Solution of the stationary 2D inverse heat conduction problem by Treffetz method

Abstract

The paper presents analysis of a solution of Laplace equation with the use of FEM harmonic basic functions. The essence of the problem is aimed at presenting an approximate solution based on possibly large finite element. Introduction of harmonic functions allows to reduce the order of numerical integration as compared to a classical Finite Element Method. Numerical calculations conform good efficiency of the use of basic harmonic functions for resolving direct and inverse problems of stationary heat conduction. Further part of the paper shows the use of basic harmonic functions for solving Poisson's equation and for drawing up a complete system of biharmonic and polyharmonic basic functions

Application of the finite element method to the determining of boiling heat transfer coefficient for minichannel flow

“…The problem thus formulated was solved by means of the Trefftz functions (T -functions) [7][8][9][10][11][12]. These functions are used to solve both direct and inverse problems.…”

“…The idea of the Trefftz method was presented in [7] and consists in representing the approximate solution to the problem as a linear combination of functions which satisfy the governing equation strictly, while the set boundary conditions are satisfied approximately. Additional information on this method can be found in [8][9][10][11][12]. Combinations of Trefftz method and FEM was showed in [13][14][15][16][17][18][19].…”

The solution of the two-dimensional inverse heat transfer problem with the use of the FEM in combination with Trefftz functions

“…The problem thus formulated is solved by means of Trefftz functions (T-functions) [2,3,4,6,14,15]. These functions are used to solve both simple and the inverse problems.…”

“…The idea of this method was presented in [14] and consists in representing the approximate solution to the problem as a linear combination of functions which satisfy the governing equation strictly and the set boundary conditions approximately. Additional information on the Trefftz method is included in [2,4,6,15].…”

Regularized collocation Trefftz method for void detection in two-dimensional steady-state heat conduction problems

“…The MFS in particular has been used extensively for the solution of inverse problems [30]. Trefftz methods have been used for the solution of inverse Cauchy linear problems [7,8,9,10,31,43,54]. In the case of inverse geometric problems the TCM has been recently used by Fan and his co-workers [3,14,15].…”