The following statistics is based on the number test problems that could be
solved using a prescribed drop tolerance. "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 | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 12.1 | 12.1 | 24.2 | 24.2 | 24.2 | 36.4 | 39.4 | 60.6 | 63.6 |
---|
MMD | 33 | 12.1 | 12.1 | 21.2 | 21.2 | 21.2 | 36.4 | 42.4 | 60.6 | 66.7 |
---|
RCM | 33 | 12.1 | 12.1 | 21.2 | 21.2 | 21.2 | 36.4 | 39.4 | 54.5 | 63.6 |
---|
| ILUTP + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 42.4 | 42.4 | 63.6 | 63.6 | 63.6 | 75.8 | 84.8 | 84.8 | 90.9 |
---|
MMD | 33 | 42.4 | 42.4 | 69.7 | 69.7 | 69.7 | 75.8 | 84.8 | 84.8 | 90.9 |
---|
RCM | 33 | 42.4 | 42.4 | 69.7 | 69.7 | 69.7 | 78.8 | 84.8 | 84.8 | 90.9 |
---|
|
|
IB-ILUC |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 12.1 | 15.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 |
---|
MMD | 33 | 12.1 | 18.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 |
---|
RCM | 33 | 12.1 | 18.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 | 21.2 |
---|
| IB-ILUC + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 42.4 | 54.5 | 72.7 | 72.7 | 75.8 | 78.8 | 84.8 | 84.8 | 84.8 |
---|
MMD | 33 | 48.5 | 54.5 | 75.8 | 75.8 | 75.8 | 81.8 | 84.8 | 84.8 | 100.0 |
---|
RCM | 33 | 42.4 | 54.5 | 63.6 | 72.7 | 78.8 | 78.8 | 84.8 | 87.9 | 100.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 45.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 87.9 | 90.9 | 97.0 |
---|
MMD | 33 | 36.4 | 48.5 | 54.5 | 57.6 | 66.7 | 72.7 | 78.8 | 84.8 | 100.0 |
---|
RCM | 33 | 48.5 | 63.6 | 72.7 | 81.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 45.5 | 51.5 | 69.7 | 78.8 | 78.8 | 87.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 75.8 | 75.8 | 84.8 | 84.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 |
---|
MMD | 33 | 75.8 | 81.8 | 84.8 | 90.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 |
---|
RCM | 33 | 72.7 | 84.8 | 84.8 | 87.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 90.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 75.0 | 75.0 | 78.1 | 81.2 | 84.4 | 84.4 | 90.6 | 90.6 | 90.6 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 45.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 87.9 | 90.9 | 97.0 |
---|
MMD | 33 | 36.4 | 48.5 | 54.5 | 57.6 | 66.7 | 72.7 | 78.8 | 84.8 | 100.0 |
---|
RCM | 33 | 48.5 | 63.6 | 72.7 | 81.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 45.5 | 51.5 | 69.7 | 78.8 | 78.8 | 87.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 75.8 | 75.8 | 84.8 | 84.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 |
---|
MMD | 33 | 75.8 | 81.8 | 84.8 | 90.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 |
---|
RCM | 33 | 72.7 | 84.8 | 84.8 | 87.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 90.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 75.0 | 75.0 | 78.1 | 81.2 | 84.4 | 84.4 | 90.6 | 90.6 | 90.6 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 45.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 90.9 | 90.9 | 100.0 |
---|
MMD | 33 | 36.4 | 45.5 | 57.6 | 57.6 | 66.7 | 72.7 | 81.8 | 84.8 | 97.0 |
---|
RCM | 33 | 48.5 | 63.6 | 75.8 | 78.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 48.5 | 54.5 | 69.7 | 78.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 75.8 | 81.8 | 84.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 |
---|
MMD | 33 | 78.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 97.0 |
---|
RCM | 33 | 81.8 | 84.8 | 87.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 97.0 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 90.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 78.1 | 78.1 | 84.4 | 84.4 | 84.4 | 90.6 | 90.6 | 90.6 | 93.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 45.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 90.9 | 90.9 | 100.0 |
---|
MMD | 33 | 36.4 | 45.5 | 57.6 | 57.6 | 66.7 | 72.7 | 81.8 | 84.8 | 97.0 |
---|
RCM | 33 | 48.5 | 63.6 | 75.8 | 78.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 48.5 | 54.5 | 69.7 | 78.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 75.8 | 81.8 | 84.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 |
---|
MMD | 33 | 78.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 97.0 |
---|
RCM | 33 | 81.8 | 84.8 | 87.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 97.0 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 90.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 78.1 | 78.1 | 84.4 | 84.4 | 84.4 | 90.6 | 90.6 | 90.6 | 93.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 45.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 90.9 | 93.9 | 100.0 |
---|
MMD | 33 | 42.4 | 48.5 | 57.6 | 57.6 | 63.6 | 72.7 | 81.8 | 84.8 | 97.0 |
---|
RCM | 33 | 48.5 | 63.6 | 72.7 | 81.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 45.5 | 54.5 | 69.7 | 78.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 75.8 | 81.8 | 84.8 | 87.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 |
---|
MMD | 33 | 78.8 | 84.8 | 87.9 | 90.9 | 93.9 | 93.9 | 93.9 | 97.0 | 100.0 |
---|
RCM | 33 | 81.8 | 84.8 | 90.9 | 90.9 | 90.9 | 90.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 87.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 78.1 | 81.2 | 84.4 | 84.4 | 87.5 | 90.6 | 90.6 | 93.8 | 93.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 45.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 90.9 | 93.9 | 100.0 |
---|
MMD | 33 | 42.4 | 48.5 | 57.6 | 57.6 | 63.6 | 72.7 | 81.8 | 84.8 | 97.0 |
---|
RCM | 33 | 48.5 | 63.6 | 72.7 | 81.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 45.5 | 54.5 | 69.7 | 78.8 | 84.8 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 75.8 | 81.8 | 84.8 | 87.9 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 |
---|
MMD | 33 | 78.8 | 84.8 | 87.9 | 90.9 | 93.9 | 93.9 | 93.9 | 97.0 | 100.0 |
---|
RCM | 33 | 81.8 | 84.8 | 90.9 | 90.9 | 90.9 | 90.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 87.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 78.1 | 81.2 | 84.4 | 84.4 | 87.5 | 90.6 | 90.6 | 93.8 | 93.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 48.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 90.9 | 93.9 | 100.0 |
---|
MMD | 33 | 39.4 | 48.5 | 57.6 | 57.6 | 66.7 | 72.7 | 84.8 | 87.9 | 97.0 |
---|
RCM | 33 | 48.5 | 63.6 | 72.7 | 81.8 | 84.8 | 93.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 48.5 | 54.5 | 69.7 | 78.8 | 84.8 | 93.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 78.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 78.8 | 84.8 | 87.9 | 90.9 | 93.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
RCM | 33 | 81.8 | 84.8 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 87.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 78.1 | 84.4 | 84.4 | 84.4 | 90.6 | 90.6 | 93.8 | 93.8 | 93.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 48.5 | 54.5 | 63.6 | 69.7 | 75.8 | 78.8 | 90.9 | 93.9 | 100.0 |
---|
MMD | 33 | 39.4 | 48.5 | 57.6 | 57.6 | 66.7 | 72.7 | 84.8 | 87.9 | 97.0 |
---|
RCM | 33 | 48.5 | 63.6 | 72.7 | 81.8 | 84.8 | 93.9 | 100.0 | 100.0 | 100.0 |
---|
PQ | 33 | 48.5 | 54.5 | 69.7 | 78.8 | 84.8 | 93.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
| ILUPACK + MC64 |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 33 | 78.8 | 84.8 | 84.8 | 90.9 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 |
---|
MMD | 33 | 78.8 | 84.8 | 87.9 | 90.9 | 93.9 | 93.9 | 97.0 | 100.0 | 100.0 |
---|
RCM | 33 | 81.8 | 84.8 | 90.9 | 90.9 | 93.9 | 93.9 | 93.9 | 97.0 | 97.0 |
---|
PQ | 33 | 72.7 | 75.8 | 84.8 | 84.8 | 87.9 | 90.9 | 100.0 | 100.0 | 100.0 |
---|
ND | 32 | 78.1 | 84.4 | 84.4 | 84.4 | 90.6 | 90.6 | 93.8 | 93.8 | 93.8 |
---|
|
|