The singular function boundary integral method for Laplacian problems with boundary singularities in two and three-dimensions
SourceProcedia Computer Science
10th International Conference on Computational Science 2010, ICCS 2010
Google Scholar check
MetadataShow full item record
We present a Singular Function Boundary Integral Method (SFBIM) for solving elliptic problems with a boundary singularity. In this method the solution is approximated by the leading terms of the asymptotic solution expansion, which exists near the singular point and is known for many benchmark problems. The unknowns to be calculated are the singular coefficients, i.e. the coefficients in the asymptotic expansion, also called (generalized) stress intensity factors. The discretized Galerkin equations are reduced to boundary integrals by means of Green's theorem and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers, the values of which are introduced as additional unknowns in the resulting linear system. The method is described for two-dimensional Laplacian problems for which the analysis establishes exponential rates of convergence as the number of terms in the asymptotic expansion is increased. We also discuss the extension of the method to three-dimensional Laplacian problems with exhibits edge singularities.
Showing items related by title, author, creator and subject.
The singular function boundary integral method for 3-D Laplacian problems with a boundary straight edge singularity Christodoulou, Evgenia; Elliotis, Miltiades C.; Xenophontos, Christos A.; Georgiou, Georgios C. (2012)Three-dimensional Laplace problems with a boundary straight-edge singularity caused by two intersecting flat planes are considered. The solution in the neighbourhood of the straight edge can be expressed as an asymptotic ...
The Singular Function Boundary Integral Method for singular Laplacian problems over circular sections Christodoulou, Evgenia; Xenophontos, Christos A.; Georgiou, Georgios C. (2010)The Singular Function Boundary Integral Method (SFBIM) for solving two-dimensional elliptic problems with boundary singularities is revisited. In this method the solution is approximated by the leading terms of the asymptotic ...
Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity Christodoulou, Evgenia; Elliotis, Miltiades C.; Georgiou, Georgios C.; Xenophontos, Christos A. (2012)In this article, we analyze the singular function boundary integral method (SFBIM) for a two-dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick-slip flow problem. In the SFBIM, ...