Summer Semester 2009/10
Finite element method and finite difference method D06W03
Course content:
Mathematical formulations, fundamental theorems and concepts (uniqueness theorem, principle of equivalence).
Finite difference discretizations: elliptic, parabolic and hyperbolic problems, explicit and implicit formulations, FDTD.
Finite element discretizations: Ritz formulation, Galerkin formulation, Whitney forms.
Boundary element discretizations.
Numerical analysis of fractional differential equations.
Asymptotic techniques: ray and beam fields.
Iterative solution methods.
Analysis of some electromagnetic and thermal problems. Coupled fields.
Learning outcomes:
(a) manage with some BVP and IVP using numerical methods;
(b) implement numerical algorithms and commercial software to solve ODE and PDE problems.
(c) asses reliability of numerical results;
(d) validate and interpret the results of numerical analysis of electric and thermal field phenomena.
(in Polish) Rodzaj przedmiotu
Course coordinators
Bibliography
a) basic references:
Zienkiewicz O.C., Taylor R.L., Zhu J.Z.: The finite element method. Elsevier, 2005.
Monk P.: Finite element methods for Maxwell’s equations. Oxford University Press, 2003.
Kącki E.: Równania różniczkowe cząstkowe w zagadnieniach fizyki i techniki. WNT, Warszawa, 1995.
Kleiber M.: Wprowadzenie do metody elementów skończonych. PWN, Warszawa, 1989.
Langtangen H. P.: Computational partial differential equations. Springer, Berlin, 1999.
Sikora J.: Boundary Element Method for impedance and optical tomography. Wydaw. Politechniki Warszawskiej, 2007.
Taflove A.: Computational electrodynamics. Artech House, 1995.
b) supplementary references:
Yu W.: Electromagnetic Simulation Techniques Based on the FDTD Method. Wiley& Sons, 2009.
Jianming J.: The finite element method in electromagnetics. Wiley & Sons, 1993.
Chen Y., Qunsheng C., Raj M.: Multiresolution time domain scheme for electromagnetic engineering applications. Wiley & Sons, 2005.