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Sylvester-based pre...
Sylvester-based preconditioning for the waveguide eigenvalue problem
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- Ringh, Emil (author)
- KTH,Optimeringslära och systemteori
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- Mele, Giampaolo (author)
- KTH,Numerisk analys, NA
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- Karlsson, Johan (author)
- KTH,Optimeringslära och systemteori
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- Jarlebring, Elias (author)
- KTH,Numerisk analys, NA
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(creator_code:org_t)
- Elsevier, 2018
- 2018
- English.
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In: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 542:1, s. 441-463
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Abstract
Subject headings
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- We consider a nonlinear eigenvalue problem (NEP) arising from absorbing boundary conditions in the study of a partial differential equation (PDE) describing a waveguide. We propose a new computational approach for this large-scale NEP based on residual inverse iteration (Resinv) with preconditioned iterative solves. Similar to many preconditioned iterative methods for discretized PDEs, this approach requires the construction of an accurate and efficient preconditioner. For the waveguide eigenvalue problem, the associated linear system can be formulated as a generalized Sylvester equation AX+XB+A1XB1+A2XB2+K(ring operator)X=C, where (ring operator) denotes the Hadamard product. The equation is approximated by a low-rank correction of a Sylvester equation, which we use as a preconditioner. The action of the preconditioner is efficiently computed by using the matrix equation version of the Sherman-Morrison-Woodbury (SMW) formula. We show how the preconditioner can be integrated into Resinv. The results are illustrated by applying the method to large-scale problems.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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