3-D spectral-element elastic wave modelling in freq. domain, C. Sinclair, Univ. Adelaide
Name 3Dspectralwave2
Group Sinclair
Matrix ID 1857
Num Rows 292,008
Num Cols 292,008
Nonzeros 12,935,272
Pattern Entries 14,322,744
Kind Materials Problem
Symmetric No
Date 2007
Author C. Sinclair
Editor T. Davis
Structural Rank 292,008
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 1,387,472
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 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 ;