JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Course Objectives:

• 1. To give a source of basic information on applied mathematical topics.
• 2. To Provide an efficient and accurate formulations for electromagnetics applications and their numerical treatment
• 3. To solve Integral and Differential equations using the method of moments and finite-element procedures
• 4. To addressed the advanced computational techniques for the solution of partial differential equations and integral equations encountered in electromagnetic boundary value problems.

Course Outcomes

Students will be able to:

• 1. Hands on source for solution methods and techniques on applied mathematical topics.
• 2. Apply a Finite Difference Methods to solve different PDE
• 3. Solve Integral and Differential equations using method of moments and finite-elements analysis.
• 4. Apply a Finite Difference Time domain methods for different problems.

UNIT - I

Fundamental Concepts: Integral equations vs. differential equations, radiation and edge conditions, modal representation of fields in bounded and unbounded media, Greens functions.

UNIT - II

Finite Difference Methods: Introduction, Finite Difference Schemes, Finite differencing of Parabolic PDE, Finite Differencing of Hyperbolic PDE, Finite differencing of elliptic PDE, Accuracy and stability of Finite Difference Solutions.

UNIT - III

Integral Equations: Formulation of typical problems integral equations: wire antennas, scattering, apertures in conducting screens and waveguides, discontinuities in waveguides and Microstrip lines Solution of Integral Equations: General Method of Moments(MoM) for the solution of integro-differential equations, choice of expansion and weighting functions, application of MoM to typical electromagnetic problems.

UNIT - IV

Finite Element Method: Typical finite elements, Solution of two-dimensional Laplace and Poisson’s equations, Solution of scalar Helmholtz equation.

UNIT - V

Finite-difference Time-domain Method: Finite difference, finite difference representation of Maxwell’s equations and wave equation, numerical dispersion, Yee’s finite difference algorithm, stability conditions, absorbing boundary conditions.

TEXT BOOKS:

• 1. Andrew F. Peterson, Scott L. Ray, Raj Mittra - Computational Methods for Electromagnetics, 1997
• 2. Collin, R. E.-Field Theory of Guided Waves, 2nd Ed., Wiley-IEEE Press. 1991

REFERENCE BOOKS:

• 1. Harrington, R. F- Field Computation by Moment Methods, Wiley- IEEE Press. 1993
• 2. Sadiku, M. N. O - Numerical Techniques in Electromagnetics, 2nd Ed., CRC Press 2001
• 3. Volakis, J. L., Chatterjee, A. and Kempel, L.C.- Finite Method for Electromagnetics, Wiley IEEE Press. 1998
• 4. Taflov, A. and Hagness, S.C.- Computational Electrodynamics, 3rd Ed., Artech House. M.TECH.- I YEAR- I SEMESTER MICROWAVE AND RADAR ENGINEERING