RIP 2004 1

Computational Electromagnetics&

Computational BioimagingQianqian Fang

Research In Progress (RIP 2004)

THAYERSCHOOL OF

ENGINEERINGD A R T M O U T H C O L L E G E

THAYERSCHOOL OF

ENGINEERINGD A R T M O U T H C O L L E G E

RIP 2004 2

Outline

• Macroscopic Electromagnetics

• Computational Electromagnetics (CEM)

• Inverse Problems• Computational Biomedical

Imaging (CBI)• CBI and CEM

RIP 2004 3

From DC to LightCircuit

Theory

Matrix

Electromagnetics

Wave

Electromagnetics

Quantum

MechanicsOptics

http://www.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html

RIP 2004 4

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)

RIP 2004 5

Macroscopic Electromagnetics

Energy

Conservation

Poynting theorem

Momentum

Conservation

Auxiliary Functions

vector/scalar elec. potential

vector/scalar mag. potential

vector/scalar Herzian potential

Scalar/dyadic Green’s function

Wave equations

Transient EM wave/

Time-Harmonic EM wave/

Time/Frequency domain/

Vector/Scalar Helmholtz equation

Vector/Scalar Wave equation

Material Properties:

isotropic/anisotropic/

Bi-anisotropic/uniaxial/

Positive/negative axial/

Dispersive/stationary

Lorenz force

Mechanics

Maxwell equations

Constitutive relations

Boundary Conditions

Core

RIP 2004 6

Electromagnetics: Core Theorems

Duality

Principal

Equivalen

ce

Theorem

Reciprocit

y

Theorem

Uniquene

ss

Theorem

Huygens’

Principal

Green’s

Theorem

RIP 2004 7

Computational Electromagnetics

• Definition• Numerical <-> Linearization• High-frequency-> geometric

approx• Low-frequency->

difference/variational

RIP 2004 8

Computational Electromagnetics

Computational

Electromagnetics

Computational

Electromagnetics

Forward ProblemsForward Problems Inverse ProblemsInverse Problems

High-Frequency MethodsHigh-Frequency Methods Low-Frequency MethodsLow-Frequency Methods Analytical methodsAnalytical methods Inverse Source ProblemInverse Source Problem Inverse ScatteringInverse Scattering

RIP 2004 9

Forward: Integration

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

http://www.lcp.nrl.navy.mil/cfd-cta/CFD3/img_gallery/f117/

RIP 2004 10

Forward: Differential

http://sdcd.gsfc.nasa.gov/ESS/annual.reports/ess98/kma.html

http://www.remcom.com/xfdtd6/

Finite Element Method (FEM) Finite Difference-Time Domain (FDTD)

RIP 2004 11

Comparison: IE/DEIntegral Equ.

MethodsDiff. Equ. Methods

Math foundations Gauss/Stokes TheoremGreen’s Theorem

Maxwell equationVariational 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#

RIP 2004 12

Inverse Problems

• Inverse Source Problems

• Inverse Scattering Problems

• Mixed Inverse Problems

response knownstructure known

source unknown

mine

source known

structure unknown

response known

fuL (?)

?(?) uL

?)( uL

Forward operator

System Parameter

Measurement

Source

RIP 2004 13

Approaches of Solving Inverse Problems

• Operator Equation

• Root Finding

• Optimization

fuL )(

0)( fuL

fuL )(

)()(min uRuE Misfit functional

Regularization functional

RIP 2004 14

Biomedical Imaging

• Principal– Encoding/Decoding of information

• Imaging Agent

• Functional Imaging and Structural Imaging

Particles SPECT(photons),PET(positron)

Wave

Mechanical Ultrasound,Elastography,Seismology

Electromagnetic

EIT,MWI,NIR,CT,X-Ray,MR,SAR

RIP 2004 15

CBI and CEM

• CT -> Linear attenuation -> Filted Backprojection -> Linear Inverse problem

• MRI -> Inverse Fourier Transform• Ultrasound• EIT, MWI, NIR, GPR, …

-> Nonlinear propagation -> iterative reconstructions -> Nonlinear inverse problem

RIP 2004 16

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.

RIP 2004 17

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.

RIP 2004 18

Questions?