Tensor-product vertex patch smoothers for biharmonic problems
We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we discuss low rank tensor approximations for their efficient implem...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2025-07-01
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| In: |
Computational methods in applied mathematics
Year: 2025, Volume: 25, Issue: 3, Pages: 695-708 |
| ISSN: | 1609-9389 |
| DOI: | 10.1515/cmam-2024-0192 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1515/cmam-2024-0192 Verlag, lizenzpflichtig, Volltext: https://www.degruyterbrill.com/document/doi/10.1515/cmam-2024-0192/html 
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| Author Notes: | Julius Witte, Cu Cui, Francesca Bonizzoni, Guido Kanschat |
| Summary: | We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we discuss low rank tensor approximations for their efficient implementation. Our experiments demonstrate that the inexact local solver yields a method which converges fast and uniformly with respect to mesh refinement and polynomial degree. The multiplicative smoother shows superior performance in terms of solution efficiency, requiring fewer iterations in both two- and three-dimensional cases. Additionally, the solver infrastructure supports a mixed-precision approach, executing the multigrid preconditioner in single precision while performing the outer iteration in double precision, thereby increasing throughput by up to 70 %. |
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| Item Description: | Online veröffentlicht: 29. Mai 2025 Gesehen am 12.09.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1609-9389 |
| DOI: | 10.1515/cmam-2024-0192 |