| | Standard Course Syllabus | Course Supervisor | Date of Approval |
| | Dept. of Electrical and Computer Engineering | Teixeira | 1/07 |
| | 817 | Discrete Electromagnetics |
| | 2. | CATALOG DESCRIPTION |
| | Discretization techniques for Maxwell equations, and associated numerical methods, with emphasis on finite difference, |
| | finite volumes, and finite elements. |
| | Quarters of Offering | Credits | | Level | Class Meeting |
| | Wi Qtr (odd years). | 3 | G | 3 cl. |
| | Course Prerequisites |
| | Prereq: 715. Not open to students with credit for 894K. |
| | 3. | PREREQUISITES BY TOPIC |
| | Maxwell's equations, electromagnetic theorems, scattering |
| | Courses that require this as a direct prerequisite |
| | none |
| | 4. | Text(s) and Other Course Materials | Author(s) | Publisher |
| | Computational Electromagnetics (Texts in Applied | Bondeson, Rylander, and | Springer |
| | Mathematics), 2005 | Ingelstrom |
| | References (supplemental reading) |
| | [1] Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House: |
| | Boston, 2002. |
| | [2] J.L. Volakis, A. Chatterjee and L.C. Kempel, Finite Element Method for Electromagnetics, IEEE Press: New York, |
| | 1998. |
| | [3] P. Monk, Finite Element Methods for Maxwell's Equations, Oxford University Press, 2003. |
| | 5. | COURSE OBJECTIVES |
| | 1. Students will learn discretization methods from first principles to solve Maxwell's equations in structured, unstructured, |
| | regular, and irregular grids. |
| | 2. Students will study and develop computational examples to analyze the accuracy and limitations of each discretization |
| | method. |
| | 3. Course material will be supplemented by reading from current technical literature. |
| | 6. | TOPICS AND (# OF LECTURES) |
| | 1. Classification of partial differential equations into hyperbolic, parabolic, and elliptic types. Review of finite-difference |
| | approximations: consistency, stability, and convergence. (2) |
| | 2. Finite-difference time-domain (FDTD) method in homogeneous and complex media with emphasis on error analysis: |
| | truncation, staircasing, and numerical dispersion errors. Courant criterion and stability analysis. Symplectic time |
| | integration. Higher-order FDTD schemes. (6) |
| | 3. Finite-volume time-domain (FVTD) method. Semi-discrete analysis. Consistency and stability analysis. Origin of |
| | unconditional instabilities. (3) |
| | 4. Absorbing boundary conditions (2) |
| | 5. Introduction to differential forms and cell complexes. Exterior calculus for an arbitrary lattice: exterior derivative, |
| | boundary operator, incidence matrices, Hodge operator. (5) |
| | 6. Whitney forms and the vector finite-element method (FEM). Construction of discrete Hodge operators. Galerkin duality. |
| | Finite-element time domain (FETD). From lumped FETD to FDTD. Sparse apporximations. (6) |
| | 7. De Rham complex, exact sequences, and the origin of spurious discrete solutions. Discrete Hodge-Helmholtz |
| | decomposition. (2) |
| | 8. Higher order Whitney forms (2) |
| | 9. Non-conformal discretizations: application to FDTD subgridding and FE domain decomposition. (2) |
| | 7. | CLASS MEETING PATTERN | (For example, "3cl." means 3 48-min classes per week.) |
| | 3 cl. |
| | Thursday, August 14, 2008 09:23 AM |
| | Page 1 of 2 |