The following statistics is based on the number test problems that could be
solved using a prescribed fill-in factor. "Solved" in this context means that
restarted GMRES(30) converged within 500 steps of iteration (using a relative
tolerance of sqrt(eps)~10-8
Abbreviations for Preconditioners
|
ILUPACK
|
inverse-based Multilevel ILU. Uses the concept of ARMS and an
inverse based partial ILUC
|
ILUPACK - MEDIUM VERSION
|
medium Schur-complement used, less
sensitive w.r.t. drop tolerances
|
ILUPACK - SIMPLE VERSION
|
simple Schur-complement used, more
sensitive w.r.t. drop tolerances, but often faster if it works
|
ILUTP
|
incomplete LU decomposition with pivoting from SPARSKIT, based on
a recent binary search tree implementation
|
IB-ILUC
|
inverse-based
incomplete LU decomposition WITHOUT pivoting, based on the Crout
version. The norm of the inverse triangular factors is
included in the dropping strategy
|
PARDISO
|
sparse direct solver. For details see the
PARDISO home page
|
Performance
statistics
for chemical engineering (in tables)
|
ILUTP |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | AMF | 33 | 14.0 | 19.0 | 22.0 | 24.0 | 27.0 | 28.0 | 30.0 | 31.0 | 32.0 |
---|
MMD | 33 | 17.0 | 21.0 | 25.0 | 28.0 | 28.0 | 30.0 | 33.0 | 33.0 | 33.0 |
---|
RCM | 33 | 15.0 | 23.0 | 25.0 | 28.0 | 28.0 | 31.0 | 33.0 | 33.0 | 33.0 |
---|
ND | 33 | 17.0 | 20.0 | 26.0 | 28.0 | 29.0 | 32.0 | 33.0 | 33.0 | 33.0 |
---|
| ILUTP + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | AMF | 33 | 42.4 | 57.6 | 66.7 | 72.7 | 81.8 | 84.8 | 90.9 | 93.9 | 97.0 |
---|
MMD | 33 | 51.5 | 63.6 | 75.8 | 84.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
RCM | 33 | 45.5 | 69.7 | 75.8 | 84.8 | 84.8 | 93.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 33 | 51.5 | 60.6 | 78.8 | 84.8 | 87.9 | 97.0 | 100.0 | 100.0 | 100.0 |
---|
|
|
IB-ILUC |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | AMF | 33 | 16.0 | 19.0 | 25.0 | 25.0 | 27.0 | 27.0 | 28.0 | 28.0 | 28.0 |
---|
MMD | 33 | 18.0 | 22.0 | 27.0 | 28.0 | 28.0 | 33.0 | 33.0 | 33.0 | 33.0 |
---|
RCM | 33 | 14.0 | 22.0 | 24.0 | 28.0 | 29.0 | 32.0 | 33.0 | 33.0 | 33.0 |
---|
ND | 33 | 17.0 | 20.0 | 26.0 | 28.0 | 32.0 | 33.0 | 33.0 | 33.0 | 33.0 |
---|
| IB-ILUC + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | AMF | 33 | 48.5 | 57.6 | 75.8 | 75.8 | 81.8 | 81.8 | 84.8 | 84.8 | 84.8 |
---|
MMD | 33 | 54.5 | 66.7 | 81.8 | 84.8 | 84.8 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 33 | 42.4 | 66.7 | 72.7 | 84.8 | 87.9 | 97.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 33 | 51.5 | 60.6 | 78.8 | 84.8 | 97.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 9.1 | 66.7 | 75.8 | 87.9 | 90.9 | 93.9 | 97.0 | 97.0 | 97.0 |
---|
MMD | 33 | 9.1 | 66.7 | 75.8 | 81.8 | 90.9 | 90.9 | 97.0 | 97.0 | 100.0 |
---|
RCM | 33 | 9.1 | 63.6 | 75.8 | 84.8 | 90.9 | 93.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
ND | 0 | 300.0 | 2200.0 | 2300.0 | 2300.0 | 2500.0 | 2500.0 | 2700.0 | 2700.0 | 2700.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 36.4 | 78.8 | 84.8 | 87.9 | 90.9 | 90.9 | 90.9 | 90.9 | 90.9 |
---|
MMD | 33 | 45.5 | 78.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 | 90.9 | 90.9 |
---|
RCM | 33 | 27.3 | 72.7 | 84.8 | 90.9 | 90.9 | 90.9 | 90.9 | 90.9 | 90.9 |
---|
PQ | 33 | 33.3 | 63.6 | 81.8 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 |
---|
ND | 32 | 40.6 | 81.2 | 87.5 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 28 | 10.7 | 78.6 | 82.1 | 82.1 | 89.3 | 89.3 | 96.4 | 96.4 | 96.4 |
---|
MMD | 2 | 0.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 33 | 9.1 | 69.7 | 84.8 | 90.9 | 90.9 | 97.0 | 97.0 | 100.0 | 100.0 |
---|
PQ | 33 | 3.0 | 66.7 | 81.8 | 90.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 39.4 | 78.8 | 84.8 | 90.9 | 90.9 | 90.9 | 90.9 | 90.9 | 90.9 |
---|
MMD | 33 | 51.5 | 78.8 | 90.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
RCM | 33 | 27.3 | 72.7 | 87.9 | 87.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
PQ | 33 | 15.2 | 75.8 | 87.9 | 90.9 | 93.9 | 93.9 | 100.0 | 100.0 | 100.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 9.1 | 60.6 | 75.8 | 87.9 | 90.9 | 90.9 | 97.0 | 97.0 | 97.0 |
---|
MMD | 33 | 9.1 | 57.6 | 75.8 | 84.8 | 87.9 | 87.9 | 93.9 | 97.0 | 97.0 |
---|
RCM | 33 | 9.1 | 60.6 | 75.8 | 84.8 | 90.9 | 90.9 | 97.0 | 100.0 | 100.0 |
---|
PQ | 33 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
ND | 0 | 300.0 | 2000.0 | 2300.0 | 2500.0 | 2500.0 | 2500.0 | 2800.0 | 2800.0 | 2800.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 36.4 | 75.8 | 84.8 | 87.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 45.5 | 78.8 | 84.8 | 84.8 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
RCM | 33 | 15.2 | 69.7 | 81.8 | 87.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
PQ | 33 | 30.3 | 63.6 | 72.7 | 87.9 | 87.9 | 87.9 | 90.9 | 90.9 | 90.9 |
---|
ND | 32 | 43.8 | 81.2 | 87.5 | 93.8 | 93.8 | 93.8 | 96.9 | 96.9 | 96.9 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 28 | 10.7 | 71.4 | 82.1 | 89.3 | 89.3 | 89.3 | 100.0 | 100.0 | 100.0 |
---|
MMD | 2 | 0.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 33 | 9.1 | 63.6 | 84.8 | 90.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
PQ | 33 | 3.0 | 60.6 | 78.8 | 90.9 | 90.9 | 90.9 | 97.0 | 100.0 | 100.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 42.4 | 78.8 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 48.5 | 78.8 | 87.9 | 90.9 | 90.9 | 93.9 | 93.9 | 97.0 | 97.0 |
---|
RCM | 33 | 24.2 | 66.7 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 97.0 |
---|
PQ | 33 | 15.2 | 69.7 | 87.9 | 90.9 | 90.9 | 97.0 | 100.0 | 100.0 | 100.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 9.1 | 60.6 | 75.8 | 84.8 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
MMD | 33 | 9.1 | 57.6 | 75.8 | 84.8 | 87.9 | 87.9 | 93.9 | 97.0 | 97.0 |
---|
RCM | 33 | 9.1 | 57.6 | 69.7 | 81.8 | 87.9 | 87.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
ND | 0 | 300.0 | 2000.0 | 2300.0 | 2500.0 | 2500.0 | 2600.0 | 2700.0 | 2800.0 | 2800.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 27.3 | 69.7 | 81.8 | 87.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 33.3 | 72.7 | 81.8 | 84.8 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
RCM | 33 | 15.2 | 63.6 | 78.8 | 87.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
PQ | 33 | 21.2 | 60.6 | 69.7 | 84.8 | 87.9 | 87.9 | 90.9 | 90.9 | 90.9 |
---|
ND | 32 | 34.4 | 75.0 | 87.5 | 93.8 | 93.8 | 93.8 | 96.9 | 96.9 | 96.9 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 28 | 10.7 | 71.4 | 82.1 | 89.3 | 89.3 | 92.9 | 96.4 | 100.0 | 100.0 |
---|
MMD | 2 | 0.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 33 | 9.1 | 60.6 | 78.8 | 90.9 | 90.9 | 97.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 3.0 | 57.6 | 78.8 | 87.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 33.3 | 72.7 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 36.4 | 75.8 | 84.8 | 90.9 | 90.9 | 93.9 | 93.9 | 97.0 | 97.0 |
---|
RCM | 33 | 15.2 | 63.6 | 78.8 | 90.9 | 90.9 | 90.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 15.2 | 69.7 | 87.9 | 90.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 9.1 | 57.6 | 75.8 | 87.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
MMD | 33 | 9.1 | 57.6 | 75.8 | 87.9 | 87.9 | 87.9 | 93.9 | 93.9 | 97.0 |
---|
RCM | 33 | 9.1 | 57.6 | 69.7 | 78.8 | 87.9 | 87.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
ND | 0 | 300.0 | 1900.0 | 2300.0 | 2500.0 | 2500.0 | 2600.0 | 2700.0 | 2800.0 | 2800.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 21.2 | 66.7 | 81.8 | 84.8 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 33.3 | 66.7 | 81.8 | 84.8 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
RCM | 33 | 12.1 | 54.5 | 75.8 | 81.8 | 90.9 | 93.9 | 93.9 | 93.9 | 93.9 |
---|
PQ | 33 | 21.2 | 42.4 | 66.7 | 84.8 | 87.9 | 87.9 | 90.9 | 90.9 | 90.9 |
---|
ND | 32 | 21.9 | 75.0 | 84.4 | 93.8 | 93.8 | 93.8 | 96.9 | 96.9 | 96.9 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 28 | 10.7 | 67.9 | 82.1 | 89.3 | 89.3 | 92.9 | 96.4 | 100.0 | 100.0 |
---|
MMD | 2 | 0.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 33 | 9.1 | 60.6 | 78.8 | 87.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
PQ | 33 | 3.0 | 57.6 | 78.8 | 87.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 0.5 | 1.0 | 1.5 | 2.0 | 3.0 | 4.0 | 6.0 | 8.0 | 10.0 | AMF | 33 | 21.2 | 72.7 | 81.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 33.3 | 75.8 | 81.8 | 87.9 | 90.9 | 93.9 | 93.9 | 97.0 | 97.0 |
---|
RCM | 33 | 12.1 | 51.5 | 75.8 | 84.8 | 90.9 | 93.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 15.2 | 66.7 | 87.9 | 90.9 | 90.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
|
|
PARDISO |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | | 33 | 0.0 | 0.0 | 0.0 | 0.0 | 3.0 | 6.0 | 11.0 | 24.0 | 29.0 |
---|
| PARDISO + MC64 |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | | 33 | 0.0 | 0.0 | 0.0 | 0.0 | 9.1 | 18.2 | 33.3 | 72.7 | 87.9 |
---|
|
|