Mesh Regularization in Bank-Holst Parallel hp-Adaptive Meshing
نویسندگان
چکیده
In this work, we study mesh regularization in Bank-Holst parallel adaptive paradigm when adaptive enrichment in both h (geometry) and p (degree) is used. The paradigm was first introduced by Bank and Holst in [2, 3, 1] and later extended to hp-adaptivity in [5]. In detail, the paradigm can be summarized in the following steps. Step 1 Load Balancing: The problem is solved on a coarse mesh, and available a posteriori error estimates are used to partition the mesh into subregions. The partition is such that each subregion has approximately the same error although subregions may vary considerably in terms of number of elements, number of degrees of freedom, and polynomial degree. Step 2 Adaptive Meshing: Each processor is provided with complete data for the coarse problem and instructed to sequentially solve the entire problem, with the stipulation that its adaptive enrichment (in h or p) should be limited largely to its own subregion. The target number of degrees of freedom for each processor is the same. Step 3 Mesh Regularization: The local mesh on each processor is regularized such that the mesh for the global problem described in Step 4 is conforming in both h and p. Step 4 Global Solve: The final global problem consists of the union of the refined partitions provided by each processor. A final solution is computed using domain decomposition. This paradigm is attractive as it requires low communication and allows existing sequential adaptive finite element codes to run in parallel environment without
منابع مشابه
UN CO RR EC TE D PR O O F 1 Mesh Regularization in Bank - Holst Parallel 2 hp - Adaptive Meshing 3 Randolph
متن کامل
A Comparison of Additive Schwarz Preconditioners for Parallel Adaptive Finite Elements
The Bank-Holst parallel adaptive meshing paradigm [2, 3, 1] is utilised to solve (1) in a combination of domain decomposition and adaptivity. It can be summarised as follows: Step I Mesh Partition: Starting with a coarse mesh TH , the domain is partitioned into non-overlapping subdomains: Ω = ∪pi=1Ωi. Step II Adaptive Meshing: Each processor i is provided with TH and instructed to sequentially ...
متن کاملSome Variants of the Bank-Holst Parallel Adaptive Meshing Paradigm
The Bank-Holst adaptive meshing paradigm is an efficient approach for parallel adaptive meshing of elliptic partial differential equations. It is designed to keep communication costs low and to take advantage of existing sequential adaptive software. While in principle the procedure could be used in any parallel environment, it was mainly conceived for use on small Beowulf clusters with a relat...
متن کاملA Domain Decomposition for a Parallel Adaptive Meshing Algorithm
We describe a domain decomposition algorithm for use in the parallel adaptive meshing paradigm of Bank and Holst. Our algorithm has low communication , makes extensive use of existing sequential solvers, and exploits in several important ways data generated as part of the adaptive meshing paradigm. Numerical examples illustrate the effectiveness of the procedure. In [4, 5], we introduced a gene...
متن کاملA Domain Decomposition Solver for a Parallel Adaptive Meshing Paradigm
We describe a domain decomposition (DD) algorithm for use in the parallel adaptive meshing paradigm of Bank and Holst [3, 4]. Our algorithm has low communication, makes extensive use of existing sequential solvers, and exploits in several important ways data generated as part of the adaptive meshing paradigm. Numerical examples illustrate the effectiveness of the procedure.
متن کامل