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  • Authors: Zhilin Li;

    The immersed interface method (IIM) ?rst proposed in is an accurate numerical method for solving elliptic interface problems on Cartesian meshes. It is a sharp interface method that was intended to improve accuracy of the immersed boundary (IB) method. The IIM is second order accurate in the maximum norm (pointwise, strongest) while the IB method is ?rst order accurate. The ?rst IIM paper is one of the most downloaded one from the SIAM website and is one of the most cited papers. While IIM provided a way of accurate discretization of the partial differential equations (PDEs) with discontinuous coefficients, the augmented IIM ?rst proposed in made the IIM much more efficient and faster by utilizing existing fast Poisson solvers. More important is that the augmented IIM provides an efficient way for multi-physics models with different governing equations, problems on irregular domains, multi-scales and multi-connected domains. A brie?y introduction of the augmented strategy including some recently progress is presented in this article.

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  • Authors: Zhilin Li;

    The immersed interface method (IIM) ?rst proposed in is an accurate numerical method for solving elliptic interface problems on Cartesian meshes. It is a sharp interface method that was intended to improve accuracy of the immersed boundary (IB) method. The IIM is second order accurate in the maximum norm (pointwise, strongest) while the IB method is ?rst order accurate. The ?rst IIM paper is one of the most downloaded one from the SIAM website and is one of the most cited papers. While IIM provided a way of accurate discretization of the partial differential equations (PDEs) with discontinuous coefficients, the augmented IIM ?rst proposed in made the IIM much more efficient and faster by utilizing existing fast Poisson solvers. More important is that the augmented IIM provides an efficient way for multi-physics models with different governing equations, problems on irregular domains, multi-scales and multi-connected domains. A brie?y introduction of the augmented strategy including some recently progress is presented in this article.

    addClaim

    This Research product is the result of merged Research products in OpenAIRE.

    You have already added works in your ORCID record related to the merged Research product.
    0
    citations0
    popularityAverage
    influenceAverage
    impulseAverage
    BIP!Powered by BIP!
    more_vert
      addClaim

      This Research product is the result of merged Research products in OpenAIRE.

      You have already added works in your ORCID record related to the merged Research product.
Powered by OpenAIRE graph