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Space--time least--squares isogeometric method and efficient solver for parabolic problems.
- Source :
-
Mathematics of Computation . May2020, Vol. 89 Issue 323, p1193-1227. 35p. - Publication Year :
- 2020
-
Abstract
- In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational efficiency: thanks to the proposed formulation and to the tensor-product construction of space-time splines, we can design a preconditioner whose application requires the solution of a Sylvester-like equation, which is performed efficiently by the fast diagonalization method. The preconditioner is robust w.r.t. spline degree and mesh size. The computational time required for its application, for a serial execution, is almost proportional to the number of degrees-of-freedom and independent of the polynomial degree. The proposed approach is also well-suited for parallelization. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SYLVESTER matrix equations
*ISOGEOMETRIC analysis
*TARDINESS
*SPLINES
*SPACE
Subjects
Details
- Language :
- English
- ISSN :
- 00255718
- Volume :
- 89
- Issue :
- 323
- Database :
- Academic Search Index
- Journal :
- Mathematics of Computation
- Publication Type :
- Academic Journal
- Accession number :
- 141722211
- Full Text :
- https://doi.org/10.1090/mcom/3471