Balancing Domain Decomposition by Constraints Algorithms for Curl-Conforming Spaces of Arbitrary Order
We construct Balancing Domain Decomposition by Constraints methods for the linear systems arising from arbitrary order, finite element discretizations of the H(curl) model problem in three-dimensions. Numerical results confirm that the proposed algorithm is quasi-optimal in the coarse-to-fine mesh ratio, and poly-logarithmic in the polynomial order of the curl-conforming discretization space. Additional numerical experiments, including higher-order geometries, upscaled finite elements, and adaptive coarse spaces, prove the robustness of our algorithm. A scalable three-level extension is presented, and it is validated with large scale experiments using up to 16,384 subdomains and almost a billion of degrees of freedom.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (LLNL) under Contract DE-AC52-07NA27344 and was supported by the U.S. DOE ASCR program. The research was performed during a visit of the first author to the LLNL, Center for Applied Scientific Computing. The authors are grateful to Umberto Villa for fruitful discussions. For computer time, this research used also the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.
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