A high-resolution scalable meshless method for coupled steady poroelastic analysis, based on collocation with radial basis functions

Abstract

This work describes the application of a novel meshless numerical technique, based on local collocation with radial basis functions (RBFs), to the solution of steady poroelastic problems. Its formulation allows scalability to large problem sizes, in contrast to traditional full-domain RBF collocation methods which are restricted to small datasets due to issues with numerical conditioning and computational cost. The proposed method is validated using a benchmark linear elasticity numerical example and a coupled steady poroelastic deformation problem, for which analytical solutions are known. Highly accurate solutions are obtained in each case, and convergence rates in excess of sixth-order are observed.