Inexact Fast Multipole Boundary Element Tearing and Interconnecting Methods

Langer, Ulrich; Steinbach, Olaf; Zulehner, Walter

doi:10.1007/978-3-540-34469-8_50

Cited by 12 publications

(5 citation statements)

References 11 publications

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“…The FETI method has also been used for boundary elements, see [64] and references therein, and coupling of such methods with FETI algorithms has been investigated, see [65].…”

Section: Condition Number Estimate and Numerical Scalabilitymentioning

confidence: 99%

Parallel Iterative Substructuring in Structural Mechanics

Rheinbach

2009

Arch Computat Methods Eng

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Finite Element Tearing and Interconnecting (FETI) methods are a family of nonoverlapping domain decomposition methods which have been proven to be robust and parallel scalable for a variety of elliptic partial differential equations. Here, an introduction to the classical onelevel FETI methods is given, as well as to the more recent dual-primal FETI methods and some of their variants. With the advent of modern parallel computers with thousands of processors, certain inexact components are needed in these methods to maintain scalability. An introduction to a recent class of inexact dual-primal FETI methods is presented. Scalability results for an elasticity problem using 65 536 processor cores of the JUGENE supercomputer at Forschungszentrum Jülich show the potential of these methods. A hyperelastic problem from biomechanics is presented as an application of the methods to nonlinear finite element analysis.

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“…The FETI method has also been used for boundary elements, see [64] and references therein, and coupling of such methods with FETI algorithms has been investigated, see [65].…”

Section: Condition Number Estimate and Numerical Scalabilitymentioning

confidence: 99%

Parallel Iterative Substructuring in Structural Mechanics

Rheinbach

2009

Arch Computat Methods Eng

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“…Each has 3N × 3N entries, so the computational cost is quadratic in the vertex count and thus, unfortunately, scales worse than FEM, which scales linearly in the number of volumetric elements, in practice; we ignore the matrix inversion costs here since we perform inversion in the precomputation step. The BEM community has noticed this issue and proposed compression methods [LSSW12]. The existing methods [KS15; MS10] for elastodynamics simulations do not yet show test cases with large deformations and high compression ratios that we aim for.…”

Section: Surface‐only Dynamic Deformablesmentioning

confidence: 99%

Surface‐Only Dynamic Deformables using a Boundary Element Method

Ryusuke

Batty

Hachisuka

2022

Computer Graphics Forum

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We propose a novel surface‐only method for simulating dynamic deformables without the need for volumetric meshing or volumetric integral evaluations. While based upon a boundary element method (BEM)for linear elastodynamics, our method goes beyond simple adoption of BEM by addressing several of its key limitations. We alleviate large displacement artifacts due to linear elasticity by extending BEM with a moving reference frame and surface‐only fictitious forces, so that it only needs to handle deformations. To reduce memory and computational costs, we present a simple and practical method to compress the series of dense matrices required to simulate propagation of elastic waves over time. Furthermore, we explore a constraint enforcement mechanism and demonstrate the applicability of our method to general computer animation problems, such as frictional contact.

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“…Note that the approach presented herein offers great flexibility in terms of mesh non-conformity. By writing the system matrix as (22) where (23)…”

Section: Matrix Equationmentioning

confidence: 99%

Integral Equation Based Domain Decomposition Method for Solving Electromagnetic Wave Scattering From Non-Penetrable Objects

Peng

Wang

Lee

2011

IEEE Trans. Antennas Propagat.

194

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The integral equation (IE) method is commonly utilized to model time-harmonic electromagnetic (EM) problems. One of the greatest challenges in its applications arises in the solution of the resulting ill-conditioned matrix equation. We introduce a new domain decomposition method (DDM) for the IE solution of EM wave scattering from non-penetrable objects. The proposed method is a non-overlapping/non-conformal DDM and it provides a computationally efficient and effective preconditioner for the IE matrix equations. Moreover, the proposed approach is very suitable for dealing with multi-scale electromagnetic problems since each sub-domain has its own characteristics length and will be meshed independently. Furthermore, for each sub-domain, we are free to choose the most effective IE sub-domain solver based on its local geometrical features and electromagnetic characteristics. Additionally, the multilevel fast multi-pole algorithm (MLFMA) is utilized to accelerate the computations of couplings between sub-domains. Numerical results demonstrate that the proposed method yields rapid convergence in the outer Krylov iterative solution process. Finally, simulations of several large-scale examples testify to the effectiveness and robustness of the proposed IE based DDM.Index Terms-Domain decomposition, integral equation (IE) method, method of moments, multilevel fast multipole algorithm (MLFMA), scattering.

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Inexact Fast Multipole Boundary Element Tearing and Interconnecting Methods

Cited by 12 publications

References 11 publications

Parallel Iterative Substructuring in Structural Mechanics

Parallel Iterative Substructuring in Structural Mechanics

Surface‐Only Dynamic Deformables using a Boundary Element Method

Integral Equation Based Domain Decomposition Method for Solving Electromagnetic Wave Scattering From Non-Penetrable Objects

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