Introduction to Fundamental Solution Based Finite Element Methods

Abstract

Further to the discussion of hybrid Trefftz FEM in Chapter 1, this chapter presents an overview of applications of the fundamental solution based FEM for heat conduction and seepage problems. The fundamental solution based FEM discussed here is significantly different from the previous three FEM types mentioned in Chapter 1. In this method, a linear combination of the fundamental solution at different points approximates the field variable within the element. The independent frame field defined along the element boundary and the modified variational functional are employed to guarantee inter-element continuity, generate the final stiffness equation and establish linkage between the boundary frame field and the internal field in the element.

Keywords: Finite element method, Functionally graded material, Fundamental solution, Heat conduction, Seepage.

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