3-D spectral-element elastic wave modelling in freq. domain, C. Sinclair, Univ. Adelaide
Name 3Dspectralwave
Group Sinclair
Matrix ID 1856
Num Rows 680,943
Num Cols 680,943
Nonzeros 30,290,827
Pattern Entries 33,650,589
Kind Materials Problem
Symmetric No
Date 2007
Author C. Sinclair
Editor T. Davis
Structural Rank 680,943
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 3,359,762
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate yes
Positive Definite no
Type complex
Download MATLAB Rutherford Boeing Matrix Market
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 represents a real         
y-directed source, placed approximately in the centre.  The model size in    
elements is 20x20x20. 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 
61 nodes. There are 3 unknown components at each node - the x, y and z       
displacements. The A matrix therefore has dimension 680943 x 680943, where   
((20 x 4) - (20 - 1))^3 * 3 = 680943. The problem domain is earth sciences.  
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 ;