Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series
TL;DR: An edge-based finite-element time-domain (FETD) modeling method to simulate the electromagnetic fields in 3D dispersive medium and considers the Cole-Cole model in order to take into account the frequency-dependent conductivity dispersion.
About: This article is published in Computers & Geosciences.The article was published on 2017-12-01. It has received 35 citations till now. The article focuses on the topics: Time domain & Frequency domain.
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42 citations
TL;DR: Three-dimensional FDEM and TDEM modeling with IP effects is developed using the generic partial-differential-equation solver Comsol Multiphysics's application program interface (API) with Matlab, which could be of great importance in quantitatively studying IP effects in theFDEM andTDEM methods, in developing new field configurations, and in educational purposes.
21 citations
TL;DR: In this paper, a block rational Krylov method is proposed to accelerate three-dimensional time-domain marine controlled-source electromagnetic modeling with multiple sources, which can be as up to 10 times faster than backward Euler.
Abstract: We introduce a novel block rational Krylov method to accelerate three-dimensional time-domain marine controlled-source electromagnetic modeling with multiple sources. This method approximates the time-varying electric solutions explicitly in terms of matrix exponential functions. A main attraction is that no time stepping is required, while most of the computational costs are concentrated in constructing a rational Krylov basis. We optimize the shift parameters defining the rational Krylov space with a positive exponential weight function, thereby producing smaller approximation errors at later times and reducing iteration numbers. Furthermore, for multi-source modeling problems, we adopt block Krylov techniques to incorporate all source vectors in a single approximation space. The method is tested on two examples: a layered seafloor model and a 3D hydrocarbon reservoir model with seafloor bathymetry. The modeling results are found to agree very well with those from 1D semi-analytic solutions and finite-element time-domain solutions using a backward Euler scheme, respectively. Benchmarks of the block rational Krylov method demonstrate that it can be as up to 10 times faster than backward Euler. The block method also benefits from better memory efficiency, resulting in considerable speedup compared to non-block methods.
15 citations
TL;DR: The program is an implementation of the Edge Finite Element method, in an electric field formulation, to simulate any electromagnetic source of interest, at all frequencies that are used in the geophysical methods in the quasi-static regime.
11 citations
TL;DR: A newly developed 3-D parallelized inversion algorithm in the frequency domain with hexahedral discretization using the finite-element method (FEM) in the forward modeling and Gauss–Newton optimization technique in the inversion.
Abstract: Presently, the 3-D inversion technique has started playing a more important role in controlled-source electromagnetic (CSEM) data interpretation. With the development of hardware and computation algorithm, 3-D inversion technique has developed rapidly during the past decades. In this article, we present a newly developed 3-D parallelized inversion algorithm in the frequency domain with hexahedral discretization. Within the framework of this approach, we use the finite-element method (FEM) in the forward modeling and Gauss–Newton optimization technique in the inversion. We solve the forward modeling and adjoint problem efficiently with Math Kernel Library (MKL) Pardiso parallel direct solver. Considering the fact that the forward modeling and sensitivity calculation are frequency independent, we further parallelize the algorithm over frequency using Message Passing Interface (MPI) to speed up the modeling and inversion process. The sensitivity matrix is calculated explicitly, which enables us to estimate the optimized regularization parameter easily based on the spectral radius estimation. We proposed a new roughness operator for hexhedral discretization which works well for CSEM inversion problems. We applied the developed algorithm to several realistic CSEM models. The inversion results demonstrate the effectiveness and stability of our inversion scheme.
10 citations
Cites background from "Finite-element time-domain modeling..."
...Furthermore, the convergence of iterative solver depends significantly on the conductivity contrast and mesh aspect ratio [3], [15], [39]–[44]....
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References
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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.
14,070 citations
"Finite-element time-domain modeling..." refers methods in this paper
...The finite-difference time-domain (FDTD) methods have been used for modeling the electromagnetic response in time domain for decades (Yee, 1966)....
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Book•
19 May 1993
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Abstract: Historical Survey The Modern Approach The Riemann-Liouville Fractional Integral The Riemann-Liouville Fractional Calculus Fractional Differential Equations Further Results Associated with Fractional Differential Equations The Weyl Fractional Calculus Some Historical Arguments.
7,643 citations
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Abstract: Summary Laboratory experiments and field observations indicate that the Q of many non-ferromagnetic inorganic solids is almost frequency independent in the range 10-2-107 cis, although no single substance has been investigated over the entire frequency spectrum. One of the purposes of this investigation is to find the analytic expression for a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges. This will be obtained by introducing fractional derivatives in the stressstrain relation. Since the aim of this research is also to contribute to elucidating the dissipating mechanism in the Earth free modes, we shall treat the dissipation in the free, purely torsional, modes of a shell. The dissipation in a plane wave will also be treated. The theory is checked with the new values determined for the Q of spheroidal free modes of the Earth in the range between 10 and 5 min integrated with the Q of Rayleigh waves in the range between 5 and 0.6 min. Another check of the theory is made with the experimental values of the Q of the longitudinal waves in an aluminium rod in the range between lo-’ and 10-3s. In both checks the theory represents the observed phenomena very satisfactorily. The time derivative which enters the stress-strain relation in both cases is of order 0.15. The present paper is a generalized version of another (Caputo 1966b) in which an elementary definition of some differential operators was used. In this paper we give also a rigorous proof of the formulae to be used in obtaining the analytic expression of Q; moreover, we present two checks of the theory with experimental data. The present paper is a generalized version of another (Caputo 1966b) in which an elementary definition of some differential operators was used. In this paper we give also a rigorous proof of the formulae to be used in obtaining the analytic expression of Q; moreover, we present two checks of the theory with experimental data. In a homogeneous isotropic elastic field the elastic properties of the substance are specified by a description of the strains and stresses in a limited portion of the field since the strains and stresses are linearly related by two parameters which describe the elastic properties of the field. If the elastic field is not homogeneous nor isotropic the properties of the field are specified in a similar manner by a larger number of parameters which also depend on the position.
3,372 citations
"Finite-element time-domain modeling..." refers background in this paper
...(27) In the last formula, the fractional derivative of real order c is defined as (Caputo, 1967): ∂f(t) ∂tc = 1 Γ(n− c) t ∫...
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...(27) In the last formula, the fractional derivative of real order c is defined as (Caputo, 1967): ∂cf(t) ∂tc = 1 Γ(n− c) t∫ c f (n)(s)ds (t− s)c−n+1 , (28) where n is the nearest integer greater than c, f (n)(s) is the n-th order derivative of f (n)(s), and Γ is the gamma function....
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Book•
15 Sep 2006
TL;DR: This paper presents a meta-modelling framework for solving sparse linear systems using cholesky factorization and CSparse, and some examples show how this framework can be modified to handle sparse matrices.
Abstract: Preface 1. Introduction 2. Basic algorithms 3. Solving triangular systems 4. Cholesky factorization 5. Orthogonal methods 6. LU factorization 7. Fill-reducing orderings 8. Solving sparse linear systems 9. CSparse 10. Sparse matrices in MATLAB Appendix: Basics of the C programming language Bibliography Index.
1,366 citations
Additional excerpts
...5.3 (Davis, 2006) for matrix factorization....
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