**Matrix: Sinclair/3Dspectralwave**

Description: 3-D spectral-element elastic wave modelling in freq. domain, C. Sinclair, Univ. Adelaide

(undirected graph drawing) |

Matrix properties | |

number of rows | 680,943 |

number of columns | 680,943 |

nonzeros | 30,290,827 |

structural full rank? | yes |

structural rank | 680,943 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 3,359,762 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | complex |

structure | Hermitian |

Cholesky candidate? | yes |

positive definite? | no |

author | C. Sinclair |

editor | T. Davis |

date | 2007 |

kind | materials problem |

2D/3D problem? | yes |

Additional fields | size and type |

b | sparse 680943-by-1 |

shift | sparse 680943-by-680943 |

Notes:

The A matrix is produced using 3-D spectral-element elastic wave modelling in the frequency domain. The medium is homogeneous and isotropic with elastic coefficients: c11 = 6.30, c44 = 1.00 The B matrix represents a real y-directed source, placed approximately in the centre. The model size in elements is 20x20x20. Each element is 1m x1m x 1m. Each element is a 4x4x4 Gauss-Lobbato-Legendre mesh, so the height, width and depth of the system is 61 nodes. There are 3 unknown components at each node - the x, y and z displacements. The A matrix therefore has dimension 680943 x 680943, where ((20 x 4) - (20 - 1))^3 * 3 = 680943. The problem domain is earth sciences. Note that A is complex and b is sparse and real (b has a single nonzero). The A matrix was provided with a nonzero imaginary part, but was otherwise complex Hermitian. To save space in the Matrix Market and Rutherford/Boeing formats, the A matrix here has had this imaginary diagonal removed. The shift can be found in the aux.shift auxiliary matrix. To reproduce the original A matrix, use A = Problem.A + Problem.aux.shift ;

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 9,565,680,684 |

Cholesky flop count | 4.3e+14 |

nnz(L+U), no partial pivoting, with AMD | 19,130,680,425 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 16,486,249,140 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 34,447,602,838 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 3359762 explicit zero entries.
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*For a description of the statistics displayed above,
click here.
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*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.
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