Learn · Computational Electromagnetics
Lecture 99 of 120Week 11
Inverse Problems - Challenges
Prof. Uday Khankhoje · IIT Madras
Credits and licence
- From
- Computational Electromagnetics, IIT Madras (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Chain rule of differentiation
- Gradient, Divergence, and Curl operators
- Common theorems in vector calculus
- Corollaries of these theorems
- Mathematical History
- Different regimes of Maxwell's equations
- Different ways of solving them
- Maxwell's Equations
- Boundary Conditions
- Uniqueness Theorem
- Equivalence Theorem
- Simple Numerical Integration
- Interpolating a Function
- Gauss Quadrature
- Line Charge Problem
- Solving the Integral Equation
- Basis Functions
- Helmholtz Equation
- Solving Helmholtz Equation
- Huygen's principle & the Extinction theorem
- Formulating the integral equations
- Conclusions of surface integral equations
- Motivations for Green's functions
- A one-dimensional example
- 1-D example: alternate representation
- 2-D wave example : finding solution
- 2D wave example: boundary conds
- 2-D example : Evaluating Constants - Part 1
- 2-D example : Evaluating Constants - Part 2
- 3-D example
- Motivation for MoM
- Linear Vector Spaces
- Formulating Method of Moments
- Surface Integral Equations: Recap
- Surface Integral Equations: Evaluating the Integrals part 1
- Surface Integral Equations: Evaluating the Integrals part 2
- Surface Integral Equations: Conclusion
- Volume Integral Equations:Setting Up
- Volume Integral Equations:Solving part 1
- Volume Integral Equations:Solving part 2
- Volume Integral Equations:Summary
- Surface integral equations for PEC
- Surface v/s volume integral equations
- Definition of radar cross-section
- Computational Considerations
- History & Overview of the FEM
- Basic framework of FEM
- 1D Basis Functions
- 2D Basis Functions
- Weak form of 1D-FEM Part-1
- Weak form of 1D-FEM Part-2
- Generating System of Equations for 1D FEM
- 1D wave equation: Formulation
- 1D Wave Equation: Boundary Conditions
- 1D Wave Equation: Basis and testing functions
- 1D Wave Equation: Matrix assembly
- 2D FEM Shape Functions
- Converting to Weak Form (2D FEM)
- Radiation Boundary Condition
- Total field formulation
- Scattered field formulation
- Comparing total and scattered field formulation
- Matrix assembly - Part 1
- Matrix assembly - Part 2
- Computing Far Field
- Numerical Aspects of 2D FEM
- Summary of FEM Procedure
- Introduction to FDTD
- 2D FDTD Formulation : Stencil
- 2D FDTD Formulation : Time Stepping
- 2D FDTD Formulation : Divergence Conditions
- Stability Criteria - Part 1
- Stability Criteria - Part 2
- Stability Criteria - Higher Dimensions
- Accuracy Considerations - 1D
- Accuracy Considerations - Higher Dimensions
- Dealing with non-dispersive dielectric media
- Dealing with dispersive dielectric media
- Debye Model - Part 1
- Debye Model - Part 2
- Absorbing Boundary Conditions - 1D
- Absorbing Boundary Conditions - 2D
- Implementing ABC in FDTD
- Failure of ABC
- Perfectly Matched Layers(PML) - Introduction
- Implementing PML using Coordinate Stretching
- PML - Phase Matching
- PML - Tangential Boundary Conditions
- Perfectly Matched Interface
- PML theory - Summary
- Implementing PML into FDTD - Part 1
- Implementing PML into FDTD - Part 2
- Sources in FDTD - Currents
- Sources in FDTD - Part 2
- Summary of FDTD
- MEEP : FDTD in action
- Inverse Problems - Introduction
- Inverse Problems - Mathematical Formulation
- Inverse Problems - Challenges
- Inverse Problems - Non-Linearity
- Inverse Problems - Summary
- Antennas - Potential formulation
- Antennas - Hertz Dipole - Part 1
- Antennas - Hertz Dipole - Part 2
- Antennas - Radiation Patterns
- Antennas - Motivation for CEM
- Antennas - Pocklington's Integral Equation - Part 1
- Antennas - Pocklington's Integral Equation - Part 2
- Antennas - Source Modeling
- Antennas - Circuit Model
- Antennas - MoM details
- Antennas - Mutual Coupling - Part 1
- Antennas - Mutual Coupling - Part 2
- Hybrid Methods - Motivation
- Finite Element-Boundary Integral - Part 1
- Finite Element-Boundary Integral - Part 2
- Finite Element-Boundary Integral - Part 3
- Live Session 01-11-2019
- Live Session 23-09-2019
- Live Session 24-08-2019