Modified method of fundamental solutions for steady state heat conduction equation in anisotropic medium

Abstract

This study aims to extend, the recently developed, heat polynomial based modified method of fundamental (MFS) solutions to a steady state anisotropic problem. We successfully extend the method to two-dimensional space and test its performance with the help of numerical experiments. Two examples are tested on both convex and nonconvex domains and the results obtained are analyzed. Overcoming the problem of fictitious boundary in standard MFS, modified method in combination with regularization helps us establish that the scheme is accurate, computationally efficient and stable for approximating the solution to this inverse problem, for both exact and noisy data.

Keywords:

• Fundamental solution
• heat polynomial
• anisotropic medium
• steady state equation
• regularization