A p-multigrid method enhanced with an ILUT smoother and its comparison to h-multigrid methods within Isogeometric Analysis

Abstract

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which coarsening is applied in the approximation order p instead of the mesh width h. Since the use of classical smoothers (e.g. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated. Numerical results and a spectral analysis indicate that the resulting p-multigrid method exhibits convergence rates independent of h and p. In particular, we compare both coarsening strategies (e.g. coarsening in h or p) adopting both smoothers for a variety of two and threedimensional benchmarks.

References in corpus (4)

• Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells
• Robust multigrid solvers for the biharmonic problem in isogeometric analysis
• Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations
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Cited by in corpus (6)

• Hierarchical multigrid approaches for the finite cell method on uniform and multi-level hp-refined grids
• Towards Accuracy and Scalability: Combining Isogeometric Analysis with Deflation to Obtain Scalable Convergence for the Helmholtz Equation
• Multigrid solvers for multipoint flux approximations of the Darcy problem on rough quadrilateral grids
• A two level method for isogeometric discretizations
• Combining p-multigrid and multigrid reduced in time methods to obtain a scalable solver for Isogeometric Analysis
• Compressive Isogeometric Analysis