BEM solution of Poisson’s equation with source function satisfying \(\nabla^2\rho=\text{constant}\). (English) Zbl 0973.65105
Summary: Poisson’s equation in two dimensions is studied and different solutions with a boundary element method (BEM) are outlined depending on whether the source function is harmonic or not. When the Laplacian of the source function is zero or a constant, the Galerkin vector and the multiple-reciprocity method are applied. When the Laplacian of the source function is no longer zero, the source function is approximated by Lagrange polynomials. This method is then improved by subtracting a parabola from the source function.
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
Lagrange interpolation; boundary element method; Galerkin vector method; Poisson’s equationReferences:
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