Solve for 2D Electromagnetic Field in Material
Summary
Use numerical method (finite different frequency domain) to solve Maxwell's equations for electromagnetic field in material using MATLAB. Basically, it is to solve Ax = B, where A is a sparse matrix containing materials, x is the resulting field, and B is the source.
CollapseLearning Goals
- Students will learn how to take Maxwell's equations, break them into Matrix equations and implement it on MATLAB.
- MATLAB is used to solve a huge sparse matrix equation and visualize the result
- The result 2D field plot is created which will help student learn about the propagation of electromagnetic wave.
- MATLAB is used to solve a huge sparse matrix equation and visualize the result
- The result 2D field plot is created which will help student learn about the propagation of electromagnetic wave.
Context for Use
Special class for graduate students
Class size : 10-15
Duration : 6 hours (3 hours of theory about numerical method, 3 hours for hands-on with MATLAB)
MATLAB skills: Basic programming, basic plot
Other disciplinary skills: Linear algebra, Maxwell's equations
This activity is to compliment the hands-on experience of optics lab with the basic of numerical analysis.
Description and Teaching Materials
This is a two-part class. The first 3 hours will be the theory of electromagnetic via Maxwell's equations and the formulation into a simple matrix equation. The second part will be the translation of physical problem into a discrete matrix value.
Student will learn to read data using dlmread from file and assign them to appropriate variable, do data pre-processing, and/or interpolate using griddata. The next part is to assemble the matrix by creating a sparse empty matrix first, then populate it correctly at each indices. Since the problem is in 2D, student needs to rearrange a matrix into a vector and recombine them back after the solving process. At the core is the equation Ax = B. Student will solve it and visualize. Throughout the main m file, student will learn to create sub function to clean up the code. The result will be save in a folder with timestamp for analysis later.
Student will learn to read data using dlmread from file and assign them to appropriate variable, do data pre-processing, and/or interpolate using griddata. The next part is to assemble the matrix by creating a sparse empty matrix first, then populate it correctly at each indices. Since the problem is in 2D, student needs to rearrange a matrix into a vector and recombine them back after the solving process. At the core is the equation Ax = B. Student will solve it and visualize. Throughout the main m file, student will learn to create sub function to clean up the code. The result will be save in a folder with timestamp for analysis later.
Teaching Notes and Tips
The generation of material can be achieve by using the transformation optics theory.
Assessment
- Able to follow through the step-by-step codes and get the resulting plot.
- Able to modify the electromagnetic source (such as angle) or material parameters and see different result
- Able to modify the electromagnetic source (such as angle) or material parameters and see different result
References and Resources
Youtube video on FDFD method by Prof.Raymond C. Rumpf
https://youtu.be/4_O3gQEkydw
https://youtu.be/4_O3gQEkydw