Optimally refined isogeometric analysis

Abstract

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 $C^0$-continuity hyperplanes that act as separators during LU factorization \cite{rIGA1}. 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.