# Approximated Fundamental Solutions Based on Levi Functions

## Keywords:

Fundamental Solution, Levi Function, Functionally Graded Materials.## Abstract

Fundamental Solutions (FS) are useful for numerical methods, specifically in applications such as the Boundary Element Method (BEM) or the Method of Fundamental Solutions (MFS). Obtaining analytically the FS for a given problem is frequently unfeasible since it entails the solution of a complex system of differential equations. In this paper, a novel method for the computation of approximate FS based in enhanced Levi Function is presented. The first terms of the enhanced Levi Function are computed analytically by an iterative procedure until the residual is regular at the collocation point. The last step in the computation of the FS is completed approximating the residual by Modified Radial Base Functions that are particular solutions of the problem equations.

The method is applied to potential problems with variable coefficients, and validated comparing to available analytically computed Fundamental Solutions.

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## Published

## How to Cite

*European Journal of Computational Mechanics*,

*28*(1-2), 31–50. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/927