Title: Robust and optimal multi-iterative techniques for IgA Galerkin linear systems
Authors: Donatelli, Marco
Garoni, Carlo
Manni, Carla
Serra-Capizzano, Stefano
Speleers, Hendrik # ×
Issue Date: 2015
Publisher: North-Holland Pub. Co.
Series Title: Computer Methods in Applied Mechanics and Engineering vol:284 pages:230-264
Abstract: We consider fast solvers for large linear systems arising from the Galerkin approximation based on B-splines of classical d-dimensional elliptic problems, d>=1, in the context of isogeometric analysis. Our ultimate goal is to design iterative algorithms with the following two properties. First, their computational cost is optimal, that is linear with respect to the number of degrees of freedom, i.e. the resulting matrix size. Second, they are totally robust, i.e., their convergence speed is substantially independent of all the relevant parameters: in our case, these are the matrix size (related to the fineness parameter), the spline degree (associated to the approximation order), and the dimensionality d of the problem. We review several methods like PCG, multigrid, multi-iterative algorithms, and we show how their numerical behavior (in terms of convergence speed) can be understood through the notion of spectral distribution, i.e. through a compact symbol which describes the global eigenvalue behavior of the considered stiffness matrices. As a final step, we show how we can design an optimal and totally robust multi-iterative method, by taking into account the analytic features of the symbol. A wide variety of numerical experiments, few open problems and perspectives are presented and critically discussed.
ISSN: 0045-7825
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

Files in This Item:
File Description Status SizeFormat
published.pdfpublished manuscript Published 412KbAdobe PDFView/Open Request a copy

These files are only available to some KU Leuven Association staff members


All items in Lirias are protected by copyright, with all rights reserved.

© Web of science