## Bodendiek/CurlCurl_0

Curl-Curl operator of 2nd order Maxwell's equations, A. Bodendiek

Name | CurlCurl_0 |
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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 |

SVD Statistics | |
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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 |
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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} } |