Integral Evaluation for a Closed-Form 2-D Potential Formulation of the Galerkin BEM

Closed-form solutions are derived for the regular and adjacent-singular integrals involving the two-dimensional Laplacian's Green's function and its normal derivative that arise in the Galerkin BEM. Motivation for their use is provided by comparing the accuracy and time required to compute the BEM system matrix relative to traditional numerical integration. Specifically, it is shown that the use of the closed-form solutions reduces computation time to produce the influence matrices by approximately 95% relative to Gauss quadrature with similar accuracy. All elements of these matrices are then expressed in a form convenient for implementation.

Automated summary

Closed-form solutions are derived for regular and adjacent-singular integrals associated with the two-dimensional Laplacian's Green's function and its normal derivative in the Galerkin BEM. By comparing accuracy and computation time to traditional numerical integration, it is demonstrated that using closed-form solutions can reduce computation time for influence matrices by approximately 95% relative to Gauss quadrature, while maintaining similar accuracy. Furthermore, all elements of the matrices are expressed in a convenient form for implementation.