Journal ArticleDOI
Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods
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TLDR
It is shown 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.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.read more
Citations
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Journal ArticleDOI
The RKFIT algorithm for nonlinear rational approximation
Mario Berljafa,Stefan Güttel +1 more
TL;DR: This paper derives a strategy for the degree reduction of the approximants, as well as methods for their conversion to partial fraction form, for the efficient evaluation, and root-finding, and puts RKFIT into a general framework.
Journal ArticleDOI
Generalized Rational Krylov Decompositions with an Application to Rational Approximation
Mario Berljafa,Stefan Güttel +1 more
TL;DR: A rational Krylov method for rational least squares fitting is developed and an implicit Q theorem forrational Krylov spaces is presented.
Book ChapterDOI
A Review of Airborne Electromagnetic Methods With Focus on Geotechnical and Hydrological Applications From 2007 to 2017
TL;DR: In this paper, the authors report the major advancements that have been made within the area of airborne electromagnetics (AEM) between 2007 and 2017, with a focus on geotechnical and hydrological applications.
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A finite-element time-domain forward solver for electromagnetic methods with complex-shaped loop sources
TL;DR: In this paper, a finite element time-domain (FETD) electromagnetic forward solver for a complex-shaped transmitting loop is presented, which can be viewed as a combination of electric...
Journal ArticleDOI
Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner
TL;DR: In this paper, a finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid is presented for 3D electromagnetic simulations in conducting media with general electric anisotropy.
References
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Journal ArticleDOI
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.
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Computational Electrodynamics: The Finite-Difference Time-Domain Method
TL;DR: This paper presents background history of space-grid time-domain techniques for Maxwell's equations scaling to very large problem sizes defense applications dual-use electromagnetics technology, and the proposed three-dimensional Yee algorithm for solving these equations.
Book
Finite Element Methods for Maxwell's Equations
TL;DR: In this paper, a survey of finite element methods for approximating the time harmonic Maxwell equations is presented, and error estimates for problems with spatially varying coefficients are compared for three DG families: interior penalty type, hybridizable DG, and Trefftz type methods.
Journal ArticleDOI
Solving unsymmetric sparse systems of linear equations with PARDISO
Olaf Schenk,Klaus Gärtner +1 more
TL;DR: Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsympetric matrices from real world applications.
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