%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/Sinclair/3Dspectralwave2
% name: Sinclair/3Dspectralwave2
% [3-D spectral-element elastic wave modelling in freq. domain, C. Sinclair, Univ. Adelaide]
% id: 1857
% date: 2007
% author: C. Sinclair
% ed: T. Davis
% fields: name title A id date author ed kind Zeros b notes aux
% aux: shift
% kind: materials problem
%-------------------------------------------------------------------------------
% notes:
% The A matrix is produced using 3-D spectral-element elastic wave modelling in
% the frequency domain.The medium is homogeneous and isotropic with elastic    
% coefficients: c11 = 6.30, c44 = 1.00. The B matrix contains only one non-zero
% entry, representing a real y-directed source, placed approximately in the    
% centre.  The model size in elements is 10x10x10. Each element is 1m x1m x 1m.
% Each element is a 4x4x4 Gauss-Lobbato-Legendre mesh, so the height, width and
% depth of the system is 31 nodes. There are 3 unknown complex components at   
% each node - the x, y and z displacements. The A matrix therefore has         
% dimension 89373 x 89373.  ((10 x 4) - (10 - 1))^3 * 3 = 89373.  The solution 
% will consist of x-z planes.  Note that A is complex and b is sparse and real 
% (b has a single nonzero).                                                    
%                                                                              
% The A matrix was provided with a nonzero imaginary part, but was otherwise   
% complex Hermitian.  To save space in the Matrix Market and Rutherford/Boeing 
% formats, the A matrix here has had this imaginary diagonal removed.  The     
% shift can be found in the aux.shift auxiliary matrix.  To reproduce the      
% original A matrix, use A = Problem.A + Problem.aux.shift ;                   
%-------------------------------------------------------------------------------
