The approximate component mode synthesis special finite element method in two dimensions: Parallel implementation and numerical results

A special finite element method based on approximate component mode synthesis (ACMS) was introduced in Hetmaniuk and Lehoucq (2010). ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, a parallel implementation of ACMS is prese...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 289; pp. 116 - 133
Main Authors Heinlein, A., Hetmaniuk, U., Klawonn, A., Rheinbach, O.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2015
Subjects
Approximation
Component mode synthesis
Discretization
Domain decomposition
Eigendecomposition
FETI-DP
Finite element method
Finite elements
Mathematical analysis
Mathematical models
Multiscale
Two dimensional
Finite elements
FETI-DP
Eigendecomposition
Component mode synthesis
Domain decomposition
Multiscale
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Summary:A special finite element method based on approximate component mode synthesis (ACMS) was introduced in Hetmaniuk and Lehoucq (2010). ACMS was developed for second order elliptic partial differential equations with rough or highly varying coefficients. Here, a parallel implementation of ACMS is presented and parallel scalability issues are discussed for representative examples. Additionally, a parallel domain decomposition preconditioner (FETI-DP) is applied to solve the ACMS finite element system. Weak parallel scalability results for ACMS are presented for up to 1024 cores. Our numerical results also suggest a quadratic–logarithmic condition number bound for the preconditioned FETI-DP method applied to ACMS discretizations.
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.02.053