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  1. Article ; Online: An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method.

    Chen, Jia-Fen / Gu, Xian-Ming / Li, Liang / Zhou, Ping

    Entropy (Basel, Switzerland)

    2023  Volume 25, Issue 4

    Abstract: An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on ... ...

    Abstract An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective.
    Language English
    Publishing date 2023-04-19
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e25040693
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article: Fast permutation preconditioning for fractional diffusion equations.

    Wang, Sheng-Feng / Huang, Ting-Zhu / Gu, Xian-Ming / Luo, Wei-Hua

    SpringerPlus

    2016  Volume 5, Issue 1, Page(s) 1109

    Abstract: In this paper, an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is used to discretize the fractional diffusion equations with constant diffusion coefficients. The coefficient matrix possesses the ... ...

    Abstract In this paper, an implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is used to discretize the fractional diffusion equations with constant diffusion coefficients. The coefficient matrix possesses the Toeplitz structure and the fast Toeplitz matrix-vector product can be utilized to reduce the computational complexity from [Formula: see text] to [Formula: see text], where N is the number of grid points. Two preconditioned iterative methods, named bi-conjugate gradient method for Toeplitz matrix and bi-conjugate residual method for Toeplitz matrix, are proposed to solve the relevant discretized systems. Finally, numerical experiments are reported to show the effectiveness of our preconditioners.
    Language English
    Publishing date 2016-07-19
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2661116-8
    ISSN 2193-1801
    ISSN 2193-1801
    DOI 10.1186/s40064-016-2766-4
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article ; Online: Some refinements and generalizations of I. Schur type inequalities.

    Gu, Xian-Ming / Huang, Ting-Zhu / Xu, Wei-Ru / Li, Hou-Biao / Li, Liang / Zhao, Xi-Le

    TheScientificWorldJournal

    2014  Volume 2014, Page(s) 709358

    Abstract: Recently, extensive researches on estimating the value of e have been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some ... ...

    Abstract Recently, extensive researches on estimating the value of e have been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some novel upper and lower bounds for the I. Schur inequality have also been obtained and the upper bounds may be obtained with the help of Maple and automated proving package (Bottema). Numerical examples are employed to demonstrate the reliability of the approximation of these new upper and lower bounds, which improve some known results in the recent literature.
    MeSH term(s) Algorithms ; Mathematics ; Models, Theoretical ; Reproducibility of Results
    Language English
    Publishing date 2014-03-16
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 2075968-X
    ISSN 1537-744X ; 1537-744X
    ISSN (online) 1537-744X
    ISSN 1537-744X
    DOI 10.1155/2014/709358
    Database MEDical Literature Analysis and Retrieval System OnLINE

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