Combination Approach of Domain-Type and Boundary-Type Meshless Methods for Solving Hybrid Boundary-Value Problem of Homogeneous and Inhomogeneous Elliptic PDEs

The combination approach of the domain-type and boundary-type meshless methods has been applied to the hybrid boundary-value problem composed of the homogeneous and the inhomogeneous elliptic partial differential equations (PDEs). In addition, the performance of the proposed method has been investigated numerically. The results of computations show that the convergent rate is almost the same value regardless of the wave number. Moreover, the accuracy of the proposed method is degraded with an increase in the value of the wave number. Furthermore, the numerical solution of the proposed method has been obtained by using the GMRES method without the restart coefficient. Therefore, it is found that the proposed method can be used as one of the tools for solving the hybrid boundary-value problem composed of the homogeneous and the inhomogeneous elliptic PDEs.