Asymptotic expansions and boundary conditions for time-dependent problems
SIAM Journal on Numerical Analysis
Boundary conditions at outflow for a problem with transport and diffusion
Journal of Computational Physics
The dual reciprocity boundary element formulation for diffusion problems
Computer Methods in Applied Mechanics and Engineering
Absorbing boundary conditions for diffusion equations
Numerische Mathematik
Artificial boundary conditions for diffusion equations: numerical study
Journal of Computational and Applied Mathematics
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Journal of Computational Physics
Applied Numerical Mathematics
A fast numerical method for time-resolved photon diffusion in general stratified turbid media
Journal of Computational Physics
Wave field simulation for heterogeneous porous media with singular memory drag force
Journal of Computational Physics
A fast method for solving the heat equation by layer potentials
Journal of Computational Physics
Journal of Computational Physics
On the numerical solution of the heat equation I: Fast solvers in free space
Journal of Computational Physics
Exact artificial boundary conditions for problems with periodic structures
Journal of Computational Physics
Hi-index | 31.45 |
A high-order open boundary for transient diffusion in a semi-infinite homogeneous layer is developed. The method of separation of variables is used to derive a relationship between the modal function and the flux at the near field/far field boundary in the Fourier domain. The resulting equation in terms of the modal impedance coefficient is solved by expanding the latter into a doubly asymptotic series of continued fractions. As a result, the open boundary condition in the Fourier domain is represented by a system of algebraic equations in terms of i@w. This corresponds to a system of fractional differential equations of degree @a=0.5 in the time-domain. This temporally global formulation is transformed into a local description by introducing internal variables. The resulting local high-order open boundary condition is highly accurate, as is demonstrated by a number of heat transfer examples. A significant gain in accuracy is obtained in comparison with existing singly-asymptotic formulations at no additional computational cost.