Large-scale application of some modern CSM methodologies by parallel computation
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
A parallelized meshfree method with boundary enrichment for large-scale CFD
Journal of Computational Physics
Parallel Support Set Searches for Meshfree Methods
SIAM Journal on Scientific Computing
Error estimates for the finite point method
Applied Numerical Mathematics
Computational complexity and parallelization of the meshless local Petrov-Galerkin method
Computers and Structures
Parallel EFG algorithm for heat transfer problems
Advances in Engineering Software
An Introduction to Meshfree Methods and Their Programming
An Introduction to Meshfree Methods and Their Programming
Parallel meshfree computation for parabolic equations on graphics hardware
International Journal of Computer Mathematics - APPLICATIONS OF COMPUTATIONAL MATHEMATICS IN SCIENCE AND ENGINEERING
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This study solves the numerical problems associated with the element-free Galerkin method (EFGM) to perform analyses efficiently in shared-memory computers. The truncation error is generally large for the moving least-squares approximation, and this can be overcome by using orthogonal basis functions, 16-byte floats, or the local origin. Then, the analysis accuracy is similar to that obtained with the reproducing kernel particle approximation. Determining the index array of the global stiffness matrix requires a large amount of computer memory. We thus propose a scheme to overcome this problem using slightly more computer time but much less computer memory. A binary search is also proposed to find the support domain nodes for Gaussian points, and this method is much more efficient than the linear search one. A Fortran module is developed to establish parallel solutions in the EFGM, and the programmer does not need to handle the global stiffness directly.