%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/MaxPlanck/shallow_water1
% name: MaxPlanck/shallow_water1
% [shallow water modelling, Max-Planck Inst. of Meteorology]
% id: 2261
% date: 2009
% author: K. Leppkes, U. Naumann
% ed: T. Davis
% fields: name title A id date author ed kind notes
% kind: computational fluid dynamics problem
%-------------------------------------------------------------------------------
% 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.               
%-------------------------------------------------------------------------------
