Hongxu Liu

Hongxu Liu

Seattle, Washington, United States
735 followers 500+ connections

About

Experienced Software Engineer with a demonstrated history of working in the internet…

Activity

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Experience

  • OfferUp Graphic

    OfferUp

    Greater Seattle Area

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    Greater Seattle Area

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    Greater New York City Area

Education

  • Stony Brook University Graphic

    Stony Brook University

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    Activities and Societies: Stony Brook Table Tennis Club

    Computational Applied Mathematics track

  • -

Licenses & Certifications

Publications

  • WLS-ENO: Weighted-Least-Squares Based Essentially Non-Oscillatory Schemes for Finite Volume Methods on Unstructured Meshes

    Journal of Computational Physics

    We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. This scheme does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some…

    We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. This scheme does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.

    Other authors

Courses

  • Analysis of Algorithm

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  • Analytical Methods for AMS

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  • C Programming

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  • Computational Geometry

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  • Data Structure

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  • Linear Programming

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  • Numerical Analysis

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  • Numerical Partial Differential Equations

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  • Probability

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Projects

  • Weighted-Least-Squares Based Essentially Non-Oscillatory Schemes for Generalized Finite Difference Methods on Unstructured Meshes

    - Present

    ● Developed WLS-ENO finite difference schemes which are the first type of finite difference schemes for unstructured meshes by combining the ideas of several available schemes
    ● Analyzed and proved the accuracy and stability of WLS-ENO finite difference schemes
    ● Improved the efficiency of WLS-ENO finite difference schemes, resulting in 15 times faster runtime than WENO finite volume schemes on unstructured meshes
    ● Implemented the algorithm and achieved the good performance on…

    ● Developed WLS-ENO finite difference schemes which are the first type of finite difference schemes for unstructured meshes by combining the ideas of several available schemes
    ● Analyzed and proved the accuracy and stability of WLS-ENO finite difference schemes
    ● Improved the efficiency of WLS-ENO finite difference schemes, resulting in 15 times faster runtime than WENO finite volume schemes on unstructured meshes
    ● Implemented the algorithm and achieved the good performance on unstructured meshes

  • WLS-ENO: Weighted-Least-Squares Based Essentially Non-Oscillatory Schemes for Finite Volume Methods on Unstructured Meshes

    -

    ● Developed WLS-ENO finite volume schemes for solving PDEs with discontinuities by generalizing specially designed and widely used WENO schemes in a more systematic way
    ● Addressed the instability and mesh quality dependence of WENO schemes by analyzing and proving the stability and accuracy of WLS-ENO finite volume schemes
    ● Implemented the algorithm using Matlab and C++ and compared the performance with WENO finite volume schemes, concluding that WLS-ENO schemes can deliver better…

    ● Developed WLS-ENO finite volume schemes for solving PDEs with discontinuities by generalizing specially designed and widely used WENO schemes in a more systematic way
    ● Addressed the instability and mesh quality dependence of WENO schemes by analyzing and proving the stability and accuracy of WLS-ENO finite volume schemes
    ● Implemented the algorithm using Matlab and C++ and compared the performance with WENO finite volume schemes, concluding that WLS-ENO schemes can deliver better accuracy and stability than WENO finite volume schemes by 90% and 21% respectively

    See project

Languages

  • Chinese(Mandarin)

    Native or bilingual proficiency

  • English

    Professional working proficiency

Organizations

  • Institute of Advanced Computational Science

    Research Assistant

    - Present
  • Stony Brook University

    Research Assistant

    - Present

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