A combination of the fast multipole boundary element method and Krylov subspace recycling solvers

Keuchel, Sören; Biermann, Jan; Estorff, Otto von

doi:10.1016/j.enganabound.2016.01.008

Cited by 16 publications

(9 citation statements)

References 35 publications

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“…Another important area is nonlinear optimization, such as nonlinear least-squares, for example, in tomography [90,100,111,130] and blind deconvolution [78]. Many applications arise in engineering, such as computational fluid dynamics and nonlinear structural problems [8,74,95,96,124,154,155], acoustics [89,99], and problems from electromagnetics and electrical circuits [49,72,73,84,118,156]. Recycling has found many applications in uncertainty quantification and partial differential equations with stochastic components [46,83].…”

Section: Computational Scientific and Engineering Applicationsmentioning

confidence: 99%

A survey of subspace recycling iterative methods

2020

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This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial vectors over a sequence of linear systems with slowly changing coefficient matrices, multiple right-hand sides, or both. The subspace information that is recycled is usually generated during the run of an iterative method (usually a Krylov subspace method) on one or more of the systems. Following introduction of definitions and notation, we examine the history of early augmentation schemes along with deflation preconditioning schemes and their influence on the development of recycling methods. We then discuss a general residual constraint framework through which many augmented Krylov and recycling methods can both be viewed. We review several augmented and recycling methods within this framework. We then discuss some known effective strategies for choosing subspaces to recycle before taking the reader through more recent developments that have generalized recycling for (sequences of) shifted linear systems, some of them with multiple right-hand sides in mind. We round out our survey with a brief review of application areas that have seen benefit from subspace recycling methods.

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Section: Computational Scientific and Engineering Applicationsmentioning

confidence: 99%

A survey of subspace recycling iterative methods

2020

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“…the Ritz vectors [44] of the BEM system for each frequency, is created. The presented technique resembles to the Krylov subspaces recycling for varying systems [45] that was also recently employed in the context of a series of FMM-BEM acoustics systems [46]. Krylov subspaces recycling implies that the Krylov subspaces of the j th system are utilized for accelerating the convergence of the iterative solution procedure of the (j + 1) st system.…”

Section: In That Context This Work Introduces a Novel Model Order Reduction (Mor)mentioning

confidence: 99%

Krylov subspaces recycling based model order reduction for acoustic BEM systems and an error estimator

Panagiotopoulos

Deckers

Desmet

2020

Computer Methods in Applied Mechanics and Engineering

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Boundary Element Method frequency sweep analyses in acoustics are usually accompanied by a vast numerical cost of assembling and solving numerous linear systems. In that context, this work proposes a model order reduction technique to mitigate the resulting computational cost of such analyses. First, a series expansion of the Green's function BEM kernel is leveraged to construct a series of frequency independent matrices. Next, in a model order reduction way, the arising matrices are projected on a reduced basis utilizing a Galerkin projection.By this off-line matrix projection, both the assembly and the solution of the BEM full-size linear systems degenerate into assembling and solving a reduced system for all frequencies. Significant speed-up factors can, thus, be achieved for both operations. The projection basis employed in this model reduction scheme is developed through an Arnoldi algorithm for the BEM systems on a grid of master frequencies. The method is based on Krylov subspaces recycling, as the subspaces produced at master frequencies are recycled to approximate the surface distribution of the acoustic variables on the whole frequency range of interest. Utilizing Krylov subspaces facilitates as well the definition of a robust error estimator that indicates the quality of the reduced system. The performance of the proposed method is assessed for both an exterior and an interior problem for a simple and more complicated geometry respectively.

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“…In addition, a number of publications are concerned with efficient schemes for the actual solution of linear systems in a frequency range. In particular, projection‐based model order reduction (MOR) techniques have been proposed to reduce the computational effort.…”

Section: Introductionmentioning

confidence: 99%

“…23,24 Furthermore, the high numerical complexity associated to fully populated boundary element matrices led to the development of several fast algorithms 25,26 that have also been combined with multifrequency strategies. 27 In addition, a number of publications [28][29][30] are concerned with efficient schemes for the actual solution of linear systems in a frequency range. In particular, projection-based model order reduction (MOR) techniques have been proposed to reduce the computational effort.…”

Section: Introductionmentioning

confidence: 99%

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

Baydoun

Voigt

Jelich

et al. 2019

Numerical Meth Engineering

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Summary The solution of frequency dependent linear systems arising from the discretization of vibro‐acoustic problems requires a significant computational effort in the case of rapidly varying responses. In this paper, we review the use of a greedy reduced basis scheme for the efficient solution in a frequency range. The reduced basis is spanned by responses of the system at certain frequencies that are chosen iteratively based on the response that is currently worst approximated in each step. The approximations at intermediate frequencies as well as the a posteriori estimations of associated errors are computed using a least squares solver. The proposed scheme is applied to the solution of an interior acoustic problem with boundary element method (BEM) and to the solution of coupled structural acoustic problems with finite element method and BEM. The computational times are compared to those of a conventional frequencywise strategy. The results illustrate the efficiency of the method.

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A combination of the fast multipole boundary element method and Krylov subspace recycling solvers

Cited by 16 publications

References 35 publications

A survey of subspace recycling iterative methods

A survey of subspace recycling iterative methods

Krylov subspaces recycling based model order reduction for acoustic BEM systems and an error estimator

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

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