کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
497820 862945 2015 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Robust and optimal multi-iterative techniques for IgA collocation linear systems
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Robust and optimal multi-iterative techniques for IgA collocation linear systems
چکیده انگلیسی


• We consider fast solvers for large IgA collocation linear systems.
• We design an optimal and totally robust multi-iterative method.
• The practical behavior is carefully studied through the notion of a symbol.

We consider fast solvers for the large linear systems coming from the Isogeometric Analysis (IgA) collocation approximation based on B-splines of full elliptic dd-dimensional Partial Differential Equations (PDEs). We are interested in designing iterative algorithms which are optimal and robust. The former property implies that the computational cost is linear with respect to the number of degrees of freedom (i.e. the matrix size). The latter property means that the convergence rate is completely independent of (or only mildly dependent on) all the relevant parameters: in our setting, we can mention the coefficients of the PDE, the dimensionality dd, the geometric map G describing the physical domain, the matrix size (related to the fineness parameters), and the spline degrees (associated with the IgA approximation order). Our approach is based on the spectral symbol, which describes the global eigenvalue behavior of the IgA collocation matrices. It is precisely the spectral information contained in the symbol that is exploited for the design of an optimal and robust multi-iterative solver of multigrid type. Several numerical experiments are presented and discussed in view of recent theoretical findings concerning the symbol and its properties.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 284, 1 February 2015, Pages 1120–1146
نویسندگان
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