Fast Variable Density 3-D Node Generation
Published in SIAM J. Sci. Comput., 2021
Recommended citation: van der Sande, K. and Fornberg, B. (2021). “Fast Variable Density 3-D Node Generation).” SIAM J. Sci Comput.. 43(1). https://arxiv.org/pdf/1906.00636.pdf
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 2-D and 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)
Recommended citation: van der Sande, K. and Fornberg, B. (2021). “Fast Variable Density 3-D Node Generation).” SIAM J. Sci Comput.. 43(1).