Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions

  • Authors:

  • Joseph Papac;Frédéric Gibou;Christian Ratsch

  • Affiliations:

  • Mechanical Engineering Department, University of California, Santa Barbara, CA 93106, United States;Mechanical Engineering Department, University of California, Santa Barbara, CA 93106, United States and Computer Science Department, University of California, Santa Barbara, CA 93106, United State ...;Department of Mathematics, and Institute for Pure and Applied Mathematics, University of California, Los Angeles, CA 90095, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

We present a novel and efficient method for solving the Poisson equation, the heat equation, and Stefan-type problems with Robin boundary conditions over potentially moving, arbitrarily-shaped domains. The method utilizes a level set framework, thus it has all of the benefits of a sharp, implicitly-represented interface such as the ease of handling complex topological changes. This method is straightforward to implement and leads to a linear system that is symmetric and positive definite, which can be inverted efficiently with standard iterative methods. This approach is second-order accurate for both the Poisson and heat equations, and first-order accurate for the Stefan problem. We demonstrate the accuracy in the L^1 and L^~ norms.