On Optimal Convergence Rate of the Rational Krylov Subspace Reduction for Electromagnetic Problems in Unbounded Domains

Authors:
Leonid Knizhnerman;Vladimir Druskin;Mikhail Zaslavsky
Affiliations:
mmd@cge.ru;druskin1@slb.com and mzaslavsky@slb.com;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2009

Citing 0
Cited 4

Solution of time-convolutionary Maxwell's equations using parameter-dependent Krylov subspace reduction

Journal of Computational Physics
Interpreting IDR as a Petrov-Galerkin Method

SIAM Journal on Scientific Computing
On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems

SIAM Journal on Scientific Computing
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.01

Visualization

Abstract

We solve an electromagnetic frequency domain induction problem in $\mathbf{R}^3$ for a frequency interval using rational Krylov subspace (RKS) approximation. The RKS is constructed by spanning on the solutions for a certain a priori chosen set of frequencies. We reduce the problem of the optimal choice of these frequencies to the third Zolotaryov problem in the complex plane, having an approximate closed form solution, and determine the best Cauchy-Hadamard convergence rate. The theory is illustrated with numerical examples for Maxwell's equations arising in 3D magnetotelluric geophysical exploration.