تقرير
Monolithic Multigrid Preconditioners for High-Order Discretizations of Stokes Equations
| العنوان: | Monolithic Multigrid Preconditioners for High-Order Discretizations of Stokes Equations |
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| المؤلفون: | Voronin, Alexey, Harper, Graham, MacLachlan, Scott, Olson, Luke N., Tuminaro, Raymond S. |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | This work introduces and assesses the efficiency of a monolithic $ph$MG multigrid framework designed for high-order discretizations of stationary Stokes systems using Taylor-Hood and Scott-Vogelius elements. The proposed approach integrates coarsening in both approximation order ($p$) and mesh resolution ($h$), to address the computational and memory efficiency challenges that are often encountered in conventional high-order numerical simulations. Our numerical results reveal that $ph$MG offers significant improvements over traditional spatial-coarsening-only multigrid ($h$MG) techniques for problems discretized with Taylor-Hood elements across a variety of problem sizes and discretization orders. In particular, the $ph$MG method exhibits superior performance in reducing setup and solve times, particularly when dealing with higher discretization orders and unstructured problem domains. For Scott-Vogelius discretizations, while monolithic $ph$MG delivers low iteration counts and competitive solve phase timings, it exhibits a discernibly slower setup phase when compared to a multilevel (non-monolithic) full-block-factorization (FBF) preconditioner where $ph$MG is employed only for the velocity unknowns. This is primarily due to the setup costs of the larger mixed-field relaxation patches with monolithic $ph$MG versus the patch setup costs with a single unknown type for FBF. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.07253 |
| رقم الأكسشن: | edsarx.2407.07253 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |