A Simple, Accurate and Semi-Analytical Meshless Method for Solving Laplace and Helmholtz Equations in Complex Two-Dimensional Geometries

A localized virtual boundary element–meshless collocation method (LVBE-MCM) is proposed to solve Laplace and Helmholtz equations in complex two-dimensional (2D) geometries. “Localized” refers employing the moving least square locally approximate physical quantities of computational domain after introducing traditional element method. The LVBE-MCM a semi-analytical domain-type meshless that based on fundamental solution governing equation, which different from When it comes 2D problems, only needs calculate numerical integration circular boundary. It avoids evaluation singular/strong singular/hypersingular integrals seen Compared difficulty selecting evaluating singular integrals, simple straightforward. Numerical experiments, including irregular doubly connected domains, demonstrate accurate, stable, convergent for solving both equations.