A boundary knot method for 3D time harmonic elastic wave problems

Abstract This paper makes the first attempt to apply the boundary knot method (BKM) to 3D time harmonic elastic wave problems. Unlike the famous method of fundamental solutions (MFS), the BKM employs non-singular general solutions as the basis functions to approximate the solutions. Therefore, the BKM overcomes the auxiliary boundary issue of the MFS, and inherits the advantages of the MFS, i.e., mathematically simple, easy-to-program, meshless, integration-free and accurate. Particularly, the non-singular general solutions of 3D time harmonic elastic wave problems for the BKM are firstly derived in this study. Two examples are carried out to verify the accuracy and convergence of the BKM.