%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/Bodendiek/CurlCurl_3
% name: Bodendiek/CurlCurl_3
% [Curl-Curl operator of 2nd order Maxwell's equations, A. Bodendiek]
% id: 2572
% date: 2012
% author: A. Bodendiek
% ed: T. Davis
% fields: name title A id date author ed kind notes
% kind: model reduction problem
%-------------------------------------------------------------------------------
% notes:
% Curl-Curl operator of 2nd order Maxwell's equations, A. Bodendiek    
%                                                                      
% From Andre Bodendiek, Institut Computational Mathematics,            
% TU Braunschweig                                                      
%                                                                      
% The following matrix collection consists of the curl-curl-operator   
% of a second-order Maxwell's equations with PEC boundary conditions,  
% i.e. E x n = 0, where E and n denote the electric field strength     
% and the unit outer normal of the computational domain. The           
% curl-curl-operator has been discretized using the Finite Element     
% Method with first-order Nedelec elements resulting in the weak       
% formulation                                                          
%                                                                      
%    1/mu0 ( curl E, curl v ),                                         
%                                                                      
% where v resembles a test function of H(curl) and                     
% mu0 = 1.25 1e-9 H / mm denotes the magnetic permeability of vacuum,  
% see [Hipt02].                                                        
%                                                                      
% In general, the underlying model problem of Maxwell's equations      
% results from a Coplanar Waveguide, which will be considered for      
% the analysis of parasitic effects in the development of new          
% semiconductors. Since the corresponding dynamical systems are often  
% high-dimensional, model order reduction techniques have become an    
% appealing approach for the efficient simulation and accurate analysis
% of the parasitic effects. However, different kinds of model order    
% techniques require the repeated solution of high-dimensional linear  
% systems of the original model problem, see [Bai02,An09]. Therefore,  
% the development of efficient solvers resembles an important task     
% in model order reduction.                                            
%                                                                      
% Each matrix CurlCurl_<nr> consists of a different number of degrees  
% of freedom, given in the following table:                            
%                                                                      
% <nr> = 0:   11083                                                    
% <nr> = 1:  226451                                                    
% <nr> = 2:  806529                                                    
% <nr> = 3: 1219574                                                    
% <nr> = 4: 2380515                                                    
%                                                                      
% References.                                                          
%                                                                      
% @ARTICLE{Bai02,                                                      
%   author = {Z. Bai},                                                 
%   title = {Krylov subspace techniques for reduced-order modeling     
%     of large-scale dynamical systems},                               
%   journal = {Applied Numerical Mathematics},                         
%   year = {2002},                                                     
%   volume = {43},                                                     
%   pages = {9--44},                                                   
%   number = {1--2}                                                    
% }                                                                    
%                                                                      
% @ARTICLE{Hipt02,                                                     
%   author = {R. Hiptmair},                                            
%   title = {Finite elements in computational electromagnetism},       
%   journal = {Acta Numerica, Cambridge University Press},             
%   year = {2002},                                                     
%   pages = {237-339}                                                  
% }                                                                    
%                                                                      
% @BOOK{An09,                                                          
%   title = {Approximation of {L}arge-{S}cale {D}ynamical {S}ystems},  
%   publisher = {Society for Industrial Mathematics},                  
%   year = {2009},                                                     
%   author = {Athanasios C. Antoulas}                                  
% }                                                                    
%-------------------------------------------------------------------------------
