Fast Variable Density 3-D Node Generation
Kiera van der Sande, Bengt Fornberg
Abstract
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 $O(N)$.
Topics & Concepts
MathematicsNode (physics)GeneralizationVariable (mathematics)Set (abstract data type)Partial differential equationIdeal (ethics)Applied mathematicsAlgorithmMathematical optimizationDifferential equationTopology (electrical circuits)Type (biology)Representation (politics)Differential (mechanical device)MinificationMathematical analysisComputational complexity theoryLevel set (data structures)Advanced Physical and Chemical Molecular InteractionsQuantum Computing Algorithms and ArchitectureMachine Learning in Materials Science