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 device simulation (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 | 28 | 0.0 | 0.0 | 17.9 | 17.9 | 17.9 | 32.1 | 67.9 | 78.6 | 89.3 |
---|
MMD | 28 | 3.6 | 3.6 | 32.1 | 32.1 | 32.1 | 71.4 | 71.4 | 89.3 | 100.0 |
---|
RCM | 28 | 7.1 | 7.1 | 53.6 | 53.6 | 53.6 | 71.4 | 71.4 | 92.9 | 100.0 |
---|
| 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 | 6 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 16.7 |
---|
MMD | 6 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 16.7 | 50.0 |
---|
RCM | 28 | 0.0 | 0.0 | 7.1 | 7.1 | 7.1 | 17.9 | 28.6 | 39.3 | 57.1 |
---|
|
|
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 | 28 | 0.0 | 0.0 | 17.9 | 57.1 | 60.7 | 67.9 | 67.9 | 67.9 | 67.9 |
---|
MMD | 28 | 0.0 | 21.4 | 46.4 | 64.3 | 71.4 | 71.4 | 71.4 | 89.3 | 89.3 |
---|
RCM | 28 | 3.6 | 32.1 | 53.6 | 60.7 | 67.9 | 67.9 | 71.4 | 78.6 | 89.3 |
---|
| 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 | 8 | 12.5 | 12.5 | 12.5 | 12.5 | 25.0 | 37.5 | 50.0 | 50.0 | 75.0 |
---|
MMD | 7 | 14.3 | 14.3 | 14.3 | 14.3 | 42.9 | 57.1 | 71.4 | 100.0 | 100.0 |
---|
RCM | 28 | 3.6 | 17.9 | 46.4 | 53.6 | 67.9 | 75.0 | 78.6 | 89.3 | 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 | 15 | 13.3 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 40.0 | 40.0 | 40.0 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 0.0 | 0.0 | 18.2 | 18.2 | 18.2 | 18.2 | 18.2 |
---|
PQ | 28 | 25.0 | 35.7 | 46.4 | 46.4 | 78.6 | 82.1 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 |
---|
| 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 | 15 | 33.3 | 40.0 | 53.3 | 53.3 | 66.7 | 66.7 | 93.3 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 0.0 | 33.3 | 33.3 | 33.3 | 33.3 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 26.7 | 40.0 | 53.3 | 73.3 | 73.3 | 80.0 | 86.7 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 63.2 | 78.9 |
---|
ND | 22 | 50.0 | 54.5 | 63.6 | 68.2 | 68.2 | 77.3 | 95.5 | 100.0 | 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 | 15 | 13.3 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 40.0 | 40.0 | 40.0 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 0.0 | 0.0 | 18.2 | 18.2 | 18.2 | 18.2 | 18.2 |
---|
PQ | 28 | 25.0 | 35.7 | 46.4 | 46.4 | 78.6 | 82.1 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 |
---|
| 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 | 15 | 33.3 | 40.0 | 53.3 | 53.3 | 66.7 | 66.7 | 93.3 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 0.0 | 33.3 | 33.3 | 33.3 | 33.3 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 26.7 | 40.0 | 53.3 | 73.3 | 73.3 | 80.0 | 86.7 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 63.2 | 78.9 |
---|
ND | 22 | 50.0 | 54.5 | 63.6 | 68.2 | 68.2 | 77.3 | 95.5 | 100.0 | 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 | 15 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 40.0 | 40.0 | 40.0 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 9.1 | 18.2 | 36.4 | 36.4 | 36.4 | 36.4 | 36.4 |
---|
PQ | 28 | 32.1 | 46.4 | 46.4 | 57.1 | 82.1 | 82.1 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 |
---|
| 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 | 15 | 46.7 | 53.3 | 60.0 | 60.0 | 73.3 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 33.3 | 33.3 | 33.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 40.0 | 53.3 | 60.0 | 73.3 | 80.0 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 63.2 | 78.9 |
---|
ND | 22 | 63.6 | 68.2 | 68.2 | 72.7 | 77.3 | 77.3 | 100.0 | 100.0 | 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 | 15 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 40.0 | 40.0 | 40.0 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 9.1 | 18.2 | 36.4 | 36.4 | 36.4 | 36.4 | 36.4 |
---|
PQ | 28 | 32.1 | 46.4 | 46.4 | 57.1 | 82.1 | 82.1 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 | 15.8 |
---|
| 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 | 15 | 46.7 | 53.3 | 60.0 | 60.0 | 73.3 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 33.3 | 33.3 | 33.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 40.0 | 53.3 | 60.0 | 73.3 | 80.0 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 63.2 | 78.9 |
---|
ND | 22 | 63.6 | 68.2 | 68.2 | 72.7 | 77.3 | 77.3 | 100.0 | 100.0 | 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 | 15 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 40.0 | 40.0 | 40.0 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 0.0 | 9.1 | 27.3 | 45.5 | 54.5 | 54.5 | 54.5 |
---|
PQ | 28 | 39.3 | 46.4 | 46.4 | 50.0 | 82.1 | 82.1 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 15.8 | 21.1 | 31.6 | 63.2 | 68.4 | 73.7 | 78.9 | 78.9 | 78.9 |
---|
| 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 | 15 | 46.7 | 53.3 | 53.3 | 73.3 | 80.0 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 33.3 | 33.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 46.7 | 46.7 | 60.0 | 80.0 | 80.0 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 63.2 | 78.9 |
---|
ND | 22 | 63.6 | 68.2 | 77.3 | 77.3 | 77.3 | 95.5 | 100.0 | 100.0 | 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 | 15 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 26.7 | 40.0 | 40.0 | 40.0 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 0.0 | 9.1 | 27.3 | 45.5 | 54.5 | 54.5 | 54.5 |
---|
PQ | 28 | 39.3 | 46.4 | 46.4 | 50.0 | 82.1 | 82.1 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 15.8 | 21.1 | 31.6 | 63.2 | 68.4 | 73.7 | 78.9 | 78.9 | 78.9 |
---|
| 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 | 15 | 46.7 | 53.3 | 53.3 | 73.3 | 80.0 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 33.3 | 33.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 46.7 | 46.7 | 60.0 | 80.0 | 80.0 | 80.0 | 93.3 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 63.2 | 78.9 |
---|
ND | 22 | 63.6 | 68.2 | 77.3 | 77.3 | 77.3 | 95.5 | 100.0 | 100.0 | 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 | 15 | 26.7 | 33.3 | 33.3 | 33.3 | 33.3 | 40.0 | 53.3 | 53.3 | 53.3 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 18.2 | 27.3 | 45.5 | 63.6 | 72.7 | 72.7 | 72.7 |
---|
PQ | 27 | 37.0 | 44.4 | 44.4 | 48.1 | 81.5 | 81.5 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 15.8 | 68.4 | 68.4 | 68.4 | 73.7 | 73.7 | 94.7 | 94.7 | 94.7 |
---|
| 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 | 15 | 53.3 | 60.0 | 66.7 | 73.3 | 73.3 | 73.3 | 86.7 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 33.3 | 33.3 | 66.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 46.7 | 53.3 | 80.0 | 80.0 | 80.0 | 80.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 73.7 | 89.5 |
---|
ND | 22 | 68.2 | 68.2 | 72.7 | 77.3 | 81.8 | 95.5 | 100.0 | 100.0 | 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 | 15 | 26.7 | 33.3 | 33.3 | 33.3 | 33.3 | 40.0 | 53.3 | 53.3 | 53.3 |
---|
MMD | 3 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 66.7 | 66.7 | 66.7 |
---|
RCM | 11 | 0.0 | 0.0 | 18.2 | 27.3 | 45.5 | 63.6 | 72.7 | 72.7 | 72.7 |
---|
PQ | 27 | 37.0 | 44.4 | 44.4 | 48.1 | 81.5 | 81.5 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 15.8 | 68.4 | 68.4 | 68.4 | 73.7 | 73.7 | 94.7 | 94.7 | 94.7 |
---|
| 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 | 15 | 53.3 | 60.0 | 66.7 | 73.3 | 73.3 | 73.3 | 86.7 | 100.0 | 100.0 |
---|
MMD | 3 | 0.0 | 33.3 | 33.3 | 66.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 46.7 | 53.3 | 80.0 | 80.0 | 80.0 | 80.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 19 | 0.0 | 0.0 | 5.3 | 5.3 | 21.1 | 36.8 | 52.6 | 73.7 | 89.5 |
---|
ND | 22 | 68.2 | 68.2 | 72.7 | 77.3 | 81.8 | 95.5 | 100.0 | 100.0 | 100.0 |
---|
|
|