Integral evaluation in the BEM solution of (hyper)singular integral equations. 2D problems on polygonal domains

DOI10.1016/S0377-0427(97)00007-1zbMath0879.65074OpenAlexW2052814546MaRDI QIDQ1362346

Giovanni Monegato, Mauro Diligenti

Publication date: 7 January 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(97)00007-1

zbMATH Keywords

Galerkin methodboundary element methodCauchy integralsLaplace equation\(p\) versionPoisson equationpotential problemsquadrature ruleshypersingular integrals\(h-p\) version

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical quadrature and cubature formulas (65D32) Boundary element methods for boundary value problems involving PDEs (65N38)

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Cites Work

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• The use of simple solutions in the regularization of hypersingular boundary integral equations
• On the h-, p- and h-p versions of the boundary element method. - Numerical results
• Quadrature formulas obtained by variable transformation and the DE-rule
• A Galerkin approach to boundary element elastoplastic analysis
• An energy approach to the boundary element method. I: Elastic solids
• The h-p version of the finite element method. I. The basic approximation results
• The h-p version of the finite element method. II. General results and applications
• The numerical evaluation of one-dimensional Cauchy principal value integrals
• Applications of finite-part integrals to the singular integral equations of crack problems in plane and three-dimensional elasticity
• A variational approach to boundary element elastodynamic analysis and extension to multidomain problems
• Continuity requirements for density functions in the boundary integral equation method
• Fundamental solutions for linear viscoelastic continua
• An integral equations method for solving the problem of a plane crack of arbitrary shape
• Some advances in boundary integral methods for wave-scattering from cracks
• Numerical evaluation of hypersingular integrals
• Product integration for the linear transport equation in slab geometry
• Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements: Thermal conduction formulation
• Evaluation of hypersingular integrals in the boundary element method
• Hypersingular Boundary Integral Equations: Some Applications in Acoustic and Elastic Wave Scattering
• Boundary elements and symmetry
• Boundary Integral Formulation of Crack Problems
• Kernel Properties and Representations of Boundary Integral Operators
• A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations
• A galerkin symmetric boundary-element method in elasticity: Formulation and implementation
• Product-integration rules and their convergence
• Symmetric Galerkin boundary formulations employing curved elements
• Some notes on singular integral techniques in boundary element analysis
• Singular and Near Singular Integrals in the BEM: A Global Approach
• Computational Aspects of Three-Term Recurrence Relations
• The application of integral equation methods to the numerical solution of some exterior boundary-value problems
• Hypersingular integrals in boundary element fracture analysis