The combination of the boundary element method and the numerical manifold method for potential problems

Abstract

In this study, a boundary element method coupled with numerical manifold method is developed for solving potential problems in two dimension. This approach combines an equivalent variational form of a boundary integral equation with the finite cover approximations for generating the trial and test functions of the variational formulation. This method exploits the reduced dimensionality advantages of the BEM, and is especially suited for the problems with an unbounded domain. Since the local cover function can be chosen in the covers arbitrarily, the method provides flexibility to use different cover functions for different covers and increases the solution accuracy without any local mesh refinement, and the p-adaptive analysis can also be performed conveniently. The validity and efficiency of the present method are demonstrated by some numerical examples of potential problems.