MGM: A MESHFREE GEOMETRIC MULTILEVEL METHOD FOR SYSTEMS ARISING FROM ELLIPTIC EQUATIONS ON POINT CLOUD SURFACES.
In: SIAM Journal on Scientific Computing, Jg. 45 (2023-03-01), Heft 2, S. A312- (26S.)
academicJournal
Zugriff:
We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening the point clouds and new meshfree restriction/interpolation operators based on polyharmonic splines for transferring information between the coarsened point clouds. These are then combined with standard smoothing and operator coarsening methods in a V-cycle iteration. MGM is applicable to discretizations of elliptic PDEs based on various localized meshfree methods, including RBF finite differences (RBF-FD) and generalized finite differences (GFD). We test MGM both as a standalone solver and preconditioner for Krylov subspace methods on several test problems using RBF-FD and GFD and numerically analyze convergence rates, efficiency, and scaling with increasing point cloud sizes. We also perform a side-by-side comparison to algebraic multigrid methods for solving the same systems. Finally, we further demonstrate the effectiveness of MGM by applying it to three challenging applications on complicated surfaces: pattern formation, surface harmonics, and geodesic distance. [ABSTRACT FROM AUTHOR]
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Titel: |
MGM: A MESHFREE GEOMETRIC MULTILEVEL METHOD FOR SYSTEMS ARISING FROM ELLIPTIC EQUATIONS ON POINT CLOUD SURFACES.
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Autor/in / Beteiligte Person: | WRIGHT, GRADY B. ; JONES, ANDREW ; SHANKAR, VARUN |
Zeitschrift: | SIAM Journal on Scientific Computing, Jg. 45 (2023-03-01), Heft 2, S. A312- (26S.) |
Veröffentlichung: | 2023 |
Medientyp: | academicJournal |
ISSN: | 1064-8275 (print) |
DOI: | 10.1137/22M1490338 |
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