2018/02/26 by Christoph Hofer, Ulrich Langer, Hofer, Christoph +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1802.09277
openalex publication_date 2018/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We propose and investigate new robust preconditioners for space-time Isogeometric Analysis of parabolic evolution problems. These preconditioners are based on a time parallel multigrid method. We consider a decomposition of the space-time cylinder into time-slabs which are coupled via a discontinuous Galerkin technique. The time-slabs provide the structure for the time-parallel multigrid solver. The most important part of the multigrid method is the smoother. We utilize the special structure of the involved operator to decouple its application into several spatial problems by means of generalized eigenvalue or Schur decompositions. Some of these problems have a symmetric saddle point structure, for which we present robust preconditions. Finally, we present numerical experiments confirming the robustness of our space-time IgA solver.