Session I.1 - Multiresolution and Adaptivity in Numerical PDEs
Poster
Node Subsampling for \\Multilevel Meshfree Elliptic PDE Solvers
Andrew Lawrence
University of Colorado - Boulder, United States - This email address is being protected from spambots. You need JavaScript enabled to view it.
Subsampling of node sets is useful in contexts such as multilevel methods, polynomial approximation, and numerical integration. On uniform grid-based node sets, the process of subsampling is simple. However, on non-uniform node sets, the process of coarsening a node set through node elimination is nontrivial. A novel method for such subsampling is presented here. Additionally, boundary preservation techniques and two novel node set quality measures are presented. The new subsampling method is demonstrated on the test problems of solving the Poisson and Laplace equations by multilevel radial basis function-generated finite differences (RBF-FD) iterations.
Joint work with Morten E. Nielsen and Bengt Fornberg.