A regularization scheme applied to the direct interpolation boundary element technique with radial basis functions for solving eigenvalue problem

This paper shows a regularization scheme applied to the recently developed Direct Interpolation Technique with Radial Basis Functions (DIBEM) for elimination of the singularity that exists in the kernel of the domain integral. As a simple interpolation, the kernel is approximated directly in DIBEM; however, it is composed of the fundamental solution, distinct positions between the source points and the field points being thus required. Through the proposed regularization scheme, both sets of source points and field points, as well as base points used for interpolation with radial functions may have the same coordinates. This facilitates the data entry and also the implementation of several operational steps of the DIBEM formulation. Solution of eigenvalue problem, generated by the Helmholtz Equation, is here chosen to exemplify the efficacy of the regularization procedure, but many other problems can thus be addressed, particularly the diffusive-advective problem, that has higher level of singularity in the interpolated kernel.