Mathematical Foundation of the Collocation Boundary Element Method: Consistent Formulation, Convergence Theorem and Accurate Numerical Quadrature

Abstract

Mathematical Foundation of the Collocation Boundary Element Method: Consistent Formulation, Convergence Theorem and Accurate Numerical
The use of boundary integral equations as an attempt to solve general problems of elasticity and potential has largely preceded the use of domainrelated developments, which only became feasible with the advent of powerful computational devices
We propose a revisit of the method, including, as for elasticity problems: a) conceptual reformulation in terms of weighted residuals with a consistent derivation of the single-layer potential matrix; b) an original convergence theorem for general curved boundaries and high order elements (2D and 3D problems); c) a unified numerical evaluation technique of regular, improper, quasi-singular and singular integrals that only uses Gauss-Legendre quadrature plus locally defined corrections for general curved boundaries – leading to arbitrarily high accurate results independently from singularity or quasisingularity intensity