**Matrix: Um/2cubes_sphere**

Description: FEM, electromagnetics, 2 cubes in a sphere. Evan Um, Geophysics, Stanford

(undirected graph drawing) |

Matrix properties | |

number of rows | 101,492 |

number of columns | 101,492 |

nonzeros | 1,647,264 |

structural full rank? | yes |

structural rank | 101,492 |

# 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? | yes |

positive definite? | yes |

author | E. Um |

editor | T. Davis |

date | 2008 |

kind | electromagnetics problem |

2D/3D problem? | yes |

Additional fields | size and type |

b | full 101492-by-1 |

Notes:

A matrix from Evan Um, Geophysics, Stanford. Studying finite-element time domain solvers for electromagnetic diffusion equations. The 3-D computational domain consists of 88,213 tetrahedral elements. The computational domain consists of the two parts. First, there are two 300m x 300m x 150m boxes where a fine mesh is used. Second, the two boxes are enclosed by a large sphere whose radius is 10 km. An element growth factor is used to increase the mesh size gradually inside the sphere. This is because absorbing boundary conditions are not very good choices for these problems. The finite element technique is edge-based rather than node-based. Therefore, the unknowns are amplitudes of electromagnetic fields on an edge of each element.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 88,679,332 |

Cholesky flop count | 3.0e+11 |

nnz(L+U), no partial pivoting, with AMD | 177,257,172 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 209,702,037 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 394,050,005 |

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.
*