Mikhail Zaslavsky

Solution of Large Scale Evolutionary Problems Using Rational Krylov Subspaces with Optimized Shifts

We consider the computation of

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

u(t)=\exp(-tA)\varphi

Hybrid finite-difference integral equation solver for 3D frequency domain anisotropic electromagnetic problems

using rational Krylov subspace reduction for

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

0\le t<\infty

Adaptive Tangential Interpolation in Rational Krylov Subspaces for MIMO Dynamical Systems

, where

Solution of the Time-Domain Inverse Resistivity Problem in the Model Reduction Framework Part I. One-Dimensional Problem with SISO Data

u(t),\varphi\in\mathbf{R}^N

An extended Krylov subspace model-order reduction technique to simulate wave propagation in unbounded domains

and

A model reduction approach to numerical inversion for a parabolic partial differential equation

0<A=A^*\in\mathbf{R}^{N\times N}

A Three-dimensional Multiplicative-regularized Non-linear Inversion Algorithm For Cross-well Electromagnetic And Controlled-source Electromagnetic Applications

. The objective of this work is the optimization of the shifts for the rational Krylov subspace (RKS). We consider this problem in the frequency domain and reduce it to a classical Zolotaryov problem. The latter yields an asymtotically optimal solution with real shifts. We also construct an infinite sequence of shifts yielding a nested sequence of the RKSs with the same (optimal) Cauchy-Hadamard convergence rate. The effectiveness of the developed approach is demonstrated on an example of the three-dimensional diffusion problem for Maxwells equation arising in geophysical exploration.

On combining model reduction and Gauss–Newton algorithms for inverse partial differential equation problems

We solve an electromagnetic frequency domain induction problem in