Node Placement Method by Bubble Simulation and Its Application
Y Liu and YF Nie and WW Zhang and L Wang, CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 55, 89-109 (2010).
In the light of the ideas and treatment technologies about molecular dynamics simulation and bubble meshing, a new approach of node placement for the meshless method called node placement method by bubble simulation (NPBS method), is proposed. Nodes are seen as the centers of the bubbles which can be moved by their interacting forces. Through dynamic simulation, bubbles are placed into a near-optimal configuration, and the centers of bubbles will form a good-quality node distribution in the domain. This process doesn't need updating the mesh connection constantly, i.e., is totally meshfree. Some example results show that the uniform point sets and non-uniform point sets generated by NPBS method have good construction, and the non-uniform point sets have also good gradualness which is prefer to have for numerical solution methods of partial differential equations in some case. In addition, NPBS method has good adaptability to complex regions. Since the defined interbubble force is short-range, this method has inherent parallelism. Two simple parallel example results show that the parallel generated node sets are also good-quality. Furthermore, the node sets optimized by bubble simulation are used in the meshless method, and by comparison, the advantage with the less computational error is shown. And it is easy to make use of the information of neighbor bubbles generated by NPBS method for finding the nodes on the influence domain in meshless analysis. Finally, the node sets generated by NPBS method are also used for triangular mesh generation and refinement in finite element method. The results show that the mesh has excellent quality.
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