Solving Heat Conduction Problems by the Direct Meshless Local Petrov-Galerkin (DMLPG) method

摘要

As an improvement of the Meshless Local Petrov-Galerkin (MLPG), the DirectMeshless Local Petrov-Galerkin (DMLPG) method is applied here to the numericalsolution of transient heat conduction problem. The new technique is based ondirect recoveries of test functionals (local weak forms) from values at nodeswithout any detour via classical moving least squares (MLS) shape functions.This leads to an absolutely cheaper scheme where the numerical integrationswill be done over low-degree polynomials rather than complicated MLS shapefunctions. This eliminates the main disadvantage of MLS based methods incomparison with finite element methods (FEM), namely the costs of numericalintegration.