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Yujie Ma

  1. Westervelt Equation Simulation on Manifold using DEC.

    Thu, 01/14/2010 - 16:01 — SomNambul
    Authors: Zheng Xie, Yujie Ma
    Subjects: Numerical Analysis
    Abstract

    The Westervelt equation is a model for the propagation of finite amplitude
    ultrasound. The method of discrete exterior calculus can be used to solve this
    equation numerically. A significant advantage of this method is that it can be
    used to find numerical solutions in the discrete space manifold and the time,
    and therefore is a generation of finite difference time domain method. This
    algorithm has been implemented in C++.

  2. Two unconditional stable schemes for simulation of heat equation on manifold using DEC.

    Wed, 01/13/2010 - 16:01 — SomNambul
    Authors: Zheng Xie, Yujie Ma
    Subjects: Numerical Analysis
    Abstract

    To predict the heat diffusion in a given region over time, it is often
    necessary to find the numerical solution for heat equation. With the techniques
    of discrete differential calculus, we propose two unconditional stable
    numerical schemes for simulation heat equation on space manifold and time. The
    analysis of their stability and error is accomplished by the use of maximum
    principle.

  3. Wave Equation Simulation on Manifold using Discrete Exterior Calculus.

    Tue, 09/29/2009 - 15:21 — SomNambul
    Authors: Zheng Xie, Yujie Ma, Bin Ma, Qinghua Shen
    Subjects: Numerical Analysis
    Abstract

    Numerical simulation provides a effective tool for studying both the spatial
    and temporal nature of acoustic field on 3D or 4D timespace. The paper deals
    with the description of discrete exterior calculus scheme for the wave
    equation. This method can be directly implemented on manifold, which is the
    generation of finite difference time domain method from flat space to curved
    space.

  4. Computation Electromagnetism and Discrete Exterior Calculus.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Zheng Xie, Zheng Ye, Yujie Ma
    Subjects: Numerical Analysis
    Abstract

    Computational electromagnetism is concerned with the numerical study of
    Maxwell equations. By choosing a discrete Gaussian measure on prism lattice, we
    use discrete exterior calculus and lattice gauge theory to construct discrete
    Maxwell equations in vacuum case. We implement this scheme on Java development
    plateform to simulate the behavior of electromagnetic waves.

  5. Computational Electromagnetism and Implicit Discrete Exterior Calculus.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Zheng Xie, Zheng Ye, Yujie Ma
    Subjects: Numerical Analysis
    Abstract

    Implicit discrete exterior calculus technique for Maxwell's equations in time
    domain is discussed, which provide flexibility in numerical computing Maxwell's
    equations on manifold. The implicit scheme and discrete exterior calculus can
    be united to find an unconditional stable approach, which is obtained by
    properly defining a discrete Hodge star operator. The algorithm has been
    implemented on Java development plateform.

  6. Computational Electromagnetism and Implicit Discrete Exterior Calculus.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Zheng Xie, Zheng Ye, Yujie Ma
    Subjects: Numerical Analysis
    Abstract

    Implicit discrete exterior calculus technique for Maxwell's equations in time
    domain is discussed, which provide flexibility in numerical computing Maxwell's
    equations on manifold. The implicit scheme and discrete exterior calculus can
    be united to find an unconditional stable approach, which is obtained by
    properly defining a discrete Hodge star operator. The algorithm has been
    implemented on Java development plateform.

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