A Generic Finite Element Framework on Parallel Tree-Based Adaptive Meshes
| Autor: | Alberto F. Martín, Eric Neiva, Francesc Verdugo, Santiago Badia |
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| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Work (thermodynamics) Partial differential equation Correctness Adaptive mesh refinement Applied Mathematics Parallel algorithm Numerical Analysis (math.NA) 010103 numerical & computational mathematics Data structure 01 natural sciences Finite element method Computational Mathematics FOS: Mathematics Computer Science - Mathematical Software Polygon mesh Mathematics - Numerical Analysis Engineering Geological 0101 mathematics Mathematical Software (cs.MS) Algorithm Mathematics |
| Zdroj: | Scipedia Open Access Scipedia SL SIAM Journal on Scientific Computing |
| ISSN: | 1095-7197 1064-8275 |
| Popis: | We present highly scalable parallel distributed-memory algorithms and associated data structures for a generic finite element framework that supports h-adaptivity on computational domains represented as multiple connected adaptive trees—forest-of-trees—, thus providing multi-scale resolution on problems governed by partial differential equations.The framework is grounded on a rich representation of the adaptive mesh suitable for generic finite elements that is built on top of a low-level, light-weight forest-oftrees data structure handled by a specialized, highly parallel adaptive meshing engine. Along the way, we have identified the requirements that the forest-of-trees layer must fulfill to be coupled into our framework. Essentially, it must be able to describe neighboring relationships between cells in the adapted mesh (apart from hierarchical relationships) across the lower-dimensional objects at the boundary of the cells. Atop this two-layered mesh representation, we build the rest of data structures required for the numerical integration and assembly of the discrete system of linear equations.We consider algorithms that are suitable for both subassembled and fully-assembled distributed data layouts of linear system matrices. The proposed framework has been implemented within the FEMPAR scientific software library, using p4est as a practical forest-of-octrees demonstrator. A comprehensive strong scaling study of this implementation when applied to Poisson and Maxwell problems reveals remarkable scalability up to 32.2K CPU cores and 482.2M degrees of freedom. Besides, the implementation in FEMPAR of the proposed approach is up to 2.6 and 3.4 times faster than the state-of-the-art deal.II finite element software in the h-adaptive approximation of a Poisson problem with firstand second-order Lagrangian finite elements, respectively (excluding the linear solver step from the comparison). |
| Databáze: | OpenAIRE |
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