Curl-Curl operator of 2nd order Maxwell's equations, A. Bodendiek
Name CurlCurl_0
Group Bodendiek
Matrix ID 2569
Num Rows 11,083
Num Cols 11,083
Nonzeros 113,343
Pattern Entries 113,343
Kind Model Reduction Problem
Symmetric Yes
Date 2012
Author A. Bodendiek
Editor T. Davis
Structural Rank 11,083
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate yes
Positive Definite no
Type real
SVD Statistics
Matrix Norm 4.270230e+10
Minimum Singular Value 8.515473e-10
Condition Number 5.014672e+19
Rank 9,884
sprank(A)-rank(A) 1,199
Null Space Dimension 1,199
Full Numerical Rank? no
Download Singular Values MATLAB
Download MATLAB Rutherford Boeing Matrix Market
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       
   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                                                    
  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}                                                    
  author = {R. Hiptmair},                                            
  title = {Finite elements in computational electromagnetism},       
  journal = {Acta Numerica, Cambridge University Press},             
  year = {2002},                                                     
  pages = {237-339}                                                  
  title = {Approximation of {L}arge-{S}cale {D}ynamical {S}ystems},  
  publisher = {Society for Industrial Mathematics},                  
  year = {2009},                                                     
  author = {Athanasios C. Antoulas}