Multiscale Methods For Geophysical Electromagnetics Modeling
Aug 1, 2017
The focus of this investigation is to study how to reduce the computational cost of simulating the behavior of electromagnetic fields in complicated geophysical settings. This type of simulations are crucial to the exploration of buried natural resources (mineral, groundwater and hydrocarbon deposits) using electromagnetic methods. However, the size of the computation they involve often exceeds the limits of average computers.
This investigation proposes innovative mathematical alternatives — multiscale finite elements and finite volume methods — that achieve a great reduction of the problem’s size and the simulation cost without sacrificing much accuracy. It also opens the door to use such alternatives to create more powerful computational engines capable of simulating electromagnetic fields in larger and more complex geophysical settings than currently is possible.
This project was done as part of my doctoral dissertation. To provide more context, this study was the first one in the literature to demonstrate the practical use of the proposed alternatives in the context of geophysical electromagnetic problems.
Luz Angélica Caudillo Mata
Computational Scientist & Community Builder
Passionate about driving innovation and developing cutting-edge technology at the intersection of GeoAI and computational geosciences, while fostering collaborative communities.
Publications
We have developed a mimetic multiscale method to simulate quasistatic Maxwell’s equations in the frequency domain. This is especially …
Wenke Wilhelms,
Christoph Schwarzbach,
Luz Angélica Caudillo Mata,
Eldad Haber
Accurate and efficient simulation of electromagnetic responses in realistic geophysical settings is crucial to the exploration, …
Luz Angélica Caudillo Mata
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
Publication use is subject to SEG terms of use and conditions.
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
Events
Jul 2, 2019
Pacific Northwest National Laboratory, Richland, WA, USA
Jun 20, 2019
Sandia National Laboratories, Albuquerque, NM, USA
Accurate and efficient simulation of electromagnetic responses in realistic exploration geophysical settings is computationally expensive. Such settings involve big domains with highly heterogeneous media and features at multiple spatial scales that require very large meshes to be accurately represented.
Apr 10, 2019
Oden Institute for Computational Engineering and Sciences, UT Austin, TX, USA
Efficient and accurate simulation of electromagnetic responses of geologically-rich geophysical settings is crucial in a variety of scenarios, including mineral and petroleum exploration, water resource utilizations, and geothermal power extractions. In this talk, we develop two multiscale methods to compute such type of responses in a numerically effective manner.
Feb 8, 2019
PIMS-SFU Applied & Computational Math Seminar, Simon Fraser University, Bournaby, BC, Canada
Luz Angélica Caudillo Mata,
Eldad Haber,
Wenke Wilhelms,
Christoph Schwarzbach
In this work, we present two multiscale methods with and without oversampling. These methods simulate quasi-static electromagnetic responses in the frequency domain. They lead to a significant reduction in the size of the final system of equations and the computational time.
Dec 8, 2018
Canadian Mathematical Society Winter Meeting, Vancouver, BC, Canada
Luz Angélica Caudillo Mata,
Eldad Haber,
Wenke Wilhelms,
Christoph Schwarzbach
Los métodos geofísicos electromagnéticos (EM) se han utilizado desde 1900 en aplicaciones industriales, geocientíficas y de ingeniería en todo el mundo para detectar, localizar y caracterizar recursos naturales en el subsuelo.
Oct 4, 2018
3rd International Conference on Mathematical Modelling, Oaxaca, Mexico
Luz Angélica Caudillo Mata
Jul 25, 2018
25th International Domain Decomposition Conference, Memorial University, St. John's, NL, Canada
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
Accurate and efficient simulation of electromagnetic (EM) responses in large-scale settings with highly heterogeneous media and features varying at multiple spatial scales is crucial to the exploration and imaging of geological formations in a wide range of geophysical applications.
Jul 25, 2017
Mathematical Congress of the Americas 2017, Montreal, QC, Canada
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
Mar 29, 2017
6th International Symposium on Three-Dimensional Electromagnetics (3DEM-6), Berkeley, CA, USA
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
Simulation of electromagnetic fields in geophysical settings that include highly heterogeneous media and features varying at multiple spatial scales is computationally expensive. These settings often require very fine and large meshes to be discretized accurately.
Mar 3, 2017
SIAM Conference on Computational Science and Engineering 2017, Atlanta, GA, USA
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
To reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static Maxwells equations in the frequency domain.
Oct 19, 2016
SEG Annual Meeting 2016, Dallas, TX, USA
Luz Angélica Caudillo Mata,
Eldad Haber,
Christoph Schwarzbach
Sep 2, 2016
ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, Amsterdam, Netherlands
L.A. Caudillo Mata,
E. Haber and C. Schwarzbach
La simulación de campos electromagnéticos en medios altamente heterogéneos es una de las herramientas numéricas más importantes en prospección geofísica. Actualmente, esta herramienta se usa con fin comercial, principalmente, en la identificación y caracterización de yacimientos de minerales y de petróleo.
Aug 18, 2016
3ra Reunión de Matemáticos Mexicanos en el Mundo, Centro de Investigación en Matemáticas, A. C., Guanajuato, Mexico
Luz Angélica Caudillo Mata
Geophysical simulations in large-scale heterogeneous media are computationally expensive. Discrete models require large meshes leading to solve huge systems of equations.
Spectral element-agglomeration multigrid (SA-AMGe) is a discretization framework for diffusion equations that reduces significantly the computational cost while providing accurate solutions.
Aug 4, 2016
Interns Summer Poster Symposium, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
Luz Angélica Caudillo Mata,
Xiaoye Sherry Li,
Alex Drunski,
Panayot Vassilevski,
Andrew Barker
Efficient and accurate simulation of transient electromagnetic fields and fluxes of complex geological settings is crucial in a variety of scenarios, including mineral and petroleum exploration, water resource utilizations and geothermal power extractions.
Mar 24, 2016
14th Copper Mountain Conference on Iterative Methods, Copper Mountain, CO, USA
Luz Angélica Caudillo Mata,
Eldad Haber
Jun 30, 2015
SIAM conference on Mathematical and Computational Issues in the Geosciences, Stanford University, Stanford, CA, USA
Luz Angélica Caudillo Mata,
Eldad Haber
In Geophysics, simulation of low-frequency Electromagnetic (EM) fields in highly heterogeneous, anisotropic media is computationally very expensive. One reason being the multiple length scales that coexist in a given realistic setting.
Apr 13, 2015
Eleventh Annual IAM Retreat 2015, Institute of Applied Mathematics, University of British Columbia, Copper Mountain, CO, USA
Luz Angélica Caudillo Mata,
Eldad Haber,
Lars Ruthotto,
Christoph Schwarzbach
In Geophysics, simulation of low-frequency Electromagnetic (EM) fields in highly heterogeneous, anisotropic media is computationally very expensive. One reason being the multiple length scales that coexist in a given realistic setting.
Mar 27, 2015
17th Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO, USA
Luz Angélica Caudillo Mata,
Eldad Haber,
Lars Ruthotto,
Christoph Schwarzbach
In Geophysics, simulation of low-frequency Electromagnetic (EM) fields in highly heterogeneous, anisotropic media is computationally expensive. One reason being the multiple length scales that coexist in a given realistic setting. Discrete models require very fine meshes leading to solve large linear systems of equations.
Mar 18, 2015
SIAM Conference in Computational Science and Engineering 2015, Salt Lake City, UT, USA
Luz Angélica Caudillo Mata,
Eldad Haber,
Lars Ruthotto,
Christoph Schwarzbach