Matrix: MaxPlanck/shallow_water2

Description: shallow water modelling, Max-Planck Inst. of Meteorology

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• Matrix group: MaxPlanck
• download as a MATLAB mat-file, file size: 2 MB. Use UFget(2262) or UFget('MaxPlanck/shallow_water2') in MATLAB.

 Matrix properties number of rows 81,920 number of columns 81,920 nonzeros 327,680 structural full rank? yes structural rank 81,920 # 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 K. Leppkes, U. Naumann editor T. Davis date 2009 kind computational fluid dynamics problem 2D/3D problem? yes

Notes:

```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.
```

 Ordering statistics: result 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