EE699 — Course Syllabus Computational Electromagnetics: The Finite-Element Method Instructor: Prof. Stephen D. Gedney 687C Anderson Hall E-mail: [email protected] WWW: http://www.engr.uky.edu/~gedney Office hours: Tuesdays & Thursdays, 9:30 – 11:30 a.m., or by appointment Course Text: The Finite Element Method in Electromagnetics , J.-M. Jin, Wiley-IEEE Press; 2 edition (May 27, 2002), ISBN: 0471438189 EE699 URL: http://www.engr.uky.edu/~gedney/courses/ee699 EE699 Course Description: A course on the application of the finite-element method for the full-wave simulation of time-harmonic electromagnetic waves in complex media. EE699 Course Outcomes: The following competencies should be imparted to the students: 1. Ritz and Galerkin methods for formulating variational problems 2. Development and use of scalar and vector shape functions 3. Finite Element Analysis (FEA) for the solution of boundary value problems 4. 1D FEA for static and dynamic solution of Maxwell’s equations 5. 2D FEA for static and dynamic solution of Maxwell’s equations 6. 3D FEA for the dynamic solution of Maxwell’s equations Homeworks will be assigned during the course of the semester. The due date will vary with the length of each assignment. The homeworks and due dates will be posted on the course web page. All assignments are due at the beginning of the class period. You will be allowed one late assignment, which will be due the following class period. Otherwise, late assignments will not be accepted. Some homeworks will require computer simulations, which can be performed using mathematical software such as Matlab, MathCad, Maple, or Mathematica. Programming assignments are expected to be performed via a high-level programming language such as FORTRAN 95 or C++, as specified. If you are not experienced with a high-level programming language, then you should consult with the instructor at the beginning of the semester. For all assignments, graphical results are expected to be computer generated and printed on a laser or ink-jet printer. Paper Summary. A one page written summary of a journal paper will be due every second Thursday at the beginning of class. You can pick any paper of interest to you and pertinent to this course (specifically an application or development of FEM) published in a peer reviewed journal, such as the IEEE Transactions. The summary should be typed and should briefly summarize the main contribution of the paper.Final Project A final computer project will be due at the end of the semester. The project will consist of developing a computer program to solve a problem agreed to by the instructor. A final report presenting the theory, numerical methods, and validating results will be handed in according to specified guidelines. A final presentation (15 minutes) of the project will be given during the final exam week. Attendance of all the presentations is mandatory. Grade Distribution Requirement % of Final Grade Homework Projects 55 % Paper Summaries 10 % Final Project and Presentation 35 % Grade Assessment Final Grade Letter Grade 90-100 % A 80-90 % B 70-80 % C 60-70 % D Below 60 % ECourse Syllabus Lec. Reading Topic 1 1.1 – 1.4 Review: Maxwell’s Equations, Boundary Conditions, Wave Equation 2 1.5 – 1.10 Review: Vector Potential Theory, Wave Polarization, Solutions to Maxwell’s Equations 3 2..1 Introduction to the Finite Element Method (FEM) – Ritz and Galerkin methods 4 2.2, 2.3 Example: Static Solution via the FEM method 5 3.1 - 3.2 1D FEM – Dynamic Solution – Deriving the Boundary Value Problem 6 3.3 Linear Shape Functions, Simplex Coordinates, and Assembly 7 3.4 1D Example in Cartesian Coordinate 8 3.6 Higher-Order shape functions 9 4.1, 4.2 2D FEM – Reactional Form of the Wave Equation 10 4.3 2D Shape Functions on triangles 11 4.3 2D Finite Element Analysis 12 4.4 – 4.5 2D Applications – Static & Dynamic 13 4.6 Absorbing Boundary Conditions 14 4.7 Higher-order elements on a 2D triangle 15 4.7 Numerical Integration on 2D triangles 16 4.8 Isoparametric 2D Triangular Elements 17 5.1 – 5.3 3D Finite Elements 18 5.4 Shape Functions – Tetraheron, Hexahedron, and Prisms 19 5.5 Numerical Integration – 3D Cubature Rules 20 5.6 – 5.8 Applications of 3D FEM 21 8.1 Vector Edge Elements for 2D triangular & quadrilateral elements 22 8.2 Reaction integrals, assembly and analysis with edge functions 23 8.3 Vector Edge Elements for 3D tetrahedral elements 24 8.4 Reaction integrals, assembly and applications with 3D edge functions 25 8.5 Waveguide analysis with 3D edge functions – modal analysis 26 8.6 Higher-order vector edge elements 27 8.6 Higher-order vector edge elements continued 28 9.1 2D Absorbing boundary conditions 29 9.2 3D Absorbing boundary