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- Barbarino, Giovanni, et al.
(författare)
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Matrix-Less Eigensolver for Large Structured Matrices
- 2021
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Sequences of structured matrices of increasing size arise in many scientific applications and especially in the numerical discretization of linear differential problems. We assume as a working hypothesis that the eigenvalues of a matrix X_n belonging to a sequence of this kind are given by a regular expansion. Based on this working hypothesis, which is illustrated to be plausible through numerical experiments, we propose an eigensolver for the computation of the eigenvalues of X_n for large n and we provide a theoretical analysis of its convergence. The eigensolver is called matrix-less because it does not operate on the matrix X_n but on a few similar matrices of smaller size combined with an interpolation-extrapolation strategy. Its performance is benchmarked on several numerical examples, with a special focus on matrices arising from the discretization of differential problems.
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- Garoni, Carlo, et al.
(författare)
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NURBS in isogeometric discretization methods : A spectral analysis
- 2020
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Ingår i: Numerical Linear Algebra with Applications. - : Wiley. - 1070-5325 .- 1099-1506. ; 27:6
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Tidskriftsartikel (refereegranskat)abstract
- Nonuniform rational B-splines (NURBS) are the most common representation form in isogeometric analysis. In this article, we study the spectral behavior of discretization matrices arising from isogeometric Galerkin and collocation methods based ond-variate NURBS of degrees(p(1), horizontal ellipsis ,p(d)), and applied to general second-order partial differential equations defined on ad-dimensional domain. The spectrum of these matrices can be compactly and accurately described by means of a so-called symbol. We compute this symbol and show that it is the same as in the case of isogeometric discretization matrices based ond-variate polynomial B-splines of degrees(p(1), horizontal ellipsis ,p(d)). The theoretical results are confirmed with a selection of numerical examples.
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