Efficient iteration methods for complex systems with an indefinite matrix term

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F22%3A00555974" target="_blank" >RIV/68145535:_____/22:00555974 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s10092-022-00461-w" target="_blank" >https://link.springer.com/article/10.1007/s10092-022-00461-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10092-022-00461-w" target="_blank" >10.1007/s10092-022-00461-w</a>

Result language
angličtina
Original language name
Efficient iteration methods for complex systems with an indefinite matrix term
Original language description
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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