Computational Electromagnetics

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Computational ElectromagneticsComputational
Bioimaging

• Qianqian Fang
• Research In Progress (RIP 2004)

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Outline

• Macroscopic Electromagnetics
• Computational Electromagnetics (CEM)
• Inverse Problems
• Computational Biomedical Imaging (CBI)
• CBI and CEM

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From DC to Light
Circuit Theory
Matrix Electromagnetics
Wave Electromagnetics
Quantum Mechanics
Optics
http//www.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSp
ec2.html
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Electromagnetism

• Macroscopic Electromagnetism
• Foundation
• Core equations
• Core theorems
• Wave (amplitudes,phase,wavelength,polarization..)
• Radiation
• Scattering
• Circuit(Network)(impedance,S parameters,power,gain
  ...)
• Distributed parameter circuit networks analysis
• Filter design
• Quantum Electro-Dynamics (QED)

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Macroscopic Electromagnetics
Wave equations Transient EM wave/ Time-Harmonic
EM wave/ Time/Frequency domain/ Vector/Scalar
Helmholtz equation Vector/Scalar Wave equation
Core
Energy Conservation Poynting theorem
Maxwell equations
Momentum Conservation
Constitutive relations
Boundary Conditions
Auxiliary Functions vector/scalar elec.
potential vector/scalar mag. potential vector/scal
ar Herzian potential Scalar/dyadic Greens
function
Material Properties isotropic/anisotropic/ Bi-ani
sotropic/uniaxial/ Positive/negative
axial/ Dispersive/stationary
Lorenz force
Mechanics
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Electromagnetics Core Theorems
Duality Principal
Uniqueness Theorem
Greens Theorem
Reciprocity Theorem
Huygens Principal
Equivalence Theorem
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Computational Electromagnetics

• Definition
• Numerical lt-gt Linearization
• High-frequency-gt geometric approx
• Low-frequency-gt difference/variational

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Computational Electromagnetics
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Forward Integration

• Integration Equation MoM, BEM, EFIE/MFIE/CFIE

http//www.lcp.nrl.navy.mil/cfd-cta/CFD3/img_galle
ry/f117/
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Forward Differential
Finite Element Method (FEM)
Finite Difference-Time Domain (FDTD)
http//www.remcom.com/xfdtd6/
http//sdcd.gsfc.nasa.gov/ESS/annual.reports/ess98
/kma.html
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Comparison IE/DE
Integral Equ. Methods Diff. Equ. Methods
Math foundations Gauss/Stokes Theorem Greens Theorem Maxwell equation Variational Principal
Problem Dimensions n-1 n
Constains Global Local
Linearization Dense matrix equation Sparse matrix equation
Discretization Surface mesh Volume mesh
Mesh truncation (RBC/ABC) Typically no need Needed for unbounded problems
Pros Large problems, far fields Near field, inhomogeneous
Cons Inhomogeneous Large unknown
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Inverse Problems

• Inverse Source Problems
• Inverse Scattering Problems
• Mixed Inverse Problems

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Approaches of Solving Inverse Problems

• Operator Equation
• Root Finding
• Optimization

Misfit functional
Regularization functional
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Biomedical Imaging

• Principal
• Encoding/Decoding of information
• Imaging Agent
• Functional Imaging and Structural Imaging

Particles Particles SPECT(photons),PET(positron)
Wave Mechanical Ultrasound,Elastography,Seismology
Wave Electromagnetic EIT,MWI,NIR,CT,X-Ray,MR,SAR
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CBI and CEM

• CT -gt Linear attenuation -gt Filted
  Backprojection -gt Linear Inverse problem
• MRI -gt Inverse Fourier Transform
• Ultrasound
• EIT, MWI, NIR, GPR, -gt Nonlinear propagation
  -gt iterative reconstructions -gt Nonlinear inverse
  problem

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Reference

• W.C. Chew, Waves and Fields in Inhomogeneous
  Media, Van Nostrand Reinhold, New York, 1990.
• J.A. Kong, Electromagnetic Wave Theory,
  Wiley-Interscience, New York, 1990.
• Yvon Jarny, The Inverse Engineering Handbook,
  Chapter 3, CRC Press, 2003.
• C. Vogel, Computational methods for inverse
  problem, SIAM, Philadelphia, 2002.

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Acknowledgement

• Prof. Paul M. Meaney
• Prof. Keith D. Paulsen
• Margaret Fanning
• Dun Li
• Sarah A. Pendergrass
• Colleen J. Fox
• Timothy Raynolds
• Thanks for all my friends at Thayer School.

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Questions?