A simple and accurate scheme based on complex space \(\mathbb C\) to calculate boundary integrals of 2D boundary elements method. (English) Zbl 1362.65132
Summary: In this work a semi-analytical algorithm is presented to calculate the boundary integrals of higher order which appear in boundary elements method (BEM). In fact treating singularity and near singularity of the boundary integrals using complex space \(\mathbb C\) is the main aim of this paper. The integrals are computed for linear, quadratic, cubic and other higher order elements when the geometry of the boundary elements is curved. The main advantages of the new algorithm are its applicability, simplicity and high accuracy which enable the conventional higher order BEM to solve Poisson’s problems, accurately. The potentials at the interior points very close to boundary can be evaluated by the scheme developed in this report. Some test problems are given and numerical simulations are presented. Numerical results demonstrate that the new algorithm proposed in the current paper can effectively handle singular and near singular boundary integrals of BEM, specially for solving partial differential equations which arise in thin body problems.
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
boundary elements method; singular and near singular integrals; higher order boundary elements method; Poisson’s equation; potential theory and thin body problemsReferences:
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