Accurate Evaluation of Weakly Singular Integral in Combined Field Integral Equation on Clifford Algebra with Numerical Integration

In this paper, the formulation of multi-dimensional Cauchy integral equation, which is in an integral form of Maxwell's equations, is presented on Clifford algebra to increase the accuracy of numerical solutions. The advantage of this formulation is the kernel integral concerning without the strongly singular function. To obtain the solution of the Cauchy integral equation, the boundary element technique is exploited to numerically solve with the quadrilateral function via Gauss-Quadrature technique. The accuracy of the obtained fields is investigated by comparing with those from the known analytical method.