Space-time spectral penalty method for a one-dimensional  parabolic inverse problem

Ying Fu; Huiqing Liao

doi:10.1117/12.3025560

8 April 2024 Space-time spectral penalty method for a one-dimensional parabolic inverse problem

Ying Fu, Huiqing Liao

Proceedings Volume 13090, International Conference on Computer Application and Information Security (ICCAIS 2023); 130900E (2024) https://doi.org/10.1117/12.3025560
Event: International Conference on Computer Application and Information Security (ICCAIS 2023), 2023, Wuhan, China

Abstract

In this work, for a parabolic inverse problem with control parameters, a space-time spectral penalty method based on a Legendre-Galerkin-Chebyshev collocation in space, and a Legendre-tau method in time is presented. According to the scheme of space-time spectral penalty method, the convergence analysis is carried out, and the approximation results of the Chebyshev interpolation operator in the Legendre norm are given. Suitable basis functions are used in each direction, which yields an algebraic system of sparse matrices. Numerical examples are compared with some other methods to confirm the efficiency and capability of the proposed method.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Ying Fu and Huiqing Liao "Space-time spectral penalty method for a one-dimensional parabolic inverse problem", Proc. SPIE 13090, International Conference on Computer Application and Information Security (ICCAIS 2023), 130900E (8 April 2024); https://doi.org/10.1117/12.3025560

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