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 circuit simulation(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 | 15 | 8.0 | 13.0 | 14.0 | 15.0 | 15.0 | 15.0 | 15.0 | 15.0 | 15.0 |
---|
MMD | 23 | 15.0 | 21.0 | 22.0 | 23.0 | 23.0 | 23.0 | 23.0 | 23.0 | 23.0 |
---|
RCM | 25 | 14.0 | 18.0 | 20.0 | 21.0 | 23.0 | 23.0 | 23.0 | 24.0 | 24.0 |
---|
ND | 25 | 15.0 | 22.0 | 24.0 | 25.0 | 25.0 | 25.0 | 25.0 | 25.0 | 25.0 |
---|
| 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 | 15 | 53.3 | 86.7 | 93.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 23 | 65.2 | 91.3 | 95.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 25 | 56.0 | 72.0 | 80.0 | 84.0 | 92.0 | 92.0 | 92.0 | 96.0 | 96.0 |
---|
ND | 25 | 60.0 | 88.0 | 96.0 | 100.0 | 100.0 | 100.0 | 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 | 20 | 14.0 | 17.0 | 20.0 | 20.0 | 20.0 | 20.0 | 20.0 | 20.0 | 20.0 |
---|
MMD | 23 | 17.0 | 23.0 | 23.0 | 23.0 | 23.0 | 23.0 | 23.0 | 23.0 | 23.0 |
---|
RCM | 25 | 17.0 | 21.0 | 23.0 | 24.0 | 25.0 | 25.0 | 25.0 | 25.0 | 25.0 |
---|
ND | 19 | 11.0 | 18.0 | 19.0 | 19.0 | 19.0 | 19.0 | 19.0 | 19.0 | 19.0 |
---|
| 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 | 20 | 70.0 | 85.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 23 | 73.9 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 25 | 68.0 | 84.0 | 92.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 19 | 57.9 | 94.7 | 100.0 | 100.0 | 100.0 | 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 | 20 | 40.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 42.1 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 |
---|
RCM | 17 | 11.8 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 8.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 |
---|
ND | 6 | 116.7 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 |
---|
| 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 | 20 | 40.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 42.1 | 94.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 9.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 28.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 |
---|
ND | 12 | 75.0 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 |
---|
|
|
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 | 22 | 27.3 | 86.4 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 |
---|
MMD | 16 | 31.2 | 68.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 |
---|
RCM | 18 | 5.6 | 83.3 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 |
---|
PQ | 22 | 18.2 | 86.4 | 90.9 | 100.0 | 100.0 | 100.0 | 100.0 | 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 | 22 | 40.9 | 86.4 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 22 | 40.9 | 81.8 | 90.9 | 95.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 22 | 9.1 | 86.4 | 95.5 | 95.5 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 |
---|
PQ | 22 | 22.7 | 86.4 | 95.5 | 95.5 | 100.0 | 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 | 20 | 30.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 26.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 11.8 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 12.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 |
---|
ND | 6 | 100.0 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 |
---|
| 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 | 20 | 35.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 36.8 | 94.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 9.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 20.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 |
---|
ND | 12 | 75.0 | 158.3 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 |
---|
|
|
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 | 22 | 22.7 | 86.4 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 |
---|
MMD | 16 | 12.5 | 81.2 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 |
---|
RCM | 18 | 5.6 | 83.3 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 |
---|
PQ | 22 | 18.2 | 86.4 | 90.9 | 95.5 | 100.0 | 100.0 | 100.0 | 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 | 22 | 36.4 | 81.8 | 90.9 | 95.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 22 | 31.8 | 81.8 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 22 | 9.1 | 81.8 | 90.9 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 22 | 22.7 | 86.4 | 95.5 | 95.5 | 100.0 | 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 | 20 | 25.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 26.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 11.8 | 88.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 12.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 |
---|
ND | 6 | 83.3 | 300.0 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 |
---|
| 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 | 20 | 35.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 36.8 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 9.5 | 90.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 28.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 |
---|
ND | 12 | 58.3 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 |
---|
|
|
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 | 22 | 18.2 | 77.3 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 |
---|
MMD | 16 | 12.5 | 81.2 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 |
---|
RCM | 18 | 5.6 | 72.2 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 |
---|
PQ | 22 | 13.6 | 86.4 | 90.9 | 95.5 | 100.0 | 100.0 | 100.0 | 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 | 22 | 31.8 | 86.4 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 22 | 31.8 | 86.4 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 22 | 9.1 | 77.3 | 90.9 | 95.5 | 95.5 | 95.5 | 95.5 | 100.0 | 100.0 |
---|
PQ | 22 | 18.2 | 86.4 | 95.5 | 95.5 | 100.0 | 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 | 20 | 25.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 26.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 5.9 | 82.4 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 8.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 | 24.0 |
---|
ND | 6 | 83.3 | 300.0 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 | 333.3 |
---|
| 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 | 20 | 35.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 36.8 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 9.5 | 81.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 24.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 | 48.0 |
---|
ND | 12 | 66.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 | 166.7 |
---|
|
|
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 | 22 | 18.2 | 77.3 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 | 95.5 |
---|
MMD | 16 | 12.5 | 81.2 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 | 93.8 |
---|
RCM | 18 | 5.6 | 66.7 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 | 94.4 |
---|
PQ | 22 | 13.6 | 86.4 | 90.9 | 95.5 | 100.0 | 100.0 | 100.0 | 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 | 22 | 31.8 | 86.4 | 95.5 | 95.5 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 |
---|
MMD | 22 | 31.8 | 86.4 | 90.9 | 95.5 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 |
---|
RCM | 22 | 9.1 | 63.6 | 90.9 | 95.5 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 |
---|
PQ | 22 | 18.2 | 86.4 | 95.5 | 95.5 | 100.0 | 100.0 | 100.0 | 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 | | 25 | 0.0 | 1.0 | 8.0 | 12.0 | 19.0 | 22.0 | 24.0 | 24.0 | 25.0 |
---|
| 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 | | 25 | 0.0 | 4.0 | 32.0 | 48.0 | 76.0 | 88.0 | 96.0 | 96.0 | 100.0 |
---|
|
|