Convergence of the High-Accuracy Algorithm for Solving the Dirichlet Problem of the Modified Helmholtz Equation

Abstract

In this paper, we derive the convergence for the high-accuracy algorithm in solving the Dirichlet problem of the modified Helmholtz equation. By the boundary element method, we transform the system to be a boundary integral equation. The high-accuracy algorithm using the specific quadrature rule is developed to deal with weakly singular integrals. The convergence of the algorithm is proved based on Anselone’s collective compact theory. Moreover, an asymptotic error expansion shows that the algorithm is of order Oh03. The numerical examples support the theoretical analysis.