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FROM IIM TO AUGMENTED IIM: A POWERFUL TOOL FOR COMPLEX PROBLEMS USING CARTESIAN MESHES

Authors: Zhilin Li;

FROM IIM TO AUGMENTED IIM: A POWERFUL TOOL FOR COMPLEX PROBLEMS USING CARTESIAN MESHES

Abstract

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.

Subjects by Vocabulary

Microsoft Academic Graph classification: Computer science Computational science law.invention law Polygon mesh Cartesian coordinate system Complex problems

Keywords

Cultural Studies, Sociology and Political Science, Social Psychology, Epidemiology, Economics, Econometrics and Finance (miscellaneous), Physical Therapy, Sports Therapy and Rehabilitation, Development, Environmental Science (miscellaneous), Management, Monitoring, Policy and Law, Education, Physiology (medical), Ecology, Evolution, Behavior and Systematics, Nature and Landscape Conservation, General Environmental Science, Chemical Health and Safety, Ecology, Public Health, Environmental and Occupational Health, General Medicine, Pollution, Agricultural and Biological Sciences (miscellaneous), Psychiatry and Mental health, Clinical Psychology, Infectious Diseases, Insect Science, Animal Science and Zoology

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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Average
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