Journal of Computational and Applied Mathematics
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Dimension Reduction of Large-Scale Second-Order Dynamical Systems via a Second-Order Arnoldi Method
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Preconditioning Lanczos Approximations to the Matrix Exponential
SIAM Journal on Scientific Computing
Fast and Oblivious Convolution Quadrature
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Solution of Large Scale Evolutionary Problems Using Rational Krylov Subspaces with Optimized Shifts
SIAM Journal on Scientific Computing
Error Estimates and Evaluation of Matrix Functions via the Faber Transform
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
We suggest a new algorithm for the solution of the time domain Maxwell equations in dispersive media. After spacial discretization we obtain a large system of time-convolution equations. Then this system is projected onto a small subspace consisting of the Laplace domain solutions for a preselected set of Laplace parameters. This approach is a generalization of the rational Krylov subspace approach for the solution of non-dispersive Maxwell's systems. We show that the projected system preserves such properties of the initial system as stability and passivity. As an example we consider the 3D quasistationary induced polarization problem with the Cole-Cole conductivity model important for geophysical oil exploration. Our numerical experiments show that the introduction of the induced polarization does not have significant effect on convergence.