One of the advantages of the element⁃free Galerkin method(EFGM)is that the shape function can be customized.Variation form of the general acoustic problem is modified by introducing Dirichlet boundary conditions with ...One of the advantages of the element⁃free Galerkin method(EFGM)is that the shape function can be customized.Variation form of the general acoustic problem is modified by introducing Dirichlet boundary conditions with Lagrange multipliers in the paper.Corresponding to the variation formulation based on EFGM,the discrete equations are obtained.By taking the phase of the wave into account to build the mesh less basis,more exact solution of the acoustic problem is obtained than the traditional EFGM through multiple iterative.The feasibility and validity of this method are validated through a practical instance via self⁃compiling MATLAB program.展开更多
The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method （EFGM） for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables...The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method （EFGM） for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm.展开更多
文摘One of the advantages of the element⁃free Galerkin method(EFGM)is that the shape function can be customized.Variation form of the general acoustic problem is modified by introducing Dirichlet boundary conditions with Lagrange multipliers in the paper.Corresponding to the variation formulation based on EFGM,the discrete equations are obtained.By taking the phase of the wave into account to build the mesh less basis,more exact solution of the acoustic problem is obtained than the traditional EFGM through multiple iterative.The feasibility and validity of this method are validated through a practical instance via self⁃compiling MATLAB program.
基金The project supported by the National Natural Science Foundation of China （10421002. 10472019 and 10172024） NKBRSF （2005CB321704） and the Fund of Disciplines Leaders of Young and Middle Age Faculty in Colleges of Liaoning Province. The English text was polished by Yunming Chen.
文摘The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method （EFGM） for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm.
