BEM performance with the addition of polynomials solving stationary thermal problems with functional gradation

Abstract

This work presents the formulation and numerical results of the Dual Reciprocity Boundary Element Method (DRBEM), adapted to include the procedure known as the addition of polynomial functions. This technique is used to improve the interpolation scheme’s accuracy using radial basis functions. This idea works quite effectively in simple interpolation procedures, especially when the field profile to be approximated has similarities with added polynomials. Although applied as a supplementary resource in some works, the efficiency and restrictions of the procedure were not discussed in detail as necessary. In this article, the addition of functions is applied to solve non-homogeneous stationary heat transfer problems. The main objective is to analyze its capability, especially in reducing the demand for internal interpolation points. The three simulations show that although introducing polynomials can improve the results, other characteristics are mandatory for achieving suitable accuracy. Three examples of numerical simulation are solved and show that its effectivity is relative, mainly limited by the type of application.

Keywords:

• Boundary element method
• non-homogeneous problems
• dual reciprocity
• radial basis functions
• polynomial functions

Disclosure statement

No potential conflict of interest was reported by the authors.