An efficient analysis of steady-state heat conduction involving curved line/surface heat sources in two/three-dimensional isotropic media

Abstract

In this paper, a new formulation based on the method of fundamental solutions for two/three-dimensional steady-state heat conduction problems involving internal curved line/surface heat sources is presented. Arbitrary shapes and non-uniform intensities of the curved heat sources can be modeled by an assemblage of several parts with quadratic variations. The presented mesh-free modeling does not require any internal points as in domain methods. Four numerical examples are studied to verify the validity and efficiency of the proposed method. Our analyses have shown that the presented mesh-free formulation is very efficient in comparison with conventional boundary or domain solution techniques.

Comparison of the Boundary Element Method and the Method of Fundamental Solutions for Analysis of Potential and Elasticity Problems in Convex and Concave Domains

“…Karageorghis and Fairweather [14] employed the MFS for axisymmetric potential problems for the first time. Later, it was successfully applied to a variety of potential and elastic problems, see for example Fam and Rashed [15], Young et al [16], Marin et al [17], Karageorghis et al [18], Fan and Li [19], Mohammadi et al [20]. Suitable arrangement of source points and collocation points in the MFS has been always disputable and under discussion among the researchers.…”

The Method of Fundamental Solutions for Two-Dimensional Elastostatic Problems with Stress Concentration and Highly Anisotropic Materials

“…The weak-form meshfree methods need suitable techniques for the computation of domain integrals [10][11][12]; however, the MFS is a strong-form and truly meshfree method without any need for evaluating any domain or boundary integral. These features make the MFS suitable for problems with moving/unknown boundary [13][14][15], for problems with concentrated loads [16][17][18], and moving load problems [19]. The boundary element method (BEM) is also a boundary-type method, which is based on the fundamental solutions of the problem, as in the MFS, and results in accurate solutions.…”