Performance of direct solvers strongly depends upon the employed discretization method. In particular, it is possible to improve the performance of solving Isogeometric Analysis (IGA) discretizations by introducing multiple C-continuity hyperplanes that act as separators during LU factorization [8]. In here, we further explore this venue by introducing separators of arbitrary continuity. Moreover, we develop an efficient method to obtain optimal discretizations in the sense that they minimize the time employed by the direct solver of linear equations. The search space consists of all possible discretizations obtained by enriching a given IGA mesh. Thus, the best approximation error is always reduced with respect to its IGA counterpart, while the solution time is decreased by up to a factor of 60.

David Pardo has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 644602, the Projects of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU), and MTM2016-81697-ERC, the BCAM "Severo Ochoa" accreditation of excellence SEV-2013-0323, and the Basque Government through the BERC 2014-2017 program, and the Consolidated Research Group Grant IT649-13 on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI).