Description: contact mechanics for model of a faulted gas reservoir
|(undirected graph drawing)|
|number of rows||638,802|
|number of columns||638,802|
|structural full rank?||yes|
|# of blocks from dmperm||21,880|
|# strongly connected comp.||21,880|
|explicit zero entries||1,368,620|
|nonzero pattern symmetry||symmetric|
|numeric value symmetry||symmetric|
|author||C. Janna, M. Ferronato|
Authors: Carlo Janna and Massimiliano Ferronato Symmetric Positive Definite Matrix # equations: 638802 # non-zeroes: 28614564 Problem description: contact mechanics The matrix Fault_639 is obtained from a structural problem discretizing a faulted gas reservoir with tetrahedral Finite Elements and triangular Interface Elements. The Interface Elements are used with a Penalty formulation to simulate the faults behaviour. The problem arises from a 3D discretization with three displacement unknowns associated to each node of the grid. Some further information may be found in the following papers: 1) M. Ferronato, G. Gambolati, C. Janna, P. Teatini. "Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs", International Journal for Numerical and Analytical Methods in Geomechanics, 32, pp. 633-657, 2008. 2) M. Ferronato, C. Janna, G. Gambolati. "Mixed constraint preconditioning in computational contact mechanics", Computer Methods in Applied Mechanics and Engineering, 197, pp. 3922-3931, 2008. 3) C. Janna, M. Ferronato, G. Gambolati. "Multilevel incomplete factorizations for the iterative solution of non-linear FE problems". International Journal for Numerical Methods in Engineering, 80, pp. 651-670, 2009. 4) C. Janna, M. Ferronato, G. Gambolati. "A Block FSAI-ILU parallel preconditioner for symmetric positive definite linear systems". SIAM Journal on Scientific Computing, 32, pp. 2468-2484, 2010.
|nnz(chol(P*(A+A'+s*I)*P')) with AMD||3,179,862,040|
|Cholesky flop count||6.4e+13|
|nnz(L+U), no partial pivoting, with AMD||6,359,085,278|
|nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD||3,950,893,717|
|nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD||6,902,951,841|
Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1368620 explicit zero entries.
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.