Closed-form evaluation of potential integrals in the Boundary Element Method
This work provides a more accurate and efficient integration technique for practitioners of the Boundary Element Method, though it is an incremental improvement over existing numerical methods.
The paper presents a closed-form method for evaluating singular and near-singular integrals in the Boundary Element Method for the Helmholtz equation, achieving accuracy comparable to machine precision.
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such integrals on a plane element, and used to develop a criterion for the selection of quadrature rules. The analytical approach is based on an optimized expansion of the Green's function for the problem, selected to limit the error to some required tolerance. Results are presented showing accuracy to tolerances comparable to machine precision.