Abstract
Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gained much attention since then. If large spline degrees are considered, one obtains the approximation power of a high-order method , but the number of degrees of freedom behaves like for a low-order method. One important ingredient to use a discretization with large spline degree, is a robust and preferably parallelizable solver. While numerical evidence shows that multigrid solvers with standard smoothers (like Gauss Seidel) does not perform well if the spline degree is increased, the multigrid solvers proposed by the authors and their co-workers proved to behave optimal both in the grid size and the spline degree. In the present paper, the authors want to show that those solvers are parallelizable and that they scale well in a parallel environment.
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Notes
- 1.
Message Passing Interface, see http://mpi-forum.org/.
- 2.
We use up to 32 out of 68 available nodes, each equipped with 2x Xeon E5-2630v3 “Haswell” CPU (8 cores, 2.4 GHz, 20 MB cache) and 128 GB RAM. More information is available at https://www.ricam.oeaw.ac.at/hpc/.
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Acknowledgements
The first author would like to thank the Austrian Science Fund (FWF) for the financial support through the DK W1214-04, while the second author was supported by the FWF grant NFN S117-03.
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Hofer, C., Takacs, S. (2019). A Parallel Multigrid Solver for Multi-Patch Isogeometric Analysis. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-030-14244-5_11
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