1. RIP 20041 Computational Electromagnetics & Computational Bioimaging Qianqian Fang Research In Progress (RIP 2004)

2. RIP 20042 Outline Macroscopic Electromagnetics Computational Electromagnetics (CEM) Inverse Problems Computational Biomedical Imaging (CBI) CBI and CEM

3. RIP 20043 From DC to Light Circuit Theory Matrix Electromagnetics Wave Electromagnetics Quantum Mechanics Optics http://www.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html

4. RIP 20044 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)

5. RIP 20045 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

6. RIP 20046 Electromagnetics: Core Theorems Duality Principal Equivalenc e Theorem Reciprocity Theorem Uniquenes s Theorem Huygens’ Principal Green’s Theorem

7. RIP 20047 Computational Electromagnetics Definition Numerical Linearization High-frequency-> geometric approx Low-frequency-> difference/variational

8. RIP 20048 Computational Electromagnetics Computati onal Electromag netics Forward Problems High- Frequency Methods Low- Frequency Methods Analytical methods Inverse Problems Inverse Source Problem Inverse Scattering

9. RIP 20049 Forward: Integration Integration Equation: MoM, BEM, EFIE/MFIE/CFIE http://www.lcp.nrl.navy.mil/cfd-cta/CFD3/img_gallery/f117/

10. RIP 200410 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)

11. RIP 200411 Comparison: IE/DE Integral Equ. MethodsDiff. Equ. Methods Math foundationsGauss/Stokes Theorem Green’s Theorem Maxwell equation Variational Principal Problem Dimensions n -1 n ConstainsGlobalLocal LinearizationDense matrix equationSparse matrix equation DiscretizationSurface meshVolume mesh Mesh truncation (RBC/ABC) Typically no needNeeded for unbounded problems ProsLarge problems, far fields Near field, inhomogeneous ConsInhomogeneousLarge unknown#

12. RIP 200412 Inverse Problems Inverse Source Problems Inverse Scattering Problems Mixed Inverse Problems response known structure known source unknown mine source known structure unknown response known Forward operator System Parameter Measurement Source

13. RIP 200413 Approaches of Solving Inverse Problems Operator Equation Root Finding Optimization Misfit functional Regularization functional

14. RIP 200414 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

15. RIP 200415 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

16. RIP 200416 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.

17. RIP 200417 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.

18. RIP 200418 Questions?