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Efficient low rank ...
Efficient low rank approximations for parabolic control problems with unknown heat source
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- Arjmand, Doghonay, 1987- (författare)
- Uppsala universitet,Avdelningen för beräkningsvetenskap,Numerisk analys
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- Ashyraliyev, Maksat (författare)
- Mälardalens universitet,Utbildningsvetenskap och Matematik,Mälardalen Univ, Div Math & Phys, Box 883, S-72123 Västerås, Sweden.
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(creator_code:org_t)
- Elsevier B.V. 2024
- 2024
- Engelska.
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier B.V.. - 0377-0427 .- 1879-1778. ; 450
- Relaterad länk:
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Abstract
Ämnesord
Stäng
- An inverse problem of finding an unknown heat source for a class of linear parabolic equations is considered. Such problems can typically be converted to a direct problem with non-local conditions in time instead of an initial value problem. Standard ways of solving these non-local problems include direct temporal and spatial discretization as well as the shooting method, which may be computationally expensive in higher dimensions. In the present article, we present approaches based on low-rank approximation via Arnoldi algorithm to bypass the computational limitations of the mentioned classical methods. Regardless of the dimension of the problem, we prove that the Arnoldi approach can be effectively used to turn the inverse problem into a simple initial value problem at the cost of only computing one-dimensional matrix functions while still retaining the same accuracy as the classical approaches. Numerical results in dimensions d=1,2,3 are provided to validate the theoretical findings and to demonstrate the efficiency of the method for growing dimensions.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Arnoldi algorithm
- Control problems
- Heat equation
- Inverse problems
- Low rank approximations
- Parabolic PDEs
- Approximation algorithms
- Approximation theory
- Initial value problems
- Numerical methods
- Partial differential equations
- Direct problems
- Heat sources
- Initial-value problem
- Linear parabolic equation
- Parabolics
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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