Improved finite-difference formulation in frequency domain for three-dimensional scattering problems

Beilenhoff, K.; Heinrich, W.; Hartnagel, H.L.

doi:10.1109/22.121730

Cited by 62 publications

(30 citation statements)

References 8 publications

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“…The resulting equations are cumbersome; however, presenting each expression using matrices provides a compact form. Thus, extending the lossless and isotropic methods of Beilenhoff et al [19] to our case of lossy and anisotropic media, and using notation defined in the Appendix, (1) and (2) become…”

Section: Fig 2 the Field Quantities Associated With The Mth Cell (Imentioning

confidence: 99%

“…The FDFD formulation presented here is an extension to lossy media of a method developed for lossless media in [19]. The mesh-truncation approach involves using an anisotropic absorbing PML following the ideas in [7,24].…”

Section: Fdfd Algorithmmentioning

confidence: 99%

“…For these applications, we have developed a new 3D code for use in electromagnetic induction tomography, especially for environmental imaging problems. The finite-difference frequency-domain (FDFD) formulation is based on that in [19], and an anisotropic perfectly matched layer (PML) approach [7,20] is used to specify the nonreflecting boundary conditions. The unique features of the method include perfectly matched layer boundaries [7,20], specifically tailored to provide optimum results in the target frequency range (the lower kHz regime), and code structure that permits convenient computation of the adjoint field operator (which is needed for the data-inversion method developed in parallel [21]).…”

Section: Introductionmentioning

confidence: 99%

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FDFD: A 3D Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography

Champagne

Berryman

Buettner

2001

Journal of Computational Physics

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Section: Fig 2 the Field Quantities Associated With The Mth Cell (Imentioning

confidence: 99%

Section: Fdfd Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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FDFD: A 3D Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography

Champagne

Berryman

Buettner

2001

Journal of Computational Physics

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“…Because of the practical frequency range (< 1 MHz), it is adequate to ignore displacement currents in the formulation as is typically done by other researchers, but it is not essential to do so in the particular implementation that we have chosen. We have used the finite-difference frequency-domain formulation of Beilenhoff et al (1992) and the anisotropic PML (perfectly matched layer) approach (Berenger, 1994) to boundary conditions of Wu et al (1997) to deal with the fact that the computations must be done in a finite domain even though the real problem is effectively of infinite domain. The resulting formulas for the forward solver reduce to a problem of the form (1) Ax=y, where A is a non-Hermitian matrix with real values off the diagonal and complex values along its diagonal (Smith, 1996a,b).…”

Section: Progress In Code Developmentmentioning

confidence: 99%

Surface and Borehole Electromagnetic Imaging of Conducting Contaminant Plumes

Berryman¹

2000

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Electromagnetic induction tomography is a promising new tool for imaging electrical conductivity variations in the earth. The EM source field is produced by induction coil (magnetic dipole) transmitters deployed at the surface or in boreholes. Vertical and horizontal component magnetic field detectors are deployed in other boreholes or on the surface. Sources and receivers are typically deployed in a configuration surrounding the region of interest. The goal of this procedure is to image electrical conductivity variations in the earth, much as x-ray tomography is used to image density variations through cross-sections of the body. Although such EM field techniques have been developed and applied, the algorithms for inverting the magnetic field data to produce the desired images of electrical conductivity have not kept pace. One of the main reasons for the lag in the algorithm development has been the fact that the magnetic induction problem is inherently three dimensional; other imaging methods such as x-ray and seismic can make use of two-dimensional approximations that are not too far from reality, but we do not have this luxury in EM induction tomography. In addition, previous field experiments were conducted at controlled test sites that typically do not have much external noise or extensive surface clutter problems often associated with environmental sites. To use the same field techniques in environments more typical of cleanup sites requires a new set of data processing tools to remove the effects of both noise and clutter. The goal of this project is to join theory and experiment to produce enhanced images of electrically conducting fluids underground, allowing better localization of contaminants and improved planning strategies for the subsequent remediation efforts. After explaining the physical context in more detail, this report will summarize the progress made in the first 18 months of this project: (1) on code development and (2) on field tests of these methods. We conclude with a brief statement of the research directions for the remainder of this three year project.

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“…Because of the practical frequency range (C 1 MHz), it is adequate to ignore displacement currents in the formulation as is typically done by other researchers, but it is not essential to do so in the particular implementation that we have chosen. We have used the finite-difference frequency-domain formulation of Beilenhoff et al (1992) and the anisotropic PML (perfectly matched layer) approach (Berenger, 1994) to boundary conditions of Wu et al (1997) to deal with the fact that the computations must be done in a finite domain even though the real problem is effectively of infinite domain, The resulting formulas for the forward solver reduce to a problem of the form fix =.Y, where A is a non-Hermitian matrix with real values off the diagonal and complex values along its diagonal (Smith, 1996a,b). The matrix A may be either symmetric or nonsymmetric depending on details of the boundary conditions chosen (i.e., the particular PML used in the applcation).…”

Section: Forward Modelingmentioning

confidence: 99%

Environmental management science program FY1997 progress report

Carrigan¹

1998

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Research ObjectiveThe objective of this work is to determine the fundamental data needed to predict the behavior of Sr at temperature and time scales appropriate to thermal remediation, because 9oSr is a major contaminant at Hanford and INEL sites (Duncan, 1995) and thermally-enhanced technologies used to remediate organic contaminants (Newmark and Aines, 1995) may improve the efficiency and speed of metal remediation as well. Research StatementOur approach combines macroscopic sorption/precipitation and desorption/dissolution kinetic experiments, which track changes in solution composition, with direct molecular characterization of Sr in the solid phase using X-ray absorption spectroscopy. These experiments will be used to identify mechanistic geochemical reactions and their thermochemical properties that will be incorporated into geochemical computer codes. Research ProgressThis report consists of three sections: 1. Results of Sr sorption to kaolinite and goethite from pH 4 to 10 at 25,50, and 80-C and atmospheric CO,(g); 2. Preliminary spectroscopy results; and 3. Review of the available thermodyanimc data in the is Fe-Sr-Na-N03-C02-H20 system. 1.Strontium sorption to goethite and kaolinite at 25, 50, and 80-C. In our goethite and kaolinite experiments, Sr-uptake begins in solutions undersaturated with respect to strontianite (SrCO,) and increases in more supersaturated solutions. We know that Sr-uptake is enhanced by kaolinite and goethite, because Sr is not removed from solution over the same experimental run conditions in the absence of solid phases. It is possible that ternary Sr-carbonate complexes form at the kaolinite and goethite surfaces, and that they provide the needed "seed carbonate" to precipitate strontianite.This idea builds from direct observation of multinuclear-cobalt-surface complexes on kaolinite (O'Day et al. 1994) and the formation of a mixed nickel-aluminum hydroxide during pyrophyllite dissolution and nickel-uptake (Scheidegger et al. 1996). We expect Sr-uptake to involve the formation of multinuclearSr-carbonate complexes because strontianite is much less soluble than Sr(OH),(s).Temperature-dependence of Sr-uptake to goethite and kaolinite is minimal. This is consistent with the small (about 0.2 orders of magnitude) temperature-dependence of strontianite solubility from 25 to 80-C.Figures l-4 show the results of Sr sorption to goethite and kaolinite at atmospheric pCO,(g) as a function of pH and temperature.In the presence of goethite, significant Sr-uptake occurs at 25, 50, and 80-C from solutions containing pH > 8 and [Sr], = 10T7 to 10m4 M ( Fig. 2 and 3). The absolute Sr-2 uptake increases with increasing [Sr], at constant temperature and at pH 2. There is a slight increase in Sr-uptake with increasing temperature for 65 -1 lo-lo -2 lo'ot""""""""""""""""'~' 3 4 5 8 9 10Figure 1 (continued).-510-8""""I',"""(","""""',, 3;H fincll Similar to goethite, significant Sr-uptake occurs at 25, 50, and 80-C from solutions containing pH > 8 and [Sr], = 10m6 to 10e4 M (Fig. 5 and 6). Minim...

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Improved finite-difference formulation in frequency domain for three-dimensional scattering problems

Cited by 62 publications

References 8 publications

FDFD: A 3D Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography

FDFD: A 3D Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography

Surface and Borehole Electromagnetic Imaging of Conducting Contaminant Plumes

Environmental management science program FY1997 progress report

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