A preconditioning strategy for linear systems arising from nonsymmetric schemes in isogeometric analysis

In the context of isogeometric analysis, we consider two discretization approaches that make the resulting stiffness matrix nonsymmetric even if the differential operator is self-adjoint. These are the collocation method and the recently-developed weighted quadrature for the Galerkin discretization....

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2017-10, Vol.74 (7), p.1690-1702
Main Author: Tani, Mattia
Format: Article
Language:English
Subjects:
Analysis
Applied mathematics
Collocation
Collocation methods
Differential equations
Discretization
Galerkin method
Isogeometric analysis
Linear equations
Linear systems
Preconditioning
Robustness (mathematics)
Stiffness matrix
Weighted quadrature
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Summary:In the context of isogeometric analysis, we consider two discretization approaches that make the resulting stiffness matrix nonsymmetric even if the differential operator is self-adjoint. These are the collocation method and the recently-developed weighted quadrature for the Galerkin discretization. In this paper, we are interested in the solution of the linear systems arising from the discretization of the Poisson problem using one of these approaches. In Sangalli and Tani (2016), a well-established direct solver for linear systems with tensor structure was used as a preconditioner in the context of Galerkin isogeometric analysis, yielding promising results. In particular, this preconditioner is robust with respect to the mesh size h and the spline degree p. In the present work, we discuss how a similar approach can be applied to the considered nonsymmetric linear systems. The efficiency of the proposed preconditioning strategy is assessed with numerical experiments on two-dimensional and three-dimensional problems.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.06.013