Physics

Mathematical optimization

Engineering

Mathematical analysis

Finite element method

Exponential function

Thermal conduction

Regularized meshless method

Boundary value problem

Domain decomposition methods

Solver

Applied mathematics

Mathematics

Boundary element method

Structural engineering

Discretization

Singular boundary method

Partial differential equation

Thermodynamics

Laplace transform

Computers & Mathematics with Applications

This study presents a parallel meshless solver for transient heat conduction analysis of slender functionally graded materials (FGMs) with exponential variations. In the present parallel meshless solver, a strong-form boundary collocation method, the boundary knot method (BKM), in conjunction with Laplace transform is implemented to solve the heat conduction equations of slender FGMs with exponential variations. This method is mathematically simple, easy-to-parallel, meshless, and without domain discretization. However, two ill-posed issues, the ill-conditioning dense BKM matrix and numerical inverse Laplace transform process, may lead to incorrect numerical results. Here the extended precision arithmetic (EPA) and the domain decomposition method (DDM) have been adopted to alleviate the effect of these two ill-posed issues on numerical efficiency of the present method. Then the parallel algorithm has been employed to significantly reduce the computational cost and enhance the computational capacity for the FGM structures with larger length-width ratio. To demonstrate the effectiveness of the present parallel meshless solver for transient heat conduction analysis, several benchmark examples are considered under slender FGMs with exponential variations. The present results are compared with the analytical solutions, the conventional boundary knot method and COMSOL simulation.

A boundary-type meshless solver for transient heat conduction analysis of slender functionally graded materials with exponential variations