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 circuit 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 | 20 | 55.0 | 55.0 | 80.0 | 80.0 | 80.0 | 90.0 | 95.0 | 95.0 | 100.0 |
---|
MMD | 23 | 47.8 | 47.8 | 73.9 | 73.9 | 73.9 | 87.0 | 95.7 | 100.0 | 100.0 |
---|
RCM | 25 | 52.0 | 52.0 | 76.0 | 76.0 | 76.0 | 84.0 | 96.0 | 100.0 | 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 | 15 | 46.7 | 46.7 | 66.7 | 66.7 | 66.7 | 66.7 | 86.7 | 93.3 | 93.3 |
---|
MMD | 23 | 43.5 | 43.5 | 60.9 | 60.9 | 60.9 | 78.3 | 87.0 | 91.3 | 95.7 |
---|
RCM | 25 | 40.0 | 40.0 | 56.0 | 56.0 | 56.0 | 68.0 | 88.0 | 92.0 | 96.0 |
---|
|
|
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 | 20 | 60.0 | 70.0 | 75.0 | 80.0 | 85.0 | 95.0 | 95.0 | 95.0 | 95.0 |
---|
MMD | 23 | 52.2 | 60.9 | 60.9 | 65.2 | 65.2 | 87.0 | 91.3 | 95.7 | 95.7 |
---|
RCM | 25 | 52.0 | 64.0 | 72.0 | 72.0 | 72.0 | 88.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 50.0 | 65.0 | 65.0 | 70.0 | 70.0 | 75.0 | 85.0 | 100.0 | 100.0 |
---|
MMD | 23 | 43.5 | 52.2 | 56.5 | 60.9 | 60.9 | 69.6 | 87.0 | 100.0 | 100.0 |
---|
RCM | 25 | 40.0 | 52.0 | 60.0 | 60.0 | 64.0 | 72.0 | 96.0 | 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 | 20 | 80.0 | 85.0 | 85.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 78.9 | 84.2 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 |
---|
RCM | 17 | 88.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 92.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 75.0 | 80.0 | 85.0 | 90.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 78.9 | 84.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 71.4 | 76.2 | 90.5 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 68.0 | 68.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 75.0 | 75.0 | 75.0 | 75.0 | 75.0 | 100.0 | 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 | 20 | 80.0 | 85.0 | 85.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 78.9 | 84.2 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 | 89.5 |
---|
RCM | 17 | 88.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 92.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 75.0 | 80.0 | 85.0 | 90.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 78.9 | 84.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 71.4 | 76.2 | 90.5 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 68.0 | 68.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 75.0 | 75.0 | 75.0 | 75.0 | 75.0 | 100.0 | 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 | 20 | 85.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 84.2 | 84.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 88.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 88.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 83.3 | 83.3 | 83.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 75.0 | 80.0 | 85.0 | 90.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 84.2 | 84.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 71.4 | 85.7 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 68.0 | 68.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 75.0 | 75.0 | 75.0 | 83.3 | 100.0 | 100.0 | 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 | 20 | 85.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 84.2 | 84.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 88.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 88.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 83.3 | 83.3 | 83.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 75.0 | 80.0 | 85.0 | 90.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 84.2 | 84.2 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 71.4 | 85.7 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 68.0 | 68.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 75.0 | 75.0 | 75.0 | 83.3 | 100.0 | 100.0 | 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 | 20 | 95.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 89.5 | 89.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 88.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 83.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 75.0 | 80.0 | 85.0 | 90.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 84.2 | 84.2 | 94.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 76.2 | 90.5 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 68.0 | 72.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 66.7 | 66.7 | 75.0 | 100.0 | 100.0 | 100.0 | 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 | 20 | 95.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 89.5 | 89.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 88.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 83.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 75.0 | 80.0 | 85.0 | 90.0 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 78.9 | 84.2 | 84.2 | 94.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 76.2 | 90.5 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 68.0 | 72.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 66.7 | 66.7 | 75.0 | 100.0 | 100.0 | 100.0 | 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 | 20 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 84.2 | 94.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 88.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 66.7 | 83.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 80.0 | 80.0 | 90.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 84.2 | 84.2 | 89.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 81.0 | 95.2 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 72.0 | 72.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 66.7 | 66.7 | 91.7 | 100.0 | 100.0 | 100.0 | 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 | 20 | 95.0 | 95.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 84.2 | 94.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 17 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 80.0 | 88.0 | 92.0 | 96.0 | 96.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
ND | 6 | 66.7 | 83.3 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
| 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 | 20 | 80.0 | 80.0 | 90.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 19 | 84.2 | 84.2 | 89.5 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 21 | 81.0 | 95.2 | 95.2 | 95.2 | 95.2 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 25 | 72.0 | 72.0 | 76.0 | 84.0 | 84.0 | 88.0 | 88.0 | 92.0 | 96.0 |
---|
ND | 12 | 66.7 | 66.7 | 91.7 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
|
|