Předmět Numerical Computations with Partial Differential Equations (FEKT-DTE2A)

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Materiál	Typ	Datum	Počet stažení

Cíl

Introduction to the functional analysis, differential operators, survey of the partial differential equations. Boundary and initial conditions. Finite difference methods (FDM).Finite element methods (FEM). – introduction. Discretization of a region into the finite elements. Approximation of the field from the nodal or edge values. Forward problem. Setup of equations for nodal and edge values by the Galerkin method.Application of the Galerkin method to the static and quasistatic fields (Poisson’s and Helmholtz’s equation).Application of FEM and FDM on the time variable problems (the diffusion and wave equation). Connection of the field region with the lumped parameter circuit. Coupled problems.The field optimization problem. Survey of the deterministic methods. The local and global minima.Unconstrained problems – gradient method, method of the steepest descent, Newton’s methods.Constrained optimization problems together with FEM.Inverse problems for the elliptic equations. The Least Square method. Deterministic regularization methods.A survey on level set methods for inverse problems and optimal design. A survey on inverse problems in tomography.A note: Practical examples using the ANSYS and MATLAB environment will be a part of each point of the curriculum.

Osnova

Introduction to the functional analysis, differential operators, survey of the partial differential equations. Boundary and initial conditions. Finite difference methods (FDM).Finite element methods (FEM). – introduction. Discretization of a region into the finite elements. Approximation of the field from the nodal or edge values. Forward problem. Setup of equations for nodal and edge values by the Galerkin method.Application of the Galerkin method to the static and quasistatic fields (Poisson’s and Helmholtz’s equation).Application of FEM and FDM on the time variable problems (the diffusion and wave equation). Connection of the field region with the lumped parameter circuit. Coupled problems.The field optimization problem. Survey of the deterministic methods. The local and global minima.Unconstrained problems – gradient method, method of the steepest descent, Newton’s methods.Constrained optimization problems together with FEM.Inverse problems for the elliptic equations. The Least Square method. Deterministic regularization methods.A survey on level set methods for inverse problems and optimal design. A survey on inverse problems in tomography.A note: Practical examples using the ANSYS and MATLAB environment will be a part of each point of the curriculum.

Literatura

Rektorys Karel: Přehled užité matematiky I, II. Prometheus, 1995 (CS)Inverse Problems. IoP Electronic Journals, http://www.iop.org/EJ/journal/IP http://www.inverse-problems.com/ (EN)IEEE Transactions on Magnetics, ročník 1996 a výše (EN)Fotokopie nejnovějších výzkumných zpráv ze serverů zahraničních špičkových pracovišť ke studované problematice budou dodávány průběžně (EN)SIAM Journal on Control and Optimization, ročník 1996 a výše (EN)metoda hladinových množin http://www.math.ucla.edu/applied/cam/index.html (EN)Dědek, L., Dědková J.: Elektromagnetismus. Skripta VUTIUM Brno, 2000 (CS)Inverse Problems. IoP Electronic Journals, http://www.iop.org/EJ/journal/IP (EN)Bossavit Alain.: Computational Electromagnetism – Variational formulations, complementarity, edge elements. Academic Press, 1998 (EN)Sadiku Mathew: Electromagnetics (second edition), CRC Press, 2001 (EN)Chari, M, V. K., Salon S. J.: Numerical Methods in Electromagnetism. Academic Press, 2000 (EN)

Požadavky

Mathematical calculus, Physics, Electromagnetism on the level of MSc.

Garant

prof. Ing. Pavel Fiala, Ph.D.

Vyučující

prof. Ing. Pavel Fiala, Ph.D.