Overlapping Domain Decomposition Methods Based on Tensor Format for Solving High-Dimensional Partial Differential Equations

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  • 1 School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China;
    2 School of Mathematics and Computing Science, Center for Applied Mathematics of Guangxi (GUET), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, Guangxi, China

Received date: 2023-11-14

  Revised date: 2024-05-20

  Accepted date: 2024-05-21

  Online published: 2025-05-23

Supported by

This work was supported by the National Natural Science Foundation of China (12161027), the Guangxi Natural Science Foundation of China (2020GXNSFAA159143), and partially supported by the Science and Technology Project of Guangxi of China (Guike AD23023002).

Abstract

Based on the equivalence between the Sylvester tensor equation and the linear equation obtained by discretization of partial differential equations (PDEs), an overlapping Schwarz alternative method based on the tensor format and an overlapping parallel Schwarz method based on the tensor format for solving high-dimensional PDEs are proposed. The complexity of the new algorithms is discussed. Finally, the feasibility and effectiveness of the new methods are verified by some numerical examples.

Cite this article

Yu-Han Chen, Chen-Liang Li . Overlapping Domain Decomposition Methods Based on Tensor Format for Solving High-Dimensional Partial Differential Equations[J]. Communications on Applied Mathematics and Computation, 2025 , 7(3) : 987 -1001 . DOI: 10.1007/s42967-024-00429-3

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