A local weighted meshless method based on compactly supported radial basis functions and its application in ocean engineering

Meshless methods with compactly supported radial basis function (CSRBF) are attractive, because implementation of computer code, computation cost, and computer resource can be largely reduced for multi-dimensional problems. The applications of CSRBFs to PDE numerical solutions have made great progress such as in collocation method, Galerkin form and Petrov-Galerkin form. The Petrov-Galerkin weak form can be expressed in a local domain, thus being promising. So far, this local-domain weak form has not been applied to Biot's consolidation theory. This paper proposes a local weighted meshless method based on CSRBF and applies it to the wave-induced seabed response analysis.