Imposing boundary conditions in the meshless local Petrov-Galerkin method

A particular meshless method, named meshless local Petrov-Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computational cost, the RBFp imposes in a direct manner the essential boundary conditions. Thus, dividing the domain into different regions a hybrid method has been developed. Results show that it leads to a good trade-off between computational time and precision.