**Matrix: Dziekonski/dielFilterV2real**

Description: High-order vector finite element method in EM

(undirected graph drawing) |

Matrix properties | |

number of rows | 1,157,456 |

number of columns | 1,157,456 |

nonzeros | 48,538,952 |

structural full rank? | yes |

structural rank | 1,157,456 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | A. Dziekonski, A. Lamecki, M. Mrozowski |

editor | T. Davis |

date | 2011 |

kind | electromagnetics problem |

2D/3D problem? | yes |

Additional fields | size and type |

b | full 1157456-by-1 |

Notes:

High order vector finite element method in electromagnetics The dielFilter* matrices came from analysis of a 4th-pole dielectric resonator [4] generated with Finite Element Method. The tetrahedral mesh of the structure was generated with the Netgen mesher [2]. The matrices were used as an example in our paper [3]. dielFilterV2clx - complex symmetric matrix (607,232 x 607,232), 25,309,272 nonzero (real) and 728,900 nonzero (imag) elements. First 109,108 unknowns correspond to lowest level base functions. dielFilterV2real - real symmetric matrix (1,157,456 x 1,157,456) and 48,538,952 nonzero elements. First 209,432 unknowns correspond to lowest level base functions. dielFilterV3clx - complex symmetric matrix (420,408 x 420,408), 32,886,208 nonzero (real) and 3,706,513 (imag) elements. First 24,716 unknowns correspond to lowest level base functions, next 116,152 unknowns correspond to the second level. dielFilterV3real - real symmetric matrix (1,102,824 x 1,102,824) and 89,306,020 nonzero elements. First 66,353 unknowns correspond to lowest level base functions, next 305,729 unknowns correspond to the second level. All matrices are sparse and come with right-hand-sides. [2] J. Schoberl, "NETGEN An advancing front 2D/3D-mesh generator based on abstract rules," Computing and Visualization in Science, vol. 1, No. 1, pp. 41-52, July 1997 [3] A. Dziekonski, A. Lamecki, M. Mrozowski, Tuning A Hybrid GPU-CPU V-cycle Multilevel Preconditioner for Solving Large Real and Complex Systems of FEM Equations. [4] F. Alessandri, M. Chiodetti, A. Giugliarelli; D. Maiarelli, G. Martirano, D. Schmitt, L. Vanni and F. Vitulli. The electric-field Integral-equation method for the analysis and design of a class of rectangular cavity filters loaded by dielectric and metallic cylindrical pucks, Microwave Theory and Techniques, IEEE Transactions on, vol. 52, no 8, pp. 1790-1797, Aug. 2004.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 1,160,556,168 |

Cholesky flop count | 4.8e+12 |

nnz(L+U), no partial pivoting, with AMD | 2,319,954,880 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 2,693,105,368 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 6,428,054,924 |

For a description of the statistics displayed above, click here.

*Maintained by Tim Davis, last updated 12-Mar-2014.Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.
*