• Corpus ID: 203626584

Fast integral equation methods for linear and semilinear heat equations in moving domains

  title={Fast integral equation methods for linear and semilinear heat equations in moving domains},
  author={Jun Wang and Leslie Greengard and Shidong Jiang and Shravan K. Veerapaneni},
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite difference methods in terms of accuracy, stability and space-time adaptivity. In order to be practical, however, a number of technical capabilites are required: fast algorithms for the evaluation of heat potentials, high-order accurate quadratures for singular and… 
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Fast Adaptive Methods for the Free-Space Heat Equation
  • J. Strain
  • Computer Science
    SIAM J. Sci. Comput.
  • 1994
Efficient and accurate new adaptive methods that solve the free-space heat equation with large timesteps that combine the fast Gauss transform with an adaptive refinement scheme that represents the solution as a continuous piecewise polynomial, to a user-specified degree of accuracy are presented.
An Efficient Galerkin Boundary Element Method for the Transient Heat Equation
If the parabolic multipole method is used to apply parabolic boundary integral operators, the overall complexity of the scheme is log-linear while preserving the convergence of the Galerkin discretization method.
On the numerical solution of the heat equation I: Fast solvers in free space
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Efficient high-order integral equation methods for the heat equation
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