their robustness: they can, to a large extent, be used as black boxes for solving a wide range of problems, but they are expensive in terms of computational costs. Several high quality, well parallelisable public domain direct solvers exist [32,38,42,10,6]. The FETI and AMG methods are also robust but are often much less expensive than direct solution methods and have been discussed in [23] and [49].…”

Section: Introductionmentioning

confidence: 99%

Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials

et al. 2011

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Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms. In this paper, we consider the simulation of asphalt concrete, which is a mixture of components with large differences in material stiffness. The discontinuities in material stiffness give rise to many small eigenvalues that negatively affect the convergence of iterative solution algorithms such as the preconditioned conjugate gradient (PCG) method. This paper considers the deflated preconditioned conjugate gradient (DPCG) method in which the rigid body modes of sets of elements with homogeneous material properties are used as deflation vectors. As preconditioner we consider several variants of the algebraic multigrid smoothed aggregation method. We evaluate the performance of the DPCG method on a parallel computer using up to 64 processors. Our test problems are derived from real asphalt core samples, obtained using CT scans. We show that the DPCG method is an efficient and robust technique for solving these challenging linear systems. T. B. Jönsthövel (B)·

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Multifrontal parallel distributed symmetric and unsymmetric solvers

Cited by 809 publications

References 12 publications

Scattered Field Computation With an Extended Feti-Dpem2 Method

Scattered Field Computation With an Extended Feti-Dpem2 Method

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows

Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials

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