Parallelized 3D CSEM modeling using edge-based finite element with total field formulation and unstructured mesh

doi:10.1016/J.CAGEO.2016.11.009

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Parallelized 3D CSEM modeling using edge-based finite element with total field formulation and unstructured mesh

Journal Article•DOI•

Parallelized 3D CSEM modeling using edge-based finite element with total field formulation and unstructured mesh

Hongzhu Cai, Xiangyun Hu¹, Jianhui Li¹, Masashi Endo, Bin Xiong² - Show less +1 more•Institutions (2)

China University of Geosciences (Wuhan)¹, Guilin University of Technology²

01 Feb 2017-Computers & Geosciences (Pergamon)-Vol. 99, pp 125-134

TL;DR: An edge-based finite element method for 3D CSEM modeling which is effective in modeling complex geometry such as bathymetry and capable of dealing with anisotropic conductivity is developed.

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About: This article is published in Computers & Geosciences.The article was published on 2017-02-01. It has received 66 citations till now. The article focuses on the topics: Finite element method & Computational electromagnetics.

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Journal Article•DOI•

PETGEM: A parallel code for 3D CSEM forward modeling using edge finite elements

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Octavio Castillo-Reyes¹, Josep de la Puente¹, José María Cela¹•Institutions (1)

Barcelona Supercomputing Center¹

14 May 2018-Computers & Geosciences

TL;DR: An automatic mesh adaptation strategy for a given frequency and specific source position is presented and a scalability study based on fundamental metrics for high-performance computing (HPC) architectures is presented.

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39 citations

Journal Article•DOI•

Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series

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Hongzhu Cai¹, Hongzhu Cai², Xiangyun Hu³, Bin Xiong⁴, Michael S. Zhdanov², Michael S. Zhdanov⁵ - Show less +2 more•Institutions (5)

Aarhus University¹, University of Utah², China University of Geosciences (Wuhan)³, Guilin University of Technology⁴, Moscow Institute of Physics and Technology⁵

01 Dec 2017-Computers & Geosciences

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.

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35 citations

Journal Article•DOI•

A hybrid solver based on the integral equation method and vector finite-element method for 3D controlled-source electromagnetic method modeling

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Rong Liu¹, Rongwen Guo¹, Jianxin Liu¹, Changying Ma¹, Zhenwei Guo¹ - Show less +1 more•Institutions (1)

Central South University¹

01 Sep 2018-Geophysics

TL;DR: The integral equation method (IEM) and differential equation methods have been widely applied to provide numerical solutions of the electromagnetic (EM) fields caused by inhomogeneity for t... as mentioned in this paper.

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Abstract: The integral equation method (IEM) and differential equation methods have been widely applied to provide numerical solutions of the electromagnetic (EM) fields caused by inhomogeneity for t...

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23 citations

Journal Article•DOI•

Time Domain Finite Element Method for Maxwell’s Equations

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Asad Anees¹, Lutz Angermann¹•Institutions (1)

Clausthal University of Technology¹

13 May 2019-IEEE Access

TL;DR: A time domain finite element method for the approximate solution of Maxwell’s equations with weak formulation for the electric and magnetic fields with appropriate initial and boundary conditions is derived.

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Abstract: In this paper, we discuss a time domain finite element method for the approximate solution of Maxwell's equations. A weak formulation is derived for the electric and magnetic fields with appropriate initial and boundary conditions, and the problem is discretized both in space and time. In space, Nedelec curl-conforming and Raviart-Thomas div-conforming finite elements are used to discretize the electric and magnetic fields, respectively. The backward Euler and symplectic schemes are applied to discretize the problem in time. For this system, we prove an error estimate. In addition, computational experiments are presented to validate the method, the electric and magnetic fields are visualized. The method also allows treating complex geometries of various physical systems coupled to electromagnetic fields in 3D.

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22 citations

Journal Article•DOI•

Three-dimensional modeling of frequency- and time-domain electromagnetic methods with induced polarization effects

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Youzheng Qi¹, Hesham El-Kaliouby, André Revil¹, Abdellahi Soueid Ahmed¹, Ahmad Ghorbani², Jianhui Li³ - Show less +2 more•Institutions (3)

University of Savoy¹, Yazd University², China University of Geosciences (Wuhan)³

01 Mar 2019-Computers & Geosciences

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.

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21 citations

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References

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Book•

Iterative Methods for Sparse Linear Systems

[...]

Yousef Saad

01 Apr 2003

TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.

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Abstract: Preface 1. Background in linear algebra 2. Discretization of partial differential equations 3. Sparse matrices 4. Basic iterative methods 5. Projection methods 6. Krylov subspace methods Part I 7. Krylov subspace methods Part II 8. Methods related to the normal equations 9. Preconditioned iterations 10. Preconditioning techniques 11. Parallel implementations 12. Parallel preconditioners 13. Multigrid methods 14. Domain decomposition methods Bibliography Index.

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13,484 citations

"Parallelized 3D CSEM modeling using..." refers methods in this paper

...The iterative solvers were widely used for solving 3D EM forward modeling problem for less memory requirement (Axelsson, 1994; Badea et al., 2001; Cai et al., 2014; Freund and Nachtigal, 1991; Puzyrev et al., 2013; Saad, 2003)....
[...]

Book•

The Finite Element Method in Electromagnetics

[...]

Jian-Ming Jin

01 Mar 1993

TL;DR: The Finite Element Method in Electromagnetics, Third Edition as discussed by the authors is a leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetic engineering.

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Abstract: A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagneticsThe finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration.The Finite Element Method in Electromagnetics, Third Edition explains the methods processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applicationsgiving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems.Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes:A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonicsThe finite element analysis of wave propagation, scattering, and radiation in periodic structuresThe time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomenaNovel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystalsAlong with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

...read moreread less

3,705 citations

"Parallelized 3D CSEM modeling using..." refers background or methods in this paper

...The conventional node-based FE suffers from spurious solutions since the divergence free condition in source free region and the tangential field continuity is not imposed (Jin, 2002, 2014; Puzyrev et al., 2013)....
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...The node basis functions are given by L L L L( , , , )e e e e1 2 3 4 and the vector basis function can be represented as (Nédélec, 1980; Jin, 2002, 2014): L L L L lN = ( ∇ − ∇ ) ,ie ie ie ie ie ie1 2 2 1 (6) where i1 and i2 are two nodes connected to the ith edge; li e is the edge length....
[...]
...After FE analysis, we obtain a sparse system of equations which can be solved with iterative or direct methods (Jin, 2002, 2014)....
[...]
...The integrals in (10) and (11) is calculated by using Gauss quadrature method with 11 Gauss sampling points (Jin, 2002, 2014)....
[...]
...One approach to overcome this obstacle is by adopting the electromagnetic potentials formulation (Badea et al., 2001; Jin, 2002; Puzyrev et al., 2013)....
[...]

Journal Article•DOI•

Mixed finite elements in ℝ 3

[...]

Jean-Claude Nédélec¹•Institutions (1)

École Polytechnique¹

01 Sep 1980-Numerische Mathematik

TL;DR: In this article, the authors present two families of non-conforming finite elements, built on tetrahedrons or on cubes, which are respectively conforming in the spacesH(curl) and H(div).

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Abstract: We present here some new families of non conforming finite elements in ?3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.

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3,049 citations

"Parallelized 3D CSEM modeling using..." refers background or methods in this paper

...The node basis functions are given by L L L L( , , , )e e e e1 2 3 4 and the vector basis function can be represented as (Nédélec, 1980; Jin, 2002, 2014): L L L L lN = ( ∇ − ∇ ) ,ie ie ie ie ie ie1 2 2 1 (6) where i1 and i2 are two nodes connected to the ith edge; li e is the edge length....
[...]
...The node basis functions are given by L L L L ( , , , ) e e e e 1 2 3 4 and the vector basis function can be represented as (Nédélec, 1980; Jin, 2002, 2014):...
[...]
...Another approach to overcome this problem is by using the edgebased FE formulation (Nédélec, 1980; Jin, 2002; Silva et al., 2012)....
[...]

Book•

Iterative Solution Methods

[...]

Owe Axelsson¹•Institutions (1)

Radboud University Nijmegen¹

05 Aug 2012

TL;DR: This paper presents a meta-analyses of matrix eigenvalues and condition numbers for preconditional matrices using the framework of the Perron-Frobenius theory for nonnegative matrices and some simple iterative methods.

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Abstract: Preface Acknowledgements 1. Direct solution methods 2. Theory of matrix eigenvalues 3. Positive definite matrices, Schur complements, and generalized eigenvalue problems 4. Reducible and irreducible matrices and the Perron-Frobenius theory for nonnegative matrices 5. Basic iterative methods and their rates of convergence 6. M-matrices, convergent splittings, and the SOR method 7. Incomplete factorization preconditioning methods 8. Approximate matrix inverses and corresponding preconditioning methods 9. Block diagonal and Schur complement preconditionings 10. Estimates of eigenvalues and condition numbers for preconditional matrices 11. Conjugate gradient and Lanczos-type methods 12. Generalized conjugate gradient methods 13. The rate of convergence of the conjugate gradient method Appendices.

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2,043 citations

"Parallelized 3D CSEM modeling using..." refers methods in this paper

...The iterative solvers were widely used for solving 3D EM forward modeling problem for less memory requirement (Axelsson, 1994; Badea et al., 2001; Cai et al., 2014; Freund and Nachtigal, 1991; Puzyrev et al., 2013; Saad, 2003)....
[...]

Journal Article•DOI•

QMR: a quasi-minimal residual method for non-Hermitian linear systems

[...]

Roland W. Freund¹, Noël M. Nachtigal²•Institutions (2)

Ames Research Center¹, Massachusetts Institute of Technology²

01 Dec 1991-Numerische Mathematik

TL;DR: A novel BCG-like approach, the quasi-minimal residual (QMR) method, which overcomes the problems of BCG is presented and how BCG iterates can be recovered stably from the QMR process is shown.

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Abstract: The biconjugate gradient (BCG) method is the "natural" generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. In this paper, we present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

...read moreread less

985 citations

"Parallelized 3D CSEM modeling using..." refers methods in this paper

...The iterative solvers were widely used for solving 3D EM forward modeling problem for less memory requirement (Axelsson, 1994; Badea et al., 2001; Cai et al., 2014; Freund and Nachtigal, 1991; Puzyrev et al., 2013; Saad, 2003)....
[...]