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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}
}

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