skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

Abstract

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest ordermore » adaptive FEM.« less

Authors:
 [1];  [2]
  1. ETH Zurich, Zurich (Switzerland)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1440727
Report Number(s):
LLNL-JRNL-665742
Journal ID: ISSN 0016-8033; 787283
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Geophysics
Additional Journal Information:
Journal Volume: 80; Journal Issue: 6; Journal ID: ISSN 0016-8033
Publisher:
Society of Exploration Geophysicists
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; electromagnetics; finite element; magnetotelluric; modeling; algorithm

Citation Formats

Grayver, Alexander V., and Kolev, Tzanio V. Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method. United States: N. p., 2015. Web. doi:10.1190/geo2015-0013.1.
Grayver, Alexander V., & Kolev, Tzanio V. Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method. United States. doi:10.1190/geo2015-0013.1.
Grayver, Alexander V., and Kolev, Tzanio V. Sun . "Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method". United States. doi:10.1190/geo2015-0013.1. https://www.osti.gov/servlets/purl/1440727.
@article{osti_1440727,
title = {Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method},
author = {Grayver, Alexander V. and Kolev, Tzanio V.},
abstractNote = {Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.},
doi = {10.1190/geo2015-0013.1},
journal = {Geophysics},
number = 6,
volume = 80,
place = {United States},
year = {2015},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 23 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
journal, January 2007

  • Hiptmair, Ralf; Xu, Jinchao
  • SIAM Journal on Numerical Analysis, Vol. 45, Issue 6
  • DOI: 10.1137/060660588

High-Order Symplectic Integration Methods for Finite Element Solutions to Time Dependent Maxwell Equations
journal, August 2004

  • Rieben, R.; White, D.; Rodrigue, G.
  • IEEE Transactions on Antennas and Propagation, Vol. 52, Issue 8
  • DOI: 10.1109/TAP.2004.832356

A finite-element-based domain-decomposition approach for plane wave 3D electromagnetic modeling
journal, November 2014

  • Ren, Zhengyong; Kalscheuer, Thomas; Greenhalgh, Stewart
  • GEOPHYSICS, Vol. 79, Issue 6
  • DOI: 10.1190/geo2013-0376.1

Low-frequency electromagnetic fields in applied geophysics: Waves or diffusion?
journal, July 2006

  • Løseth, Lars O.; Pedersen, Hans M.; Ursin, Bjørn
  • GEOPHYSICS, Vol. 71, Issue 4
  • DOI: 10.1190/1.2208275

Data structures and requirements for hp finite element software
journal, March 2009

  • Bangerth, W.; Kayser-Herold, O.
  • ACM Transactions on Mathematical Software, Vol. 36, Issue 1
  • DOI: 10.1145/1486525.1486529

Moving curved mesh adaptation for higher-order finite element simulations
journal, February 2010

  • Luo, Xiao-Juan; Shephard, Mark S.; Lee, Lie-Quan
  • Engineering with Computers, Vol. 27, Issue 1
  • DOI: 10.1007/s00366-010-0179-5

Adaptive Finite Element Methods with convergence rates
journal, April 2004


p4est : Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
journal, January 2011

  • Burstedde, Carsten; Wilcox, Lucas C.; Ghattas, Omar
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 3
  • DOI: 10.1137/100791634

Fast simplicial quadrature-based finite element operators using Bernstein polynomials
journal, November 2011


Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics-a marine CSEM example: 3-D FE simulation for geo-electromagnetics
journal, August 2011


Marine Electromagnetic Studies of Seafloor Resources and Tectonics
journal, June 2011


BoomerAMG: A parallel algebraic multigrid solver and preconditioner
journal, April 2002


Exploring for Geothermal Resources with Electromagnetic Methods
journal, May 2013


Numerical Modelling in Geo-Electromagnetics: Advances and Challenges
journal, October 2009


A residual-based a posteriori error estimator for the hp-finite element method for Maxwellʼs equations
journal, August 2012


An Adaptive Finite Element Method for the Eddy Current Model with Circuit/Field Couplings
journal, January 2010

  • Chen, Junqing; Chen, Zhiming; Cui, Tao
  • SIAM Journal on Scientific Computing, Vol. 32, Issue 2
  • DOI: 10.1137/080713112

A Convergent Adaptive Algorithm for Poisson’s Equation
journal, June 1996

  • Dörfler, Willy
  • SIAM Journal on Numerical Analysis, Vol. 33, Issue 3
  • DOI: 10.1137/0733054

Robust and scalable 3-D geo-electromagnetic modelling approach using the finite element method
journal, April 2014

  • Grayver, Alexander V.; Bürg, Markus
  • Geophysical Journal International, Vol. 198, Issue 1
  • DOI: 10.1093/gji/ggu119

Bernstein–Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
journal, January 2011

  • Ainsworth, Mark; Andriamaro, Gaelle; Davydov, Oleg
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 6
  • DOI: 10.1137/11082539X

Methods for modelling electromagnetic fields Results from COMMEMI—the international project on the comparison of modelling methods for electromagnetic induction
journal, October 1997


Algorithms and data structures for massively parallel generic adaptive finite element codes
journal, December 2011

  • Bangerth, Wolfgang; Burstedde, Carsten; Heister, Timo
  • ACM Transactions on Mathematical Software, Vol. 38, Issue 2
  • DOI: 10.1145/2049673.2049678

Toward an h-Independent Algebraic Multigrid Method for Maxwell's Equations
journal, January 2006

  • Hu, Jonathan J.; Tuminaro, Raymond S.; Bochev, Pavel B.
  • SIAM Journal on Scientific Computing, Vol. 27, Issue 5
  • DOI: 10.1137/040608118

Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations
journal, December 2011


Parallel Auxiliary Space AMG for H(Curl) Problems
journal, June 2009

  • Vassilevski, Tzanio V. Kolev Panayot S.
  • Journal of Computational Mathematics, Vol. 27, Issue 5
  • DOI: 10.4208/jcm.2009.27.5.013

Three-dimensional h-adaptivity for the multigroup neutron diffusion equations
journal, April 2009


Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction
journal, December 2011


The h-p version of the finite element method: Part 1: The basic approximation results
journal, March 1986


Conditioning of Hierarchic p -Version Nédélec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra
journal, January 2003


A multigrid solver for 3D electromagnetic diffusion: Multigrid for 3D EM
journal, September 2006


Efficient pre-conditioned iterative solution strategies for the electromagnetic diffusion in the Earth: finite-element frequency-domain approach
journal, March 2013

  • Um, Evan Schankee; Commer, Michael; Newman, Gregory A.
  • Geophysical Journal International, Vol. 193, Issue 3
  • DOI: 10.1093/gji/ggt071

Convergence of an automatic hp-adaptive finite element strategy for Maxwellʼs equations
journal, October 2013


A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling
journal, May 2013

  • Ren, Zhengyong; Kalscheuer, Thomas; Greenhalgh, Stewart
  • Geophysical Journal International, Vol. 194, Issue 2
  • DOI: 10.1093/gji/ggt154

The h-p version of the finite element method: Part 2: General results and applications
journal, September 1986


    Works referencing / citing this record:

    3D frequency-domain airborne EM forward modelling using spectral element method with Gauss–Lobatto–Chebyshev polynomials
    journal, June 2019


    On the forward modelling of three-dimensional magnetotelluric data using a radial-basis-function-based mesh-free method
    journal, July 2019

    • Long, Jianbo; Farquharson, Colin G.
    • Geophysical Journal International, Vol. 219, Issue 1
    • DOI: 10.1093/gji/ggz306

    3D frequency-domain airborne EM forward modelling using spectral element method with Gauss–Lobatto–Chebyshev polynomials
    journal, June 2019


    On the forward modelling of three-dimensional magnetotelluric data using a radial-basis-function-based mesh-free method
    journal, July 2019

    • Long, Jianbo; Farquharson, Colin G.
    • Geophysical Journal International, Vol. 219, Issue 1
    • DOI: 10.1093/gji/ggz306

    Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data
    journal, September 2019


    Edge-based finite-element modeling of 3D frequency-domain electromagnetic data in general dispersive medium
    journal, February 2019


    Exact solutions of the vertical gravitational anomaly for a polyhedral prism with vertical polynomial density contrast of arbitrary orders
    journal, June 2018

    • Chen, Chaojian; Ren, Zhengyong; Pan, Kejia
    • Geophysical Journal International, Vol. 214, Issue 3
    • DOI: 10.1093/gji/ggy250

    Topographic distortions of magnetotelluric transfer functions: a high-resolution 3-D modelling study using real elevation data
    journal, September 2018

    • Käufl, Johannes S.; Grayver, Alexander V.; Kuvshinov, Alexey V.
    • Geophysical Journal International, Vol. 215, Issue 3
    • DOI: 10.1093/gji/ggy375

    Parallel 3-D marine controlled-source electromagnetic modelling using high-order tetrahedral Nédélec elements
    journal, June 2019

    • Castillo-Reyes, Octavio; de la Puente, Josep; García-Castillo, Luis Emilio
    • Geophysical Journal International, Vol. 219, Issue 1
    • DOI: 10.1093/gji/ggz285

    Joint 3D inversion of multiple electromagnetic datasets: Joint 3D inversion of multiple EM datasets
    journal, October 2015


    Tippers at island geomagnetic observatories constrain electrical conductivity of oceanic lithosphere and upper mantle
    journal, February 2019

    • Morschhauser, Achim; Grayver, Alexander; Kuvshinov, Alexey
    • Earth, Planets and Space, Vol. 71, Issue 1
    • DOI: 10.1186/s40623-019-0991-0

    Multi-order vector finite element modeling of 3D magnetotelluric data including complex geometry and anisotropy
    journal, August 2019

    • Rivera-Rios, Aixa M.; Zhou, Bing; Heinson, Graham
    • Earth, Planets and Space, Vol. 71, Issue 1
    • DOI: 10.1186/s40623-019-1071-1