Scaled Boundary Finite Element Method for Two-Dimensional Linear Multi-Field Media

Abstract

This paper presents an efficient and accurate numerical technique, based on a scaled boundary finite element method (SBFEM) that is capable of solving two-dimensional, second-order, linear, multi-field boundary value problems. Basic governing equations are established in a general, unified context allowing the treatment of various classes of linear problems such as steady-state heat conduction problems, steady-state flow in porous media, linear elasticity, linear piezoelectricity, and linear piezomagnetic and piezoelectromagnetic problems. A scaled boundary finite element approximation is also formulated within a general framework integrating the influence of the distributed body source, general boundary conditions, contributions of the general side-face data, and the flexibility of scaled boundary approximations. Standard procedures for numerical integration, search of eigenvalues and eigenvectors, determination of particular solutions, and solving a system of linear algebraic equations are adopted. After fully tested with available benchmark solutions, the proposed SBFEM is applied to solve various classes of linear problems under different scenarios to demonstrate its vast capability, computational efficiency and robustness.