The Meshless Analysis of Scale-Dependent Problems for Coupled Fields.

The meshless local Petrov-Galerkin (MLPG) method was developed to analyze 2D problems for flexoelectricity and higher-grade thermoelectricity. Both problems were multiphysical and scale-dependent. The size effect was considered by the strain and electric field gradients in the flexoelectricity, and higher-grade heat flux in the thermoelectricity.