The method of fundamental solutions(MFS)and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations.Despite many attractive features of these two ...The method of fundamental solutions(MFS)and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations.Despite many attractive features of these two methods,they also experience different aspects of difficulty.Recent advances in the selection of source location of theMFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent.In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.展开更多
基金Authors acknowledge the support of the Soft Science Project of Shanxi Province of China(Project No.2016041029-5)the National Natural Science Foundation of China(Grant No.11472184)the National Youth Science Foundation of China(Grant No.11401423).
文摘The method of fundamental solutions(MFS)and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations.Despite many attractive features of these two methods,they also experience different aspects of difficulty.Recent advances in the selection of source location of theMFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent.In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.
