Classical Boundary Element Methods

This article discusses classical boundary element methods implemented in MATLAB. The boundary element method (BEM) is a highly efficient numerical computation technique applicable across various domains including fluid dynamics, structural mechanics, and electromagnetic analysis. This approach provides superior accuracy for problems that challenge traditional algorithms, particularly those involving complex boundary conditions. Compared to other numerical methods, BEM offers significant advantages such as mesh-free formulation, rapid computation speed, and high precision. The MATLAB implementation typically involves key algorithms like the collocation method, integration over boundary elements using Gaussian quadrature, and handling of singular integrals through specialized techniques. Core functions often include boundary discretization routines, fundamental solution computations, and system matrix assembly using Green's functions. The method finds extensive applications in both academic research and practical engineering projects. Typical MATLAB implementations involve boundary representation using parametric elements, calculation of influence coefficients, and solution of the resulting system equations through direct or iterative solvers. The code structure generally includes modules for pre-processing (boundary definition), core computation (integral equation solution), and post-processing (result visualization and validation).