Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Numerical solution of problems on unbounded domains. a review
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Application of the difference Gaussian rules to solution of hyperbolic problems
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Application of the difference Gaussian rules to solution of hyperbolic problems: global expansion
Journal of Computational Physics
Coulomb Interactions on Planar Structures: Inverting the Square Root of the Laplacian
SIAM Journal on Scientific Computing
Optimal grid-based methods for thin film micromagnetics simulations
Journal of Computational Physics
Hi-index | 31.45 |
A method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary. The method is an extension of the optimal grid approach for elliptic problems, based on optimal rational approximation of the associated Neumann-to-Dirichlet map in Fourier space. It is shown that, using certain types of boundary discretization, one can go from second-order accurate schemes to essentially spectrally accurate schemes in two-dimensional problems, and to fourth-order accurate schemes in three-dimensional problems without any increase in the computational complexity. The main idea of the method is to modify the impedance function being approximated to compensate for the numerical dispersion introduced by a small finite-difference stencil discretizing the differential operator on the boundary. We illustrate how the method can be efficiently applied to nonlinear problems arising in modeling of cell communication.