A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. (English) Zbl 0932.76067

Atluri, S. N.; Zhu, T.

Comput. Mech. 22, No. 2, 117-127 (1998).

A local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy. The essential boundary conditions in the present formulation are imposed by a penalty method. The present method does not need a “finite element mesh”, either for purposes of interpolation of the solution variables, or for the integration of the “energy”. All integrals can be easily evaluated over regularly shaped domains (in general, spheres in three-dimensional problems) and their boundaries. No post-smoothing technique is required for computing the derivatives of the unknown variable, since the original solution, using the moving least squares approximation, is already smooth enough. Several numerical examples illustrate the method.

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76B10	Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
74S30	Other numerical methods in solid mechanics (MSC2010)

Keywords:

patch test; Laplace equation; two-dimensional potential flow problem; local symmetric weak form; moving least squares approximation; potential problems; penalty method