A High-Order Solver for the Heat Equation in 1D Domains with Moving Boundaries

Loading...
Thumbnail Image
Penn collection
Departmental Papers (MEAM)
Degree type
Discipline
Subject
integral equations
spectral methods
chebyshev polynomials
moving boundaries
heat equation
quadratures
Nyström's method
collocation methods
potential theory
Engineering
Mechanical Engineering
Funder
Grant number
License
Copyright date
Distributor
Related resources
Contributor
Abstract

We describe a fast high-order accurate method for the solution of the heat equation in domains with moving Dirichlet or Neumann boundaries and distributed forces. We assume that the motion of the boundary is prescribed. Our method extends the work of Greengard and Strain [Comm. Pure Appl. Math., XLIII (1990), pp. 949–963]. Our scheme is based on a time-space Chebyshev pseudo-spectral collocation discretization, which is combined with a recursive product quadrature rule to accurately and efficiently approximate convolutions with Green’s function for the heat equation. We present numerical results that exhibit up to eighth-order convergence rates. Assuming N time steps and M spatial discretization points, the evaluation of the solution of the heat equation at the same number of points in space-time requires O(N M log M) work. Thus, our scheme can be characterized as “fast”; that is, it is work-optimal up to a logarithmic factor.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
2007-10-24
Journal title
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Suggested Citation: S.K. Veerapaneni and G. Biros. (2007). A High-Order Solver for the Heat Equation in 1D Domains with Moving Boundaries. SIAM Journal on Scientific Computing. Vol. 29, No. 6, pp. 2581-2606. © 2007 Society for Industrial and Applied Mathematics
Recommended citation
Collection