Multigrid methods for isogeometric discretization
نویسندگان
چکیده
منابع مشابه
Spectral Analysis of Geometric Multigrid Methods for Isogeometric Analysis
We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. We observe that the performance of standard V-cycle iteration is highly dependent on the spatial dimension as well as the spline degree of the discretization space. Conjugate gradient iteration preconditioned with one V-c...
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We consider the stiffness matrices coming from the Galerkin B-spline isogeometric analysis approximation of classical elliptic problems. By exploiting specific spectral properties compactly described by a symbol, we design efficient multigrid methods for the fast solution of the related linear systems. We prove the optimality of the two-grid methods (in the sense that their convergence rate is ...
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We investigate geometric multigrid methods for solving the large, sparse linear systems which arise in isogeometric discretizations of elliptic partial differential equations. In particular, we study a smoother which incorporates the inverse of the mass matrix as an iteration matrix, and which we call mass-Richardson smoother. We perform a rigorous analysis in a model setting and perform some n...
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The fast solution of linear systems arising from an isogeometric discretization of a partial differential equation is of great importance for the practical use of Isogeometric Analysis. For classical finite element discretizations, multigrid methods are well known to be fast solvers showing optimal convergence behavior. However, if a geometric multigrid solver is naively applied to a linear sys...
متن کاملTitle: Multigrid Methods Multigrid Methods Synonyms
Multigrid (MG) methods are used to approximate solutions to elliptic partial differential equations (PDEs) by iteratively improving the solution through a sequence of coarser discretizations or grids. The methodology has been developed and extended since the 1970’s to also target more general PDEs and systems of algebraic equations. A typical approach consists of a series of refinements or grid...
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ژورنال
عنوان ژورنال: Computer Methods in Applied Mechanics and Engineering
سال: 2013
ISSN: 0045-7825
DOI: 10.1016/j.cma.2012.08.015