On Optimal Convergence Rate of the Rational Krylov Subspace Reduction for Electromagnetic Problems in Unbounded Domains
Leonid Aronovich Knizhnerman, Vladimir L. Druskin, Mikhail Zaslavsky · SIAM Journal on Numerical Analysis · 2009
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.