The improved element-free Galerkin method for three-dimensional wave equation. (English) Zbl 1345.65059
Summary: The paper presents the improved element-free Galerkin (IEFG) method for three-dimensional wave propagation. The improved moving least-squares (IMLS) approximation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares (MLS) approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a discretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems isselected for the time
discretization. As the wave equations and the boundary-initial conditions depend on time, the scaling parameter, number of nodes and the time step length are considered for the convergence study.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
weighted orthogonal function; improved moving least squares (IMLS) approximation; improved element-free Galerkin (IEFG) method; penalty method; temporal discretization; wave equationSoftware:
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