88 citations · 173 across the 7 of their papers we have counts for
8 papers
High-order numerical method for solving elliptic partial differential equations on unfitted node sets
Morten E. Nielsen, Bengt Fornberg
In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-gene…
Node Subsampling for Multilevel Meshfree Elliptic PDE Solvers
Andrew P. Lawrence, Morten E. Nielsen, Bengt Fornberg
Subsampling of node sets is useful in contexts such as multilevel methods, computer graphics, and machine learning. On uniform grid-based node sets, the process of subsampling is s…
A parallel-in-time approach for wave-type PDEs
Abe C. Ellison, Bengt Fornberg
Numerical solutions to wave-type PDEs utilizing method-of-lines require the ODE solver's stability domain to include a large stretch of the imaginary axis surrounding the origin. W…
Fast variable density 3-D node generation
Kiera van der Sande, Bengt Fornberg
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…
Collective behavior of active topological solitons, knotted streamlines, and transport of cargo in liquid crystals
Hayley R. O. Sohn, Paul J. Ackerman, Timothy J. Boyle +3
Active colloids and liquid crystals are capable of locally converting the macroscopically-supplied energy into directional motion and promise a host of new applications, ranging fr…
Fast high-dimensional node generation with variable density
O. Vlasiuk, T. Michaels, N. Flyer +1
We present an algorithm for producing discrete distributions with a prescribed nearest-neighbor distance function. Our approach is a combination of quasi-Monte Carlo (Q-MC) methods…
Stable computations with flat radial basis functions using vector-valued rational approximations
Grady B. Wright, Bengt Fornberg
One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct n…
Inverting Nonlinear Dimensionality Reduction with Scale-Free Radial Basis Function Interpolation
Nathan D. Monnig, Bengt Fornberg, Francois G. Meyer
Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a sta…