Matrix: Um/2cubes_sphere

Description: FEM, electromagnetics, 2 cubes in a sphere. Evan Um, Geophysics, Stanford

 (undirected graph drawing)

• Matrix group: Um
• download as a MATLAB mat-file, file size: 13 MB. Use UFget(1919) or UFget('Um/2cubes_sphere') in MATLAB.

 Matrix properties number of rows 101,492 number of columns 101,492 nonzeros 1,647,264 structural full rank? yes structural rank 101,492 # of blocks from dmperm 1 # strongly connected comp. 1 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? yes positive definite? yes

 author E. Um editor T. Davis date 2008 kind electromagnetics problem 2D/3D problem? yes

 Additional fields size and type b full 101492-by-1

Notes:

```A matrix from Evan Um, Geophysics, Stanford.  Studying finite-element
time domain solvers for electromagnetic diffusion equations. The 3-D
computational domain consists of 88,213 tetrahedral elements.  The
computational domain consists of the two parts.  First, there are two
300m x 300m x 150m boxes where a fine mesh is used.  Second, the two
boxes are enclosed by a large sphere whose radius is 10 km.  An element
growth factor is used to increase the mesh size gradually inside the
sphere.  This is because absorbing boundary conditions are not very
good choices for these problems.  The finite element technique is
edge-based rather than node-based.  Therefore, the unknowns are
amplitudes of electromagnetic fields on an edge of each element.
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 88,679,332 Cholesky flop count 3.0e+11 nnz(L+U), no partial pivoting, with AMD 177,257,172 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 209,702,037 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 394,050,005