2024 Faculty Courses School of Environment and Society Department of Transdisciplinary Science and Engineering Graduate major in Global Engineering for Development, Environment and Society
Linear Wave Theory and Simulation
- Academic unit or major
- Graduate major in Global Engineering for Development, Environment and Society
- Instructor(s)
- Jun-Ichi Takada
- Class Format
- Lecture (HyFlex)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Mon
- Class
- -
- Course Code
- GEG.T414
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
[Description] Linear time-harmonic waves, such as radio wave, light and sound, are formulated. Then simulation techniques to predict the scattering characteristics at the object with certain boundary condition are explained.
[Aims] Students are expected to understand how the linear time-harmonic wave propagates in the open space, and scatters at the object boundary.
Course description and aims
Students can predict the scattered wave from the objects represented by boundary condition by choosing an appropriate simulation technique considering the size of the problem, computational complexity and accuracy.
Keywords
Wave equation, Helmholtz equation, Kirchhoff-Huygens principle, Green function, Dirichlet condition, Neumann condition, eigenfunction expansion, physical optics, boundary element method, boundary integral equation, finite element method
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The course consists of lectures. Homework is assigned occasionally for deep understanding of the topics.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Review of vector analysis, wave equation and Helmholtz equation | Derive the equations to govern the linear waves. |
| Class 2 | Helmholtz equation and homogeneous solution | Derive Helmholtz equation from wave equation by assuming the time-harmonic oscillation. Solve homogeneous Helmholtz equation in Cartesian coordinates. |
| Class 3 | Representation of wave function by using Green function | Derive the Kirchhoff-Huygens principle from Helmholtz equation. Derive free space Green function of Helmholtz equation. |
| Class 4 | (on demand) Eigenfunction expansion | Represent the Green function in cartesian coordinates by eigenfunction expansion |
| Class 5 | Physical optics | Simulate the wave scattering by circular cylinder. |
| Class 6 | Boundary element method (1): Boundary integral equation | Derive the boundary integral equations for Dirichlet and Neumann conditions. |
| Class 7 | Boundary element method (2): Discretization of integral equation | Derive the set of linear equations by discretizing the boundary integral equations using boundary element method. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 200 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to handouts.
Textbook(s)
Handouts are distributed via T2SCHOLA.
Reference books, course materials, etc.
R. C. Booton, "Computational Methods for Electromagnetics and Microwaves", John Wiley & Sons, 1992.
Evaluation methods and criteria
Assignment after each class (10 points x 7 times) and final report (30 points)
Related courses
- TSE.M202 ： Partial Differential Equations for Science and Engineering
- TSE.M203 ： Theory of Linear System
- TSE.A307 ： Programming and numerical analysis
- TSE.A324 ： Applied programming and numerical analysis
- TSE.A305 ： Electromagnetics (TSE)
Prerequisites
Knowledge on partial differential equations, vector analysis and Fourier analysis are expected.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
takada[at]tse.ens.titech.ac.jp