Accuracy improvement in nonlinear magnetostatic field computations with integral equation methods and indirect total scalar potential formulations

2006 ◽  
Vol 25 (3) ◽  
pp. 565-571 ◽  
Author(s):  
Wolfgang Hafla ◽  
André Buchau ◽  
Wolfgang M. Rucker
Keyword(s):  
Integral Equation ◽  
Scalar Potential ◽  
Integral Equation Method ◽  
Computational Accuracy ◽  
Magnetostatic Field ◽  
Content Type ◽  
Demagnetizing Field ◽  
Difference Field ◽  
Excitation Potential ◽  
New Formulation

PurposeThe paper seeks to solve nonlinear magnetostatic field problems with the integral equation method and different indirect formulations.Design/methodology/approachTo avoid large cancellation errors in cases where the demagnetizing field is high a difference field concept is used. This requires the computation of sources of the scalar potential of the excitation field.FindingsA new formulation to compute these sources is presented. The improved computational accuracy is demonstrated with numerical examples.Originality/valueThe paper develops a novel formulation for the computation of sources of scalar excitation potential.

Near and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method

2018 ◽  
Vol 35 (1) ◽  
pp. 432-476 ◽  
Author(s):  
Jungki Lee ◽  
Hogwan Jeong
Keyword(s):  
Integral Equation ◽  
Wave Scattering ◽  
Integral Equation Method ◽  
Far Field ◽  
Volume Integral ◽  
Sh Waves ◽  
Content Type ◽  
Volume Integral Equation ◽  
Parallel Volume ◽  
Volume Integral Equation Method

Purpose The purpose of this paper is to calculate near field and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method (PVIEM) quantitatively. Design/methodology/approach The PVIEM is applied for the analysis of elastic wave scattering problems in an unbounded solid containing multiple multilayered anisotropic circular inclusions. It should be noted that this numerical method does not require the use of the Green’s function for the inclusion – only the Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general elastodynamic problems involving inhomogeneous and/or anisotropic inclusions whose shape and number are arbitrary. Findings A detailed analysis of the SH wave scattering problem is presented for multiple multilayered orthotropic circular inclusions. Numerical results are presented for the displacement fields at the interfaces and the far field scattering patterns for square and hexagonal packing arrays of multilayered circular inclusions in a broad frequency range of practical interest. Originality/value To the best of the authors’ knowledge, the solution for scattering of SH waves by multiple multilayered anisotropic circular inclusions in an unbounded isotropic matrix is not currently available in the literature. However, in this paper, calculation of displacements on interfaces and far field scattering patterns of multiple multilayered anisotropic circular inclusions using PVIEM as a pioneer of numerical modeling enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), the multilayer’s geometry, isotropy/anisotropy and softness/hardness.

Integral equation method for 3D modeling of electromagnetic fields in complex structures with inhomogeneous background conductivity

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. G333-G345 ◽  
Author(s):  
Michael S. Zhdanov ◽  
Seong Kon Lee ◽  
Ken Yoshioka
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Problem Solution ◽  
Complex Structures ◽  
Accuracy Control ◽  
Iterative Inversion ◽  
1D Model ◽  
Em Field ◽  
New Formulation

We present a new formulation of the integral equation (IE) method for three-dimensional (3D) electromagnetic (EM) modeling in complex structures with inhomogeneous background conductivity (IBC). This method overcomes the standard limitation of the conventional IE method related to the use of a horizontally layered background only. The new 3D IE EM modeling method still employs the Green’s functions for a horizontally layered 1D model. However, the new method allows us to use an inhomogeneous background with the IE method. We also introduce an approach for accuracy control of the IBC IE method. This new approach provides us with the ability to improve the accuracy of computations by applying the IBC technique iteratively. This approach seems to be extremely useful in computing EM data for multiple geologic models with some common geoelectrical features, like terrain, bathymetry, or other known structures. It may find wide application in an inverse problem solution, where we have to keep some known geologic structures unchanged during the iterative inversion. The method was carefully tested for modeling the EM field for complex structures with a known variable background conductivity. The effectiveness of this approach is illustrated by modeling marine controlled-source electromagnetic (MCSEM) data in the area of Gemini Prospect, Gulf of Mexico.

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