A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems

Ivano Benedetti, Aliabadi

Risultato della ricerca: Article

36 Citazioni (Scopus)

Abstract

In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The preconditioners are built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. An original strategy, based on the computation of some local preconditioners only, is presented and tested to further speed up the overall analysis. The reported numerical results demonstrate the effectiveness of the technique for both uncracked and cracked solids and show significant reductions in terms of both memory storage and computational time.
Lingua originaleEnglish
pagine (da-a)1038-1067
Numero di pagine30
RivistaInternational Journal for Numerical Methods in Engineering
Volume84
Stato di pubblicazionePublished - 2010

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Elastodynamics
Boundary element method
Laplace
Preconditioner
Boundary Elements
Crack
Hierarchical Matrices
Cracks
Three-dimensional
GMRES
Laplace transforms
Approximation algorithms
Collocation
Dynamic Analysis
Laplace transform
Dynamic analysis
System of equations
Approximation Algorithms
Speedup
Data storage equipment

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Applied Mathematics
  • Engineering(all)

Cita questo

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title = "A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems",
abstract = "In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The preconditioners are built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. An original strategy, based on the computation of some local preconditioners only, is presented and tested to further speed up the overall analysis. The reported numerical results demonstrate the effectiveness of the technique for both uncracked and cracked solids and show significant reductions in terms of both memory storage and computational time.",
keywords = "dual boundary element method;laplace transform method;fast BEM solvers;large-scale computations;elastodynamics",
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T1 - A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems

AU - Benedetti, Ivano

AU - Aliabadi, null

PY - 2010

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N2 - In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The preconditioners are built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. An original strategy, based on the computation of some local preconditioners only, is presented and tested to further speed up the overall analysis. The reported numerical results demonstrate the effectiveness of the technique for both uncracked and cracked solids and show significant reductions in terms of both memory storage and computational time.

AB - In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The preconditioners are built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. An original strategy, based on the computation of some local preconditioners only, is presented and tested to further speed up the overall analysis. The reported numerical results demonstrate the effectiveness of the technique for both uncracked and cracked solids and show significant reductions in terms of both memory storage and computational time.

KW - dual boundary element method;laplace transform method;fast BEM solvers;large-scale computations;elastodynamics

UR - http://hdl.handle.net/10447/61315

M3 - Article

VL - 84

SP - 1038

EP - 1067

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

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