Description: shallow water modelling, Max-Planck Inst. of Meteorology
|(undirected graph drawing)|
|number of rows||81,920|
|number of columns||81,920|
|structural full rank?||yes|
|# of blocks from dmperm||1|
|# strongly connected comp.||1|
|explicit zero entries||0|
|nonzero pattern symmetry||symmetric|
|numeric value symmetry||symmetric|
|author||K. Leppkes, U. Naumann|
|kind||computational fluid dynamics problem|
The two shallow_water* matrices arise from weather shallow water equations (see http://www.icon.enes.org), from the Max-Plank Institute of Meteorology. The problem gives rise to an automatic differentiation problem. An iterative solver is used for the larger problem, but a direct sovler is used for finding the adjoints of a linear problem. The velocity field is integrated over a time loop with a semi-implicit method. The implicit part leads to a linear problem A*x=b, whose entries vary with time. Two of these matrices A are in this collection, with shallow_water1 at dtime=100 and shallow_water2 at dtime=200. The nonzero patterns of the two matrices are the same, but shallow_water1 is much slower. The reason is that many denormals appear during factorization, which greatly slows down the BLAS. This can be solved by compiling with gcc -ffast-math, to flush denormals to zero.
|nnz(chol(P*(A+A'+s*I)*P')) with AMD||2,357,535|
|Cholesky flop count||5.8e+08|
|nnz(L+U), no partial pivoting, with AMD||4,633,150|
|nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD||5,355,578|
|nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD||9,691,968|
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.