Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods

Börner, Ralph-Uwe and Ernst, Oliver G. and Güttel, Stefan (2014) Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods. [MIMS Preprint]

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Abstract

A computational method is given for solving the forward modeling problem for transient electromagnetic exploration. Its key features are discretization of the quasi-static Maxwell's equations in space using the first-kind family of curl-conforming Nedelec elements combined with time integration using rational Krylov subspace methods. We show how rational Krylov subspace methods may be used to solve the same problem in the frequency domain followed by a synthesis of the transient solution using the fast Hankel transform, arguing that the pure time-domain is more efficient. We also propose a simple method for selecting the pole parameters of the rational Krylov subspace method which leads to convergence within an a priori determined number of iterations independent of mesh size and conductivity structure. These poles are repeated in a cyclic fashion, which, in combination with direct solvers for the discrete problem, results in significantly faster solution times than previously proposed schemes.

Item Type: MIMS Preprint
Uncontrolled Keywords: EM modeling, transient electromagnetics, Krylov subspace methods
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 86 Geophysics
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 90 GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS > 93 Geophysical observations, instrumentation, and techniques
Depositing User: Stefan Güttel
Date Deposited: 28 Jul 2014
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2161

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