FAST VARIABLE DENSITY 3-D NODE GENERATION

Mesh-free solvers for partial differential equations perform best on scattered quasi-uniform nodes. Computational efficiency can be improved by using nodes with greater spacing in regions of less activity. However, there is no ideal way to generate nodes for these solvers. We present an advancing front type method to generate variable density nodes in two dimensions (2-D) and three dimensions (3-D) with clear generalization to higher dimensions. The exhibited cost of generating a node set of size N in 2-D and 3-D with the present method is O(N).

Automated summary

Research shows that mesh-free solvers perform best on scattered quasi-uniform nodes, and computational efficiency can be improved by using nodes with greater spacing in regions of less activity. The advancing front method presented in the study generates variable density nodes in 2-D and 3-D with the ability to be generalized to higher dimensions, with a time complexity of O(N) for generating a node set of size N in 2-D and 3-D.