Higher-order time domain boundary elements for elastodynamics: graded meshes and hp versions

被引：5

作者：

Aimi, Alessandra ^{[1
]}

Di Credico, Giulia ^{[1
,2
]}

Gimperlein, Heiko ^{[2
]}

Stephan, Ernst P. ^{[3
]}

机构：

[1] Univ Parma, Dept Math Phys & Comp Sci, Parco Area Sci 53-A, I-43124 Parma, Italy

[2] Univ Innsbruck, Engn Math, Innsbruck, Austria

[3] Leibniz Univ Hannover, Inst Appl Math, D-30167 Hannover, Germany

来源：

NUMERISCHE MATHEMATIK | 2023年 / 154卷 / 1-2期

关键词：

Primary; 65M38; Secondary; 65M15; 74S15; 35L67; NUMERICAL-INTEGRATION; DIRICHLET PROBLEM; FINITE-ELEMENTS; EQUATION METHOD; EDGE; SINGULARITIES; BEM; REFINEMENT; CRACK;

D O I：

10.1007/s00211-023-01355-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for poly- gonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.

引用

页码：35 / 101

页数：67

共 53 条

[1]

Aimi A, 1997, INT J NUMER METH ENG, V40, P1977, DOI 10.1002/(SICI)1097-0207(19970615)40:11<1977::AID-NME150>3.0.CO

[2]

2-O

[3] An energy approach to space-time Galerkin BEM for wave propagation problems [J].

Aimi, A. ;

Diligenti, M. ;

Guardasoni, C. ;

Mazzieri, I. ;

Panizzi, S. .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2009, 80 (09) :1196-1240

[4] Highly accurate quadrature schemes for singular integrals in energetic BEM applied to elastodynamics [J].

Aimi, Alessandra ;

Di Credico, Giulia ;

Diligenti, Mauro ;

Guardasoni, Chiara .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 410

[5]

Antes H., 1985, Finite Elem Anal Des, V1, P313, DOI [10.1016/0168-874X(85)90029-0, DOI 10.1016/0168-874X(85)90029-0]

[6]

Bamberger A., 1986, I. Math. Methods Appl. Sci., V8, P405, DOI [10.1002/mma.1670080127, DOI 10.1002/MMA.1670080127]

[7] SINGULARITIES OF ROTATIONALLY SYMMETRICAL SOLUTIONS OF BOUNDARY-VALUE-PROBLEMS FOR THE LAME EQUATIONS [J].

BEAGLES, AE ;

SANDIG, AM .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1991, 71 (11) :423-431

[8] A SPACE-TIME VARIATIONAL FORMULATION FOR THE BOUNDARY INTEGRAL-EQUATION IN A 2D ELASTIC CRACK PROBLEM [J].

BECACHE, E ;

DUONG, TH .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1994, 28 (02) :141-176

[9] A VARIATIONAL BOUNDARY INTEGRAL-EQUATION METHOD FOR AN ELASTODYNAMIC ANTIPLANE CRACK [J].

BECACHE, E .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1993, 36 (06) :969-984

[10] The p-version of the boundary element method for hypersingular operators on piecewise plane open surfaces [J].

Bespalov, A ;

Heuer, N .

NUMERISCHE MATHEMATIK, 2005, 100 (02) :185-209

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