Boundary element computations of 3D stationary and time-dependent problems using Bezier-spline elements

A method for computing stationary and time-dependent problems using C¹-continuous Bezier boundary elements is presented. The Bezier element and the approximation of the solution is discussed. The method is validated against a biomedical problem, the results are compared with the analytical solution of a spherical model of a human thorax excited by a single dipole inside the heart. Further investigations concerning the scattering of a transient electromagnetic wave from simple shaped bodies are carried out with isoparametric Bezier spline representation of geometry and solution. In the case of integral equations of second order, it can be shown that the solution´s smoothness is improved due to the C¹-continuity of the scatterer´s shape. First order integral equations are amenable to direct application of the boundary element method with derivation of the kernel inside the integral and point collocation