Solving Heat Conduction Problems by the Direct Meshless Local Petrov-Galerkin (DMLPG) method
For researchers in computational mechanics, this is an incremental improvement over MLPG that addresses the computational cost of numerical integration.
The paper applies the Direct Meshless Local Petrov-Galerkin (DMLPG) method to transient heat conduction problems, achieving cheaper numerical integration by avoiding MLS shape functions, thus reducing computational costs compared to traditional MLPG and FEM.
As an improvement of the Meshless Local Petrov-Galerkin (MLPG), the Direct Meshless Local Petrov-Galerkin (DMLPG) method is applied here to the numerical solution of transient heat conduction problem. The new technique is based on direct recoveries of test functionals (local weak forms) from values at nodes without any detour via classical moving least squares (MLS) shape functions. This leads to an absolutely cheaper scheme where the numerical integrations will be done over low-degree polynomials rather than complicated MLS shape functions. This eliminates the main disadvantage of MLS based methods in comparison with finite element methods (FEM), namely the costs of numerical integration.