Coupling of the mesh-free finite cloud method with the boundary element method: a collocation approach

Abstract

Meshless and mesh-based methods are among the tools frequently applied in the numerical treatment of partial differential equations (PDEs). This paper presents a coupling of the meshless finite cloud method (FCM) and the standard (mesh-based) boundary element method (BEM), which is motivated by the complementary properties of both methods. While the BEM is appropriate for solving linear PDEs with constant coefficients in bounded or unbounded domains, the FCM is appropriate for either homogeneous, inhomogeneous or even nonlinear problems in bounded domains. Both techniques (FCM and BEM) use a collocation procedure in the numerical approximation. No mesh is required in the FCM subdomain and its nodal point distribution is completely independent of the BEM subdomain. The coupling approach is demonstrated for linear elasticity problems. Because both FCM and BEM employ traction–displacement relations, no transformations between forces and tractions (typical of BEM and finite element coupling) are needed. Several numerical examples are given to demonstrate the proposed approach.