Matrix: Sinclair/3Dspectralwave2

Description: 3-D spectral-element elastic wave modelling in freq. domain, C. Sinclair, Univ. Adelaide

 (undirected graph drawing)

• Matrix group: Sinclair
• download as a MATLAB mat-file, file size: 73 MB. Use UFget(1857) or UFget('Sinclair/3Dspectralwave2') in MATLAB.

 Matrix properties number of rows 292,008 number of columns 292,008 nonzeros 12,935,272 structural full rank? yes structural rank 292,008 # of blocks from dmperm 1 # strongly connected comp. 1 explicit zero entries 1,387,472 nonzero pattern symmetry symmetric numeric value symmetry symmetric type complex structure Hermitian Cholesky candidate? yes positive definite? no

 author C. Sinclair editor T. Davis date 2007 kind materials problem 2D/3D problem? yes

 Additional fields size and type b sparse 292008-by-1 shift sparse 292008-by-292008

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 ;
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 2,070,437,023 Cholesky flop count 4.2e+13 nnz(L+U), no partial pivoting, with AMD 4,140,582,038 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 3,742,233,527 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 7,912,859,348

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 1387472 explicit zero entries.