Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems

Fermín S. V. Bazán; Luciano Bedin; Koung Hee Leem; Jun Liu; George Pelekanos; Fermín S. V. Bazán; Luciano Bedin; Koung Hee Leem; Jun Liu; George Pelekanos

doi:10.3934/nhm.2023026

Networks and Heterogeneous Media

2023, Volume 18, Issue 2: 601-621. doi: 10.3934/nhm.2023026

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Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems

1.
Department of Mathematics, Federal University of Santa Catarina, Florianopolis SC, Santa Catarina, Brazil
2.
Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA

Received: 26 October 2022 Revised: 26 December 2022 Accepted: 22 January 2023 Published: 06 February 2023

In this paper, we study the well-established quasi-boundary value methods for regularizing inverse state-dependent source problems, where the convergence analysis of three typical cases is presented in the framework of filtering regularization method under suitable source conditions. Interestingly, the quasi-boundary value methods can be interpreted as certain Lavrentiev-type regularization, which was not known in literature. As another major contribution, efficient numerical implementation based on matrix exponential in time is developed, which shows much improved computational efficiency than MATLAB's backslash solver based on the all-at-once space-time discretization scheme. Numerical examples are reported to illustrate the promising computational performance of our proposed algorithms based on matrix exponential techniques.

Keywords:

Citation: Fermín S. V. Bazán, Luciano Bedin, Koung Hee Leem, Jun Liu, George Pelekanos. Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems[J]. Networks and Heterogeneous Media, 2023, 18(2): 601-621. doi: 10.3934/nhm.2023026

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Abstract

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