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 partial differential equations (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 | 81 | 18.5 | 18.5 | 44.4 | 44.4 | 44.4 | 72.8 | 80.2 | 82.7 | 82.7 |
---|
MMD | 81 | 18.5 | 18.5 | 35.8 | 35.8 | 35.8 | 60.5 | 69.1 | 75.3 | 79.0 |
---|
RCM | 81 | 18.5 | 18.5 | 48.1 | 48.1 | 48.1 | 76.5 | 85.2 | 86.4 | 87.7 |
---|
| 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 | 81 | 16.0 | 16.0 | 46.9 | 46.9 | 46.9 | 76.5 | 81.5 | 81.5 | 81.5 |
---|
MMD | 81 | 16.0 | 16.0 | 45.7 | 45.7 | 45.7 | 77.8 | 86.4 | 87.7 | 87.7 |
---|
RCM | 81 | 14.8 | 14.8 | 43.2 | 43.2 | 43.2 | 79.0 | 84.0 | 84.0 | 85.2 |
---|
|
|
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 | 81 | 17.3 | 18.5 | 22.2 | 27.2 | 28.4 | 29.6 | 30.9 | 32.1 | 32.1 |
---|
MMD | 81 | 17.3 | 19.8 | 22.2 | 30.9 | 34.6 | 35.8 | 40.7 | 42.0 | 43.2 |
---|
RCM | 81 | 28.4 | 33.3 | 43.2 | 48.1 | 51.9 | 51.9 | 54.3 | 55.6 | 59.3 |
---|
| 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 | 81 | 16.0 | 33.3 | 49.4 | 59.3 | 61.7 | 64.2 | 67.9 | 69.1 | 71.6 |
---|
MMD | 81 | 16.0 | 30.9 | 48.1 | 53.1 | 59.3 | 64.2 | 67.9 | 70.4 | 72.8 |
---|
RCM | 81 | 17.3 | 42.0 | 72.8 | 76.5 | 76.5 | 77.8 | 80.2 | 81.5 | 85.2 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 48.8 | 71.2 | 78.8 | 78.8 | 80.0 | 85.0 | 85.0 | 88.8 | 90.0 |
---|
MMD | 80 | 48.8 | 70.0 | 80.0 | 80.0 | 82.5 | 85.0 | 86.2 | 88.8 | 90.0 |
---|
RCM | 78 | 62.8 | 73.1 | 83.3 | 85.9 | 85.9 | 85.9 | 88.5 | 92.3 | 94.9 |
---|
PQ | 80 | 46.2 | 73.8 | 83.8 | 86.2 | 87.5 | 90.0 | 92.5 | 96.2 | 97.5 |
---|
ND | 59 | 42.4 | 59.3 | 72.9 | 72.9 | 76.3 | 79.7 | 83.1 | 86.4 | 86.4 |
---|
| 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 | 80 | 57.5 | 67.5 | 77.5 | 80.0 | 80.0 | 81.2 | 86.2 | 88.8 | 90.0 |
---|
MMD | 80 | 55.0 | 67.5 | 76.2 | 80.0 | 80.0 | 82.5 | 87.5 | 90.0 | 93.8 |
---|
RCM | 78 | 57.7 | 70.5 | 80.8 | 83.3 | 83.3 | 84.6 | 84.6 | 89.7 | 92.3 |
---|
PQ | 78 | 47.4 | 73.1 | 83.3 | 84.6 | 85.9 | 85.9 | 92.3 | 96.2 | 96.2 |
---|
ND | 79 | 50.6 | 58.2 | 64.6 | 68.4 | 75.9 | 77.2 | 81.0 | 84.8 | 84.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 48.8 | 71.2 | 78.8 | 78.8 | 80.0 | 85.0 | 85.0 | 88.8 | 90.0 |
---|
MMD | 80 | 48.8 | 70.0 | 80.0 | 80.0 | 82.5 | 85.0 | 86.2 | 88.8 | 90.0 |
---|
RCM | 78 | 62.8 | 73.1 | 83.3 | 85.9 | 85.9 | 85.9 | 88.5 | 92.3 | 94.9 |
---|
PQ | 80 | 46.2 | 73.8 | 83.8 | 86.2 | 87.5 | 90.0 | 92.5 | 96.2 | 97.5 |
---|
ND | 59 | 42.4 | 59.3 | 72.9 | 72.9 | 76.3 | 79.7 | 83.1 | 86.4 | 86.4 |
---|
| 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 | 80 | 57.5 | 67.5 | 77.5 | 80.0 | 80.0 | 81.2 | 86.2 | 88.8 | 90.0 |
---|
MMD | 80 | 55.0 | 67.5 | 76.2 | 80.0 | 80.0 | 82.5 | 87.5 | 90.0 | 93.8 |
---|
RCM | 78 | 57.7 | 70.5 | 80.8 | 83.3 | 83.3 | 84.6 | 84.6 | 89.7 | 92.3 |
---|
PQ | 78 | 47.4 | 73.1 | 83.3 | 84.6 | 85.9 | 85.9 | 92.3 | 96.2 | 96.2 |
---|
ND | 79 | 50.6 | 58.2 | 64.6 | 68.4 | 75.9 | 77.2 | 81.0 | 84.8 | 84.8 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 55.0 | 70.0 | 80.0 | 82.5 | 83.8 | 85.0 | 88.8 | 91.2 | 91.2 |
---|
MMD | 80 | 53.8 | 68.8 | 80.0 | 83.8 | 85.0 | 87.5 | 88.8 | 91.2 | 91.2 |
---|
RCM | 78 | 71.8 | 80.8 | 85.9 | 87.2 | 87.2 | 88.5 | 89.7 | 91.0 | 92.3 |
---|
PQ | 78 | 48.7 | 75.6 | 83.3 | 85.9 | 87.2 | 89.7 | 92.3 | 94.9 | 96.2 |
---|
ND | 59 | 49.2 | 66.1 | 72.9 | 76.3 | 81.4 | 81.4 | 83.1 | 84.7 | 88.1 |
---|
| 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 | 79 | 72.2 | 81.0 | 83.5 | 84.8 | 84.8 | 86.1 | 87.3 | 88.6 | 91.1 |
---|
MMD | 80 | 68.8 | 77.5 | 81.2 | 81.2 | 83.8 | 85.0 | 87.5 | 87.5 | 90.0 |
---|
RCM | 77 | 74.0 | 83.1 | 84.4 | 85.7 | 85.7 | 85.7 | 85.7 | 88.3 | 90.9 |
---|
PQ | 78 | 50.0 | 71.8 | 83.3 | 84.6 | 85.9 | 85.9 | 92.3 | 96.2 | 96.2 |
---|
ND | 79 | 65.8 | 77.2 | 79.7 | 82.3 | 83.5 | 83.5 | 83.5 | 86.1 | 87.3 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 55.0 | 70.0 | 80.0 | 82.5 | 83.8 | 85.0 | 88.8 | 91.2 | 91.2 |
---|
MMD | 80 | 53.8 | 68.8 | 80.0 | 83.8 | 85.0 | 87.5 | 88.8 | 91.2 | 91.2 |
---|
RCM | 78 | 71.8 | 80.8 | 85.9 | 87.2 | 87.2 | 88.5 | 89.7 | 91.0 | 92.3 |
---|
PQ | 78 | 48.7 | 75.6 | 83.3 | 85.9 | 87.2 | 89.7 | 92.3 | 94.9 | 96.2 |
---|
ND | 59 | 49.2 | 66.1 | 72.9 | 76.3 | 81.4 | 81.4 | 83.1 | 84.7 | 88.1 |
---|
| 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 | 79 | 72.2 | 81.0 | 83.5 | 84.8 | 84.8 | 86.1 | 87.3 | 88.6 | 91.1 |
---|
MMD | 80 | 68.8 | 77.5 | 81.2 | 81.2 | 83.8 | 85.0 | 87.5 | 87.5 | 90.0 |
---|
RCM | 77 | 74.0 | 83.1 | 84.4 | 85.7 | 85.7 | 85.7 | 85.7 | 88.3 | 90.9 |
---|
PQ | 78 | 50.0 | 71.8 | 83.3 | 84.6 | 85.9 | 85.9 | 92.3 | 96.2 | 96.2 |
---|
ND | 79 | 65.8 | 77.2 | 79.7 | 82.3 | 83.5 | 83.5 | 83.5 | 86.1 | 87.3 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 57.5 | 71.2 | 83.8 | 86.2 | 86.2 | 87.5 | 88.8 | 91.2 | 92.5 |
---|
MMD | 80 | 56.2 | 68.8 | 83.8 | 86.2 | 86.2 | 87.5 | 88.8 | 91.2 | 91.2 |
---|
RCM | 78 | 75.6 | 85.9 | 85.9 | 87.2 | 87.2 | 88.5 | 88.5 | 91.0 | 92.3 |
---|
PQ | 77 | 50.6 | 76.6 | 84.4 | 87.0 | 88.3 | 90.9 | 93.5 | 96.1 | 98.7 |
---|
ND | 58 | 51.7 | 67.2 | 74.1 | 79.3 | 82.8 | 82.8 | 84.5 | 89.7 | 89.7 |
---|
| 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 | 79 | 75.9 | 79.7 | 83.5 | 84.8 | 84.8 | 87.3 | 87.3 | 88.6 | 91.1 |
---|
MMD | 79 | 72.2 | 78.5 | 83.5 | 83.5 | 86.1 | 87.3 | 88.6 | 88.6 | 91.1 |
---|
RCM | 76 | 76.3 | 84.2 | 86.8 | 86.8 | 86.8 | 86.8 | 88.2 | 89.5 | 93.4 |
---|
PQ | 78 | 57.7 | 73.1 | 83.3 | 84.6 | 85.9 | 88.5 | 92.3 | 96.2 | 96.2 |
---|
ND | 78 | 78.2 | 82.1 | 84.6 | 84.6 | 84.6 | 84.6 | 84.6 | 87.2 | 88.5 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 57.5 | 71.2 | 83.8 | 86.2 | 86.2 | 87.5 | 88.8 | 91.2 | 92.5 |
---|
MMD | 80 | 56.2 | 68.8 | 83.8 | 86.2 | 86.2 | 87.5 | 88.8 | 91.2 | 91.2 |
---|
RCM | 78 | 75.6 | 85.9 | 85.9 | 87.2 | 87.2 | 88.5 | 88.5 | 91.0 | 92.3 |
---|
PQ | 77 | 50.6 | 76.6 | 84.4 | 87.0 | 88.3 | 90.9 | 93.5 | 96.1 | 98.7 |
---|
ND | 58 | 51.7 | 67.2 | 74.1 | 79.3 | 82.8 | 82.8 | 84.5 | 89.7 | 89.7 |
---|
| 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 | 79 | 75.9 | 79.7 | 83.5 | 84.8 | 84.8 | 87.3 | 87.3 | 88.6 | 91.1 |
---|
MMD | 79 | 72.2 | 78.5 | 83.5 | 83.5 | 86.1 | 87.3 | 88.6 | 88.6 | 91.1 |
---|
RCM | 76 | 76.3 | 84.2 | 86.8 | 86.8 | 86.8 | 86.8 | 88.2 | 89.5 | 93.4 |
---|
PQ | 78 | 57.7 | 73.1 | 83.3 | 84.6 | 85.9 | 88.5 | 92.3 | 96.2 | 96.2 |
---|
ND | 78 | 78.2 | 82.1 | 84.6 | 84.6 | 84.6 | 84.6 | 84.6 | 87.2 | 88.5 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 56.2 | 70.0 | 85.0 | 86.2 | 86.2 | 87.5 | 90.0 | 91.2 | 95.0 |
---|
MMD | 80 | 56.2 | 67.5 | 82.5 | 86.2 | 87.5 | 87.5 | 88.8 | 91.2 | 93.8 |
---|
RCM | 78 | 75.6 | 85.9 | 85.9 | 88.5 | 89.7 | 89.7 | 91.0 | 92.3 | 93.6 |
---|
PQ | 80 | 53.8 | 75.0 | 82.5 | 85.0 | 86.2 | 90.0 | 91.2 | 92.5 | 97.5 |
---|
ND | 59 | 55.9 | 62.7 | 78.0 | 79.7 | 79.7 | 81.4 | 83.1 | 86.4 | 91.5 |
---|
| 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 | 79 | 74.7 | 78.5 | 83.5 | 86.1 | 87.3 | 87.3 | 88.6 | 88.6 | 92.4 |
---|
MMD | 80 | 71.2 | 77.5 | 82.5 | 82.5 | 86.2 | 86.2 | 87.5 | 87.5 | 90.0 |
---|
RCM | 77 | 80.5 | 84.4 | 87.0 | 87.0 | 87.0 | 87.0 | 89.6 | 89.6 | 92.2 |
---|
PQ | 78 | 57.7 | 73.1 | 83.3 | 84.6 | 85.9 | 87.2 | 89.7 | 92.3 | 94.9 |
---|
ND | 79 | 78.5 | 82.3 | 83.5 | 83.5 | 83.5 | 83.5 | 84.8 | 86.1 | 87.3 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 80 | 56.2 | 70.0 | 85.0 | 86.2 | 86.2 | 87.5 | 90.0 | 91.2 | 95.0 |
---|
MMD | 80 | 56.2 | 67.5 | 82.5 | 86.2 | 87.5 | 87.5 | 88.8 | 91.2 | 93.8 |
---|
RCM | 78 | 75.6 | 85.9 | 85.9 | 88.5 | 89.7 | 89.7 | 91.0 | 92.3 | 93.6 |
---|
PQ | 80 | 53.8 | 75.0 | 82.5 | 85.0 | 86.2 | 90.0 | 91.2 | 92.5 | 97.5 |
---|
ND | 59 | 55.9 | 62.7 | 78.0 | 79.7 | 79.7 | 81.4 | 83.1 | 86.4 | 91.5 |
---|
| 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 | 79 | 74.7 | 78.5 | 83.5 | 86.1 | 87.3 | 87.3 | 88.6 | 88.6 | 92.4 |
---|
MMD | 80 | 71.2 | 77.5 | 82.5 | 82.5 | 86.2 | 86.2 | 87.5 | 87.5 | 90.0 |
---|
RCM | 77 | 80.5 | 84.4 | 87.0 | 87.0 | 87.0 | 87.0 | 89.6 | 89.6 | 92.2 |
---|
PQ | 78 | 57.7 | 73.1 | 83.3 | 84.6 | 85.9 | 87.2 | 89.7 | 92.3 | 94.9 |
---|
ND | 79 | 78.5 | 82.3 | 83.5 | 83.5 | 83.5 | 83.5 | 84.8 | 86.1 | 87.3 |
---|
|
|
Performance
statistics
for partial differential equations (complex
unsymmetric case 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 | 15 | 0.0 | 0.0 | 6.7 | 6.7 | 6.7 | 26.7 | 66.7 | 100.0 | 100.0 |
---|
MMD | 15 | 0.0 | 0.0 | 6.7 | 6.7 | 6.7 | 20.0 | 66.7 | 100.0 | 100.0 |
---|
RCM | 15 | 0.0 | 0.0 | 6.7 | 6.7 | 6.7 | 20.0 | 60.0 | 93.3 | 93.3 |
---|
| |
|
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 | 15 | 0.0 | 0.0 | 6.7 | 6.7 | 6.7 | 26.7 | 66.7 | 100.0 | 100.0 |
---|
MMD | 15 | 0.0 | 0.0 | 6.7 | 6.7 | 6.7 | 26.7 | 60.0 | 93.3 | 93.3 |
---|
RCM | 15 | 0.0 | 0.0 | 6.7 | 6.7 | 6.7 | 33.3 | 66.7 | 86.7 | 86.7 |
---|
| |
|
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 | 6.7 | 6.7 | 20.0 | 33.3 | 60.0 | 93.3 | 93.3 | 93.3 | 93.3 |
---|
MMD | 15 | 6.7 | 6.7 | 26.7 | 33.3 | 40.0 | 66.7 | 93.3 | 93.3 | 93.3 |
---|
RCM | 15 | 0.0 | 6.7 | 20.0 | 33.3 | 46.7 | 80.0 | 86.7 | 86.7 | 86.7 |
---|
PQ | 15 | 6.7 | 6.7 | 13.3 | 20.0 | 40.0 | 86.7 | 86.7 | 86.7 | 86.7 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
MMD | 15 | 6.7 | 6.7 | 20.0 | 33.3 | 60.0 | 93.3 | 93.3 | 93.3 | 93.3 |
---|
RCM | 15 | 6.7 | 6.7 | 26.7 | 33.3 | 40.0 | 66.7 | 93.3 | 93.3 | 93.3 |
---|
PQ | 15 | 0.0 | 6.7 | 20.0 | 33.3 | 46.7 | 80.0 | 86.7 | 86.7 | 86.7 |
---|
|
|
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 | 6.7 | 6.7 | 20.0 | 26.7 | 40.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 15 | 6.7 | 6.7 | 20.0 | 26.7 | 40.0 | 66.7 | 93.3 | 93.3 | 93.3 |
---|
RCM | 15 | 0.0 | 6.7 | 20.0 | 40.0 | 53.3 | 80.0 | 86.7 | 86.7 | 86.7 |
---|
PQ | 15 | 6.7 | 6.7 | 13.3 | 20.0 | 40.0 | 66.7 | 80.0 | 80.0 | 80.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
MMD | 15 | 6.7 | 6.7 | 20.0 | 26.7 | 40.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 6.7 | 6.7 | 20.0 | 26.7 | 40.0 | 66.7 | 93.3 | 93.3 | 93.3 |
---|
PQ | 15 | 0.0 | 6.7 | 20.0 | 40.0 | 53.3 | 80.0 | 86.7 | 86.7 | 86.7 |
---|
|
|
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 | 6.7 | 6.7 | 20.0 | 40.0 | 53.3 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 15 | 6.7 | 6.7 | 26.7 | 33.3 | 46.7 | 66.7 | 93.3 | 93.3 | 93.3 |
---|
RCM | 15 | 0.0 | 6.7 | 26.7 | 33.3 | 46.7 | 66.7 | 86.7 | 86.7 | 86.7 |
---|
PQ | 15 | 6.7 | 6.7 | 13.3 | 13.3 | 33.3 | 60.0 | 80.0 | 80.0 | 80.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
MMD | 15 | 6.7 | 6.7 | 20.0 | 40.0 | 53.3 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 6.7 | 6.7 | 26.7 | 33.3 | 46.7 | 66.7 | 93.3 | 93.3 | 93.3 |
---|
PQ | 15 | 0.0 | 6.7 | 26.7 | 33.3 | 46.7 | 66.7 | 86.7 | 86.7 | 86.7 |
---|
|
|
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 | 6.7 | 6.7 | 20.0 | 40.0 | 53.3 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 15 | 6.7 | 6.7 | 20.0 | 40.0 | 53.3 | 80.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 0.0 | 6.7 | 26.7 | 33.3 | 46.7 | 73.3 | 93.3 | 93.3 | 93.3 |
---|
PQ | 15 | 6.7 | 6.7 | 13.3 | 13.3 | 33.3 | 66.7 | 80.0 | 80.0 | 80.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
MMD | 15 | 6.7 | 6.7 | 20.0 | 40.0 | 53.3 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 15 | 6.7 | 6.7 | 20.0 | 40.0 | 53.3 | 80.0 | 100.0 | 100.0 | 100.0 |
---|
PQ | 15 | 0.0 | 6.7 | 26.7 | 33.3 | 46.7 | 73.3 | 93.3 | 93.3 | 93.3 |
---|
|
|
Performance
statistics
for partial differential equations (symmatric
positive definite case in tables)
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 93.3 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 93.3 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 83.3 | 93.3 | 93.3 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 93.3 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 93.3 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 83.3 | 93.3 | 93.3 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 96.7 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 93.3 | 93.3 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 86.7 | 93.3 | 100.0 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 96.7 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 93.3 | 93.3 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 86.7 | 93.3 | 100.0 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 93.3 | 96.7 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 86.7 | 93.3 | 100.0 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 93.3 | 96.7 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 86.7 | 93.3 | 100.0 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 93.3 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 86.7 | 93.3 | 100.0 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|
ILUPACK |
---|
ordering | #matrices | drop tolerance |
---|
| | 5e-01 | 2e-01 | 1e-01 | 5e-02 | 3e-02 | 1e-02 | 1e-03 | 1e-04 | 1e-05 | AMF | 30 | 33.3 | 40.0 | 53.3 | 73.3 | 83.3 | 83.3 | 100.0 | 100.0 | 100.0 |
---|
MMD | 30 | 26.7 | 40.0 | 53.3 | 73.3 | 83.3 | 93.3 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 33.3 | 53.3 | 73.3 | 83.3 | 86.7 | 93.3 | 100.0 | 100.0 |
---|
PP | 24 | 37.5 | 50.0 | 54.2 | 70.8 | 70.8 | 91.7 | 95.8 | 100.0 | 100.0 |
---|
ND | 1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
---|
|
|