Multigrid Reduced in Time for Isogeometric Analysis

Abstract

[EN] Isogeometric Analysis (IgA) can be seen as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. Combined with a time integration scheme within the method of lines, IgA has become a viable alternative to FEM for time-dependent problems. However, as processors’ clock speeds are no longer increasing but the number of cores are going up, traditional (i.e., sequential) time integration schemes become more and more the bottleneck within these large-scale computations. The Multigrid Reduced in Time (MGRIT) method is a parallel-in-time integration method that enables exploitation of parallelism not only in space but also in the temporal direction. In this paper, we apply MGRIT to discretizations arising from IgA for the first time in the literature. In particular, we investigate the (parallel) performance of MGRIT in this context for a variety of geometries, MGRIT hierarchies and time integration schemes. Numerical results show that the MGRIT method converges independent of the mesh width, spline degree of the B-spline basis functions and time step size ∆t and is highly parallelizable when applied in the context of IgA.