**Matrix: Janna/ML_Laplace**

Description: 2D Poisson problem, meshless local Petrov-Galerkin method

(undirected graph drawing) |

Matrix properties | |

number of rows | 377,002 |

number of columns | 377,002 |

nonzeros | 27,582,698 |

structural full rank? | yes |

structural rank | 377,002 |

# of blocks from dmperm | 2,503 |

# strongly connected comp. | 2,503 |

explicit zero entries | 107,274 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | 0% |

type | real |

structure | unsymmetric |

Cholesky candidate? | no |

positive definite? | no |

author | C. Janna, M. Ferronato, G. Pini |

editor | T. Davis |

date | 2012 |

kind | structural problem |

2D/3D problem? | yes |

Notes:

Authors: Carlo Janna, Massimiliano Ferronato, Giorgio Pini Matrix type: Unsymmetric # equations: 377,002 # non-zeroes: 27,689,972 Problem description: Poisson problem The matrix ML_Laplace has been obtained by discretizing a 2D Poisson equation with a Meshless Local Petrov-Galerkin method. Further information can be found in the following papers: 1) G. Pini, A. Mazzia, and F. Sartoretto. Accurate MLPG solution of 3D potential problems. CMES - Computer Modeling in Engineering & Sciences 36 (2008), pp. 43-64. 2) M. Ferronato, C. Janna and G. Pini. A generalized Block FSAI preconditioner for unsymmetric indefinite matrices. Journal of Computational and Applied Mathematics (2012), submitted.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 284,522,480 |

Cholesky flop count | 5.0e+11 |

nnz(L+U), no partial pivoting, with AMD | 568,667,958 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 455,980,664 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 899,086,831 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 107274 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.
*