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Solving the Helmholtz equation numerically

Stoppels, H.T. (2018) Solving the Helmholtz equation numerically. Master's Thesis / Essay, Applied Mathematics.

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Abstract

Linear systems Ax = b involving large, sparse, indefinite and nearly singular matrices A naturally arise in interior eigenvalue problems. Classical iterative methods such as Krylov subspace methods are known to have difficulty with these problems. In this thesis we explore the possibility of obtaining cheap low-dimensional approximations to problematic eigenspaces in an attempt to deflate them. We show that approximate Schur complement techniques can be exploited to not only obtain these approximations, but to construct a preconditioner as well. The Helmholtz equation will be a guiding example throughout this work.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Applied Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:35
Last Modified: 15 Feb 2018 08:35
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/16437

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