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2023　Linear Wave Theory and Simulation

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Academic unit or major
Graduate major in Global Engineering for Development, Environment and Society
Instructor(s)
Takada Jun-Ichi 
Class Format
Lecture    (HyFlex)
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(M-156(H1103))  
Group
-
Course number
GEG.T414
Credits
1
Academic year
2023
Offered quarter
3Q
Syllabus updated
2023/10/2
Lecture notes updated
-
Language used
English
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Course description and aims

[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.

Student learning outcomes

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 that will be developed

✔ 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/Required learning

  Course schedule Required learning
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.

Out-of-Class Study Time (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.

Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

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

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