Scholarlink

<p>In [Lin, Xuelei and Ng, Michael K. <i>Appl. Numer. Math.</i>, 40 (2018), pp. A1012–A1033][<CitationRef CitationID="CR12">12</CitationRef>], 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Matching Schur Complement Preconditioning Technique for a Discrete Time Fractional Diffusion Inverse Source Problem

  • 期刊论文

  • 发表日期：

    2026年1月3日

查看全文
  • Xuelei Lin,
  • Rihuan Ke,
  • Sean Y. Hon,
  • Michael K. Ng

摘要

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.