期刊
ACTA MECHANICA SINICA
卷 28, 期 3, 页码 808-818出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10409-012-0083-x
关键词
Weighted orthogonal function; Improved moving least squares (IMLS) approximation; Improved element-free Galerkin (IEFG) method; Penalty method; Temporal discretization; Wave equation
资金
- National Natural Science Foundation of China [11171208]
- Shanghai Leading Academic Discipline Project [S30106]
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 is selected 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.
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