Performance of Compact Radial Basis Functions in the Direct Interpolation Boundary Element Method for Solving Potential Problems

摘要

This study evaluates the effectiveness of a new technique that transforms domain integrals into boundary integrals that is applicable to the boundary element method. Simulations were conducted in which two-dimensional surfaces were approximated by interpolation using radial basis functions with full and compact supports. Examples involving Poisson's equation are presented using the boundary element method and the proposed technique with compact radial basis functions. The advantages and the disadvantages are examined through simulations. The effects of internal poles, the boundary mesh refinement and the value for the support of the radial basis functions on performance are assessed.