TY - JOUR
T1 - A Matching Schur Complement Preconditioning Technique for a Discrete Time Fractional Diffusion Inverse Source Problem
AU - Lin, Xuelei
AU - Ke, Rihuan
AU - Hon, Sean Y.
AU - Ng, Michael K.
N1 - The work of Xue-Lei Lin was partially supported by research grants: 12301480 from NSFC, 2025A1515010945 from Natural Science Foundation of Guangdong Province. The work of Sean Hon was supported in part by NSFC under grant 12401544 and a start-up grant from the Croucher Foundation. The work of Michael K. Ng was supported by the GDSTC: Guangdong and Hong Kong Universities “1+1+1” Joint Research Collaboration Scheme UICR0800008-24, National Key Research and Development Program of China under Grant 2024YFE0202900, RGC GRF 12300125 and Joint NSFC and RGC N-HKU769/21.
Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
PY - 2026/2
Y1 - 2026/2
N2 - In [Lin, Xuelei and Ng, Michael K. Appl. Numer. Math., 40 (2018), pp. A1012–A1033][12], a matching Schur complement (MSC) preconditioner is proposed for an inter-order time diffusion inverse (ITDI) problem. When the integer-order time derivative in ITDI problem is replaced by fractional-order time derivative, the inverse problem becomes time fractional diffusion inverse source (TFDIS) problem. The optimal convergence theory of the MSC preconditioner is however not able to be extended to TFDIS problem directly, due to the non-local property of the time-fractional derivative. In this work, we develop a brand new theory to show the optimal convergence of the MSC preconditioner for the TFDIS problem by utilizing properties of non-singular M-matrices and triangular Toeplitz matrices. Numerical results are reported to show that the MSC preconditioner is efficient for TFDIS problems, supporting our theoretical results.
AB - In [Lin, Xuelei and Ng, Michael K. Appl. Numer. Math., 40 (2018), pp. A1012–A1033][12], a matching Schur complement (MSC) preconditioner is proposed for an inter-order time diffusion inverse (ITDI) problem. When the integer-order time derivative in ITDI problem is replaced by fractional-order time derivative, the inverse problem becomes time fractional diffusion inverse source (TFDIS) problem. The optimal convergence theory of the MSC preconditioner is however not able to be extended to TFDIS problem directly, due to the non-local property of the time-fractional derivative. In this work, we develop a brand new theory to show the optimal convergence of the MSC preconditioner for the TFDIS problem by utilizing properties of non-singular M-matrices and triangular Toeplitz matrices. Numerical results are reported to show that the MSC preconditioner is efficient for TFDIS problems, supporting our theoretical results.
KW - Fractional inverse source problem
KW - Preconditioning technique for Schur complement
KW - Saddle point system
KW - Size-independent convergence of PCG
UR - https://www.scopus.com/pages/publications/105026443831
U2 - 10.1007/s10915-025-03166-8
DO - 10.1007/s10915-025-03166-8
M3 - Journal article
AN - SCOPUS:105026443831
SN - 0885-7474
VL - 106
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 2
M1 - 37
ER -