A fast method for solving the heat equation by layer potentials
نویسنده
چکیده
Boundary integral formulations of the heat equation involve time convolutions in addition to surface potentials. If M is the number of time steps and N is the number of degrees of freedom of the spatial discretization then the direct computation of a heat potential involves order N M operations. This article describes a fast method to compute three dimensional heat potentials which is based on Chebyshev interpolation of the heat kernel in both space and time. The computational complexity is order pqNM operations, where p and q are the orders of the polynomial approximation in space and time.
منابع مشابه
A Fast and Accurate Expansion-Iterative Method for Solving Second Kind Volterra Integral Equations
This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...
متن کاملA Fast Algorithm for the Evaluation of Heat Potentials
Numerical methods for solving the heat equation via potential theory have been hampered by the high cost of evaluating heat potentials. When M points are used in the discretization of the boundary and N time steps are computed, an amount of work of the order O(N M) has traditionally been required. In this paper, we present an algorithm which requires an amount of work of the order O(NM), and we...
متن کاملSolving Some Initial-Boundary Value Problems Including Non-classical Cases of Heat Equation By Spectral and Countour Integral Methods
In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...
متن کاملPotential theory for initial-boundary value problems of unsteady Stokes flow in two dimensions
Integral equations have been of great theoretical importance for analyzing boundary value problems. There is a large amount of literature devoted to the classical potential theory and its applications on solving the boundary value problems of elliptic partial differential equations (see, for example, [5, 20, 23, 25, 26, 31, 32, 36, 37, 40]). For elliptic problems, integral equations have been c...
متن کاملEstimation of the Strength of the Time-dependent Heat Source using Temperature Distribution at a Point in a Three Layer System
In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the strength of the time- dependent heat source using the temperature distribution at a point in a three layer system. Also, the effect of noisy data on final solution is studied. The numerical solution of the governing equations is obtained b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comput. Physics
دوره 224 شماره
صفحات -
تاریخ انتشار 2007