An efficient algebraic multigrid preconditioner for a fast multipole boundary element method

Of, Günther

doi:10.1007/s00607-008-0002-y

Cited by 10 publications

(3 citation statements)

References 29 publications

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“…The two-fold saddle point problem (4.29) is solved by a preconditioned Bramble-Pasciak CG method [1] for two-fold saddle point problems including the projection P , see [14] for details. The involved preconditioners are an algebraic multigrid preconditioner [22] for the local single layer potentials V i and the preconditioners (3.14) and (4.27) presented for the local Steklov-Poincaré operators S i and the all-floating Schur complement system. All boundary integral operators are realized by the fast multipole method [8,24].…”

Section: Projection Methods and Preconditioningmentioning

confidence: 99%

The all-floating boundary element tearing and interconnecting method

Steinbach

2009

Journal of Numerical Mathematics

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The all-floating Boundary Element Tearing and Interconnecting method incooperates the Dirichlet boundary conditions by additional constraints in the dual formulation of the standard Tearing and Interconnecting methods. This simplifies the implementation, as all subdomains are considered as floating subdomains. The method shows an improved asymptotic complexity compared to the standard BETI approach. The all-floating BETI method is presented for linear elasticity in this paper.

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Section: Projection Methods and Preconditioningmentioning

confidence: 99%

The all-floating boundary element tearing and interconnecting method

Steinbach

2009

Journal of Numerical Mathematics

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“…An incomplete list of more sophisticated preconditioners, which vary in construction time and efficacy, include multilevel hierarchical preconditioners, additive or multiplicative Schwarz,() BPX, sparse approximate inverses,() approximate LU decompositions, clustering,() integral equations of opposite order, Calderon identities, and multigrid. () In the case of multigrid preconditioners, specialized smoothers must be developed since standard smoothers like Jacobi or Gauss‐Seidel will smooth the low, rather than the high, frequency components. Examples of such smoothers may require developing approximate inverses of the integral operator involving, for example, the Laplace‐Beltrami operator …”

Section: Introductionmentioning

confidence: 99%

An efficient preconditioner for the fast simulation of a 2D stokes flow in porous media

Quaife

Coulier

Darve

2017

Numerical Meth Engineering

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Summary We consider an efficient preconditioner for a boundary integral equation (BIE) formulation of the two‐dimensional Stokes equations in porous media. While BIEs are well‐suited for resolving the complex porous geometry, they lead to a dense linear system of equations that is computationally expensive to solve for large problems. This expense is further amplified when a significant number of iterations is required in an iterative Krylov solver such as generalized minimial residual method (GMRES). In this paper, we apply a fast inexact direct solver, the inverse fast multipole method, as an efficient preconditioner for GMRES. This solver is based on the framework of H2‐matrices and uses low‐rank compressions to approximate certain matrix blocks. It has a tunable accuracy ε and a computational cost that scales as scriptOfalse(N2ptnormallnormalonormalg21false/εfalse). We discuss various numerical benchmarks that validate the accuracy and confirm the efficiency of the proposed method. We demonstrate with several types of boundary conditions that the preconditioner is capable of significantly accelerating the convergence of GMRES when compared to a simple block‐diagonal preconditioner, especially for pipe flow problems involving many pores.

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“…While simple techniques such as block-diagonal preconditioners are easy to construct, they are not always capable of reducing the number of iterations significantly. An incomplete list of more sophisticated preconditioners, which vary in construction time and efficacy, include additive or multiplicative Schwarz [37,38], BPX [39], sparse approximate inverses [40,41], approximate LU decompositions [42], clustering [43,44], integral equations of opposite order [45], Calderon identities [36], or multigrid [46,47,48,49]. In the case of multigrid preconditioners, specialized smoothers must be developed since standard smoothers like Jacobi or Gauss-Seidel will smooth the low, rather than the high, frequency components.…”

Section: Introductionmentioning

confidence: 99%

An efficient preconditioner for the fast simulation of a 2D Stokes flow in porous media

Coulier¹,

Quaife²,

Darve³

2016

Preprint

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We consider an efficient preconditioner for boundary integral equation (BIE) formulations of the twodimensional Stokes equations in porous media. While BIEs are well-suited for resolving the complex porous geometry, they lead to a dense linear system of equations that is computationally expensive to solve for large problems. This expense is further amplified when a significant number of iterations is required in an iterative Krylov solver such as GMRES. In this paper, we apply a fast inexact direct solver, the inverse fast multipole method (IFMM), as an efficient preconditioner for GMRES. This solver is based on the framework of H 2 -matrices and uses low-rank compressions to approximate certain matrix blocks. It has a tunable accuracy ε and a computational cost that scales as O(N log 2 1/ε). We discuss various numerical benchmarks that validate the accuracy and confirm the efficiency of the proposed method. We demonstrate with several types of boundary conditions that the preconditioner is capable of significantly accelerating the convergence of GMRES when compared to a simple block-diagonal preconditioner, especially for pipe flow problems involving many pores.

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An efficient algebraic multigrid preconditioner for a fast multipole boundary element method

Cited by 10 publications

References 29 publications

The all-floating boundary element tearing and interconnecting method

The all-floating boundary element tearing and interconnecting method

An efficient preconditioner for the fast simulation of a 2D stokes flow in porous media

An efficient preconditioner for the fast simulation of a 2D Stokes flow in porous media

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