Efficient Numerical Evaluation of Singular Integrals in Volume Integral Equations

We present a method for the numerical evaluation of 6D and 5D singular integrals appearing in Volume Integral Equations. It is an extension Sauter-Schwab/Taylor-Duffy strategy triangle-triangle interaction to tetrahedron-tetrahedron triangle-tetrahedron integrals. The general advantages these kind quadrature that they allow use different kinds kernel basis functions. They also work on curvilinear domains. are all based relative coordinates tranformation splitting integration domain into subdomains which rules can be constructed. show how build tensor-product further improve their efficiency by using defined over 2D, 3D 4D simplices. Compared existing approach, computes integral as sequence 1D integrations, significant speedup achieved. accuracy convergence properties demonstrated experiments Additionally, we applied new approach Surface