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 partial differential equations (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 | 81 | 12.0 | 18.0 | 39.0 | 43.0 | 48.0 | 58.0 | 63.0 | 65.0 | 66.0 |
---|
MMD | 81 | 12.0 | 19.0 | 39.0 | 47.0 | 55.0 | 61.0 | 69.0 | 72.0 | 73.0 |
---|
RCM | 81 | 12.0 | 20.0 | 34.0 | 39.0 | 48.0 | 50.0 | 57.0 | 65.0 | 69.0 |
---|
ND | 81 | 12.0 | 18.0 | 39.0 | 49.0 | 58.0 | 67.0 | 74.0 | 75.0 | 75.0 |
---|
| 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 | 81 | 14.8 | 22.2 | 48.1 | 53.1 | 59.3 | 71.6 | 77.8 | 80.2 | 81.5 |
---|
MMD | 81 | 14.8 | 23.5 | 48.1 | 58.0 | 67.9 | 75.3 | 85.2 | 88.9 | 90.1 |
---|
RCM | 81 | 14.8 | 24.7 | 42.0 | 48.1 | 59.3 | 61.7 | 70.4 | 80.2 | 85.2 |
---|
ND | 81 | 14.8 | 22.2 | 48.1 | 60.5 | 71.6 | 82.7 | 91.4 | 92.6 | 92.6 |
---|
|
|
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 | 81 | 16.0 | 22.0 | 31.0 | 36.0 | 48.0 | 53.0 | 55.0 | 56.0 | 56.0 |
---|
MMD | 81 | 14.0 | 21.0 | 33.0 | 38.0 | 49.0 | 56.0 | 58.0 | 59.0 | 59.0 |
---|
RCM | 81 | 14.0 | 24.0 | 38.0 | 44.0 | 49.0 | 51.0 | 58.0 | 64.0 | 66.0 |
---|
ND | 81 | 11.0 | 15.0 | 31.0 | 37.0 | 55.0 | 63.0 | 69.0 | 69.0 | 69.0 |
---|
| 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 | 81 | 19.8 | 27.2 | 38.3 | 44.4 | 59.3 | 65.4 | 67.9 | 69.1 | 69.1 |
---|
MMD | 81 | 17.3 | 25.9 | 40.7 | 46.9 | 60.5 | 69.1 | 71.6 | 72.8 | 72.8 |
---|
RCM | 81 | 17.3 | 29.6 | 46.9 | 54.3 | 60.5 | 63.0 | 71.6 | 79.0 | 81.5 |
---|
ND | 81 | 13.6 | 18.5 | 38.3 | 45.7 | 67.9 | 77.8 | 85.2 | 85.2 | 85.2 |
---|
|
|
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 | 80 | 16.2 | 36.2 | 55.0 | 67.5 | 78.8 | 82.5 | 87.5 | 90.0 | 91.2 |
---|
MMD | 80 | 15.0 | 37.5 | 56.2 | 67.5 | 80.0 | 82.5 | 85.0 | 90.0 | 90.0 |
---|
RCM | 78 | 14.1 | 43.6 | 62.8 | 70.5 | 78.2 | 80.8 | 83.3 | 88.5 | 89.7 |
---|
PQ | 80 | 2.5 | 18.8 | 33.8 | 43.8 | 56.2 | 57.5 | 61.2 | 62.5 | 63.8 |
---|
ND | 59 | 0.0 | 6.8 | 23.7 | 35.6 | 47.5 | 49.2 | 52.5 | 52.5 | 52.5 |
---|
| 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 | 80 | 15.0 | 40.0 | 60.0 | 62.5 | 67.5 | 67.5 | 75.0 | 78.8 | 78.8 |
---|
MMD | 80 | 15.0 | 42.5 | 61.2 | 62.5 | 67.5 | 68.8 | 75.0 | 78.8 | 80.0 |
---|
RCM | 78 | 14.1 | 30.8 | 59.0 | 64.1 | 65.4 | 66.7 | 69.2 | 73.1 | 75.6 |
---|
PQ | 78 | 10.3 | 39.7 | 57.7 | 60.3 | 66.7 | 66.7 | 74.4 | 78.2 | 80.8 |
---|
ND | 79 | 15.2 | 39.2 | 62.0 | 64.6 | 70.9 | 73.4 | 77.2 | 81.0 | 84.8 |
---|
|
|
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 | 32 | 0.0 | 12.5 | 43.8 | 65.6 | 87.5 | 90.6 | 96.9 | 96.9 | 96.9 |
---|
MMD | 28 | 0.0 | 25.0 | 53.6 | 71.4 | 89.3 | 96.4 | 100.0 | 100.0 | 100.0 |
---|
RCM | 78 | 15.4 | 39.7 | 60.3 | 71.8 | 75.6 | 79.5 | 84.6 | 88.5 | 91.0 |
---|
PQ | 77 | 10.4 | 31.2 | 53.2 | 63.6 | 71.4 | 77.9 | 89.6 | 92.2 | 93.5 |
---|
| 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 | 80 | 15.0 | 38.8 | 61.2 | 63.8 | 70.0 | 72.5 | 76.2 | 80.0 | 83.8 |
---|
MMD | 80 | 15.0 | 38.8 | 61.2 | 66.2 | 68.8 | 73.8 | 78.8 | 82.5 | 86.2 |
---|
RCM | 78 | 15.4 | 28.2 | 56.4 | 62.8 | 64.1 | 66.7 | 69.2 | 75.6 | 75.6 |
---|
PQ | 76 | 7.9 | 23.7 | 59.2 | 60.5 | 67.1 | 75.0 | 86.8 | 89.5 | 92.1 |
---|
|
|
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 | 80 | 13.8 | 31.2 | 53.8 | 65.0 | 77.5 | 82.5 | 86.2 | 90.0 | 90.0 |
---|
MMD | 80 | 13.8 | 30.0 | 53.8 | 67.5 | 81.2 | 85.0 | 88.8 | 91.2 | 92.5 |
---|
RCM | 78 | 15.4 | 24.4 | 51.3 | 67.9 | 78.2 | 82.1 | 83.3 | 89.7 | 91.0 |
---|
PQ | 78 | 3.8 | 17.9 | 32.1 | 41.0 | 56.4 | 60.3 | 62.8 | 66.7 | 66.7 |
---|
ND | 59 | 0.0 | 6.8 | 18.6 | 33.9 | 44.1 | 52.5 | 54.2 | 54.2 | 54.2 |
---|
| 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 | 79 | 13.9 | 24.1 | 54.4 | 63.3 | 68.4 | 72.2 | 78.5 | 81.0 | 86.1 |
---|
MMD | 80 | 12.5 | 21.2 | 53.8 | 62.5 | 66.2 | 70.0 | 76.2 | 80.0 | 82.5 |
---|
RCM | 77 | 15.6 | 18.2 | 48.1 | 58.4 | 66.2 | 67.5 | 70.1 | 76.6 | 79.2 |
---|
PQ | 78 | 10.3 | 17.9 | 48.7 | 60.3 | 67.9 | 69.2 | 78.2 | 79.5 | 83.3 |
---|
ND | 79 | 13.9 | 21.5 | 53.2 | 67.1 | 69.6 | 74.7 | 78.5 | 82.3 | 87.3 |
---|
|
|
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 | 32 | 0.0 | 12.5 | 34.4 | 62.5 | 81.2 | 96.9 | 100.0 | 100.0 | 100.0 |
---|
MMD | 28 | 0.0 | 17.9 | 46.4 | 60.7 | 85.7 | 96.4 | 100.0 | 100.0 | 100.0 |
---|
RCM | 77 | 16.9 | 24.7 | 50.6 | 67.5 | 77.9 | 80.5 | 84.4 | 87.0 | 89.6 |
---|
PQ | 77 | 10.4 | 23.4 | 48.1 | 57.1 | 66.2 | 74.0 | 84.4 | 92.2 | 94.8 |
---|
| 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 | 78 | 14.1 | 21.8 | 53.8 | 67.9 | 70.5 | 75.6 | 79.5 | 83.3 | 88.5 |
---|
MMD | 79 | 13.9 | 20.3 | 51.9 | 64.6 | 68.4 | 74.7 | 78.5 | 83.5 | 86.1 |
---|
RCM | 75 | 16.0 | 18.7 | 42.7 | 61.3 | 66.7 | 68.0 | 73.3 | 80.0 | 82.7 |
---|
PQ | 76 | 7.9 | 23.7 | 48.7 | 57.9 | 64.5 | 71.1 | 82.9 | 86.8 | 88.2 |
---|
|
|
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 | 80 | 13.8 | 30.0 | 51.2 | 63.8 | 75.0 | 80.0 | 87.5 | 91.2 | 92.5 |
---|
MMD | 80 | 13.8 | 27.5 | 45.0 | 65.0 | 76.2 | 80.0 | 88.8 | 91.2 | 91.2 |
---|
RCM | 78 | 14.1 | 19.2 | 39.7 | 55.1 | 78.2 | 83.3 | 84.6 | 89.7 | 89.7 |
---|
PQ | 78 | 2.6 | 16.7 | 30.8 | 39.7 | 48.7 | 51.3 | 62.8 | 66.7 | 66.7 |
---|
ND | 58 | 0.0 | 6.9 | 15.5 | 31.0 | 41.4 | 43.1 | 48.3 | 48.3 | 48.3 |
---|
| 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 | 79 | 12.7 | 21.5 | 46.8 | 62.0 | 70.9 | 72.2 | 79.7 | 86.1 | 88.6 |
---|
MMD | 79 | 12.7 | 19.0 | 45.6 | 62.0 | 70.9 | 74.7 | 79.7 | 86.1 | 88.6 |
---|
RCM | 76 | 13.2 | 17.1 | 26.3 | 50.0 | 65.8 | 67.1 | 69.7 | 75.0 | 81.6 |
---|
PQ | 78 | 10.3 | 16.7 | 30.8 | 56.4 | 66.7 | 70.5 | 76.9 | 85.9 | 85.9 |
---|
ND | 78 | 14.1 | 20.5 | 42.3 | 61.5 | 70.5 | 71.8 | 78.2 | 83.3 | 87.2 |
---|
|
|
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 | 30 | 0.0 | 13.3 | 30.0 | 60.0 | 80.0 | 83.3 | 93.3 | 93.3 | 93.3 |
---|
MMD | 24 | 0.0 | 12.5 | 33.3 | 70.8 | 91.7 | 95.8 | 95.8 | 95.8 | 95.8 |
---|
RCM | 74 | 16.2 | 20.3 | 40.5 | 59.5 | 82.4 | 85.1 | 89.2 | 91.9 | 91.9 |
---|
PQ | 77 | 10.4 | 23.4 | 42.9 | 54.5 | 66.2 | 70.1 | 81.8 | 89.6 | 90.9 |
---|
| 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 | 78 | 14.1 | 20.5 | 42.3 | 61.5 | 70.5 | 71.8 | 78.2 | 83.3 | 87.2 |
---|
MMD | 79 | 12.7 | 20.3 | 39.2 | 63.3 | 70.9 | 72.2 | 77.2 | 83.5 | 86.1 |
---|
RCM | 64 | 15.6 | 20.3 | 29.7 | 56.2 | 75.0 | 78.1 | 84.4 | 87.5 | 92.2 |
---|
PQ | 75 | 8.0 | 25.3 | 46.7 | 57.3 | 62.7 | 70.7 | 81.3 | 85.3 | 89.3 |
---|
|
|
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 | 80 | 12.5 | 28.8 | 45.0 | 62.5 | 71.2 | 78.8 | 86.2 | 90.0 | 95.0 |
---|
MMD | 80 | 13.8 | 28.8 | 48.8 | 60.0 | 75.0 | 76.2 | 87.5 | 93.8 | 93.8 |
---|
RCM | 78 | 12.8 | 16.7 | 29.5 | 38.5 | 64.1 | 83.3 | 87.2 | 91.0 | 91.0 |
---|
PQ | 80 | 2.5 | 15.0 | 30.0 | 38.8 | 46.2 | 51.2 | 60.0 | 65.0 | 65.0 |
---|
ND | 59 | 0.0 | 6.8 | 13.6 | 18.6 | 35.6 | 35.6 | 39.0 | 39.0 | 39.0 |
---|
| 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 | 79 | 12.7 | 20.3 | 32.9 | 57.0 | 69.6 | 73.4 | 81.0 | 84.8 | 91.1 |
---|
MMD | 80 | 12.5 | 20.0 | 30.0 | 52.5 | 68.8 | 72.5 | 80.0 | 86.2 | 90.0 |
---|
RCM | 77 | 13.0 | 14.3 | 20.8 | 32.5 | 57.1 | 66.2 | 68.8 | 75.3 | 83.1 |
---|
PQ | 78 | 10.3 | 15.4 | 23.1 | 44.9 | 62.8 | 67.9 | 80.8 | 84.6 | 87.2 |
---|
ND | 79 | 12.7 | 20.3 | 34.2 | 57.0 | 70.9 | 74.7 | 82.3 | 82.3 | 84.8 |
---|
|
|
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 | 28 | 0.0 | 14.3 | 28.6 | 39.3 | 75.0 | 75.0 | 82.1 | 82.1 | 82.1 |
---|
MMD | 23 | 0.0 | 13.0 | 30.4 | 52.2 | 73.9 | 78.3 | 78.3 | 82.6 | 82.6 |
---|
RCM | 76 | 13.2 | 17.1 | 27.6 | 38.2 | 63.2 | 85.5 | 89.5 | 92.1 | 92.1 |
---|
PQ | 77 | 10.4 | 23.4 | 42.9 | 57.1 | 67.5 | 70.1 | 79.2 | 87.0 | 90.9 |
---|
| 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 | 74 | 13.5 | 21.6 | 36.5 | 60.8 | 75.7 | 79.7 | 87.8 | 87.8 | 90.5 |
---|
MMD | 73 | 13.7 | 20.5 | 31.5 | 57.5 | 75.3 | 78.1 | 84.9 | 84.9 | 86.3 |
---|
RCM | 63 | 15.9 | 17.5 | 25.4 | 36.5 | 63.5 | 81.0 | 85.7 | 87.3 | 93.7 |
---|
PQ | 76 | 7.9 | 23.7 | 44.7 | 53.9 | 61.8 | 65.8 | 76.3 | 82.9 | 85.5 |
---|
|
|
PARDISO |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | | 81 | 0.0 | 0.0 | 0.0 | 0.0 | 13.0 | 38.0 | 60.0 | 70.0 | 74.0 |
---|
| 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 | | 81 | 0.0 | 0.0 | 0.0 | 0.0 | 16.0 | 46.9 | 74.1 | 86.4 | 91.4 |
---|
|
|
Performance
statistics
for partial differential equations (complex
unsymmetric case 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 | 14 | 0.0 | 0.0 | 0.0 | 42.9 | 57.1 | 64.3 | 71.4 | 71.4 | 78.6 |
---|
MMD | 14 | 0.0 | 0.0 | 0.0 | 28.6 | 50.0 | 57.1 | 64.3 | 71.4 | 71.4 |
---|
RCM | 15 | 0.0 | 6.7 | 6.7 | 13.3 | 40.0 | 40.0 | 60.0 | 60.0 | 73.3 |
---|
| |
|
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 | 14 | 0.0 | 0.0 | 0.0 | 14.3 | 50.0 | 64.3 | 71.4 | 71.4 | 71.4 |
---|
MMD | 14 | 0.0 | 0.0 | 0.0 | 14.3 | 50.0 | 57.1 | 64.3 | 71.4 | 71.4 |
---|
RCM | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 26.7 | 40.0 | 60.0 | 60.0 | 66.7 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 66.7 | 100.0 |
---|
MMD | 15 | 6.7 | 6.7 | 6.7 | 26.7 | 60.0 | 60.0 | 73.3 | 73.3 | 73.3 |
---|
RCM | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 33.3 | 40.0 | 60.0 | 66.7 | 66.7 |
---|
PQ | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 13.3 | 46.7 | 60.0 | 73.3 | 80.0 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 66.7 |
---|
MMD | 15 | 6.7 | 6.7 | 6.7 | 20.0 | 46.7 | 53.3 | 60.0 | 73.3 | 73.3 |
---|
RCM | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 20.0 | 20.0 | 53.3 | 53.3 | 73.3 |
---|
PQ | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 13.3 | 20.0 | 53.3 | 66.7 | 73.3 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 100.0 | 100.0 |
---|
MMD | 15 | 6.7 | 6.7 | 6.7 | 53.3 | 60.0 | 60.0 | 73.3 | 73.3 | 80.0 |
---|
RCM | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 40.0 | 46.7 | 60.0 | 66.7 | 66.7 |
---|
PQ | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 6.7 | 40.0 | 53.3 | 60.0 | 73.3 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 66.7 |
---|
MMD | 14 | 7.1 | 7.1 | 7.1 | 42.9 | 50.0 | 64.3 | 64.3 | 71.4 | 78.6 |
---|
RCM | 14 | 0.0 | 7.1 | 7.1 | 7.1 | 21.4 | 35.7 | 57.1 | 71.4 | 71.4 |
---|
PQ | 14 | 0.0 | 7.1 | 7.1 | 7.1 | 14.3 | 14.3 | 50.0 | 64.3 | 71.4 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 100.0 | 100.0 |
---|
MMD | 15 | 6.7 | 6.7 | 6.7 | 40.0 | 60.0 | 60.0 | 66.7 | 73.3 | 80.0 |
---|
RCM | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 40.0 | 46.7 | 60.0 | 73.3 | 80.0 |
---|
PQ | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 6.7 | 33.3 | 46.7 | 53.3 | 66.7 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 66.7 | 66.7 |
---|
MMD | 12 | 8.3 | 8.3 | 8.3 | 58.3 | 66.7 | 75.0 | 75.0 | 83.3 | 83.3 |
---|
RCM | 12 | 0.0 | 8.3 | 8.3 | 8.3 | 25.0 | 58.3 | 66.7 | 83.3 | 83.3 |
---|
PQ | 13 | 0.0 | 7.7 | 7.7 | 7.7 | 15.4 | 15.4 | 46.2 | 53.8 | 76.9 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 66.7 | 100.0 |
---|
MMD | 15 | 6.7 | 6.7 | 6.7 | 46.7 | 53.3 | 60.0 | 73.3 | 73.3 | 80.0 |
---|
RCM | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 40.0 | 53.3 | 60.0 | 73.3 | 73.3 |
---|
PQ | 15 | 0.0 | 6.7 | 6.7 | 6.7 | 6.7 | 20.0 | 40.0 | 53.3 | 60.0 |
---|
| |
|
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 | 3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 33.3 | 66.7 | 66.7 | 66.7 |
---|
MMD | 13 | 7.7 | 7.7 | 7.7 | 46.2 | 61.5 | 69.2 | 69.2 | 84.6 | 84.6 |
---|
RCM | 13 | 0.0 | 7.7 | 7.7 | 7.7 | 46.2 | 61.5 | 69.2 | 76.9 | 76.9 |
---|
PQ | 13 | 0.0 | 7.7 | 7.7 | 7.7 | 15.4 | 15.4 | 38.5 | 61.5 | 61.5 |
---|
| |
|
PARDISO |
---|
ordering | #matrices | fill-in factor |
---|
| | 5e-01 | 1e+00 | 2e+00 | 2e+00 | 3e+00 | 4e+00 | 6e+00 | 8e+00 | 1e+01 | | 15 | 0.0 | 0.0 | 0.0 | 0.0 | 40.0 | 46.7 | 60.0 | 66.7 | 73.3 |
---|
| |
|
Performance
statistics
for partial differential equations (symmatric
positive definite case in tables)
|
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 | 18 | 55.6 | 77.8 | 88.9 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 44.4 | 72.2 | 77.8 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 60.0 | 83.3 | 83.3 | 90.0 | 90.0 | 93.3 | 100.0 | 100.0 |
---|
PP | 28 | 14.3 | 46.4 | 57.1 | 64.3 | 64.3 | 78.6 | 92.9 | 96.4 | 96.4 |
---|
| |
|
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 | 18 | 55.6 | 77.8 | 88.9 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 44.4 | 72.2 | 77.8 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 60.0 | 83.3 | 83.3 | 93.3 | 93.3 | 93.3 | 93.3 | 93.3 |
---|
PP | 24 | 16.7 | 50.0 | 62.5 | 75.0 | 75.0 | 75.0 | 87.5 | 95.8 | 95.8 |
---|
| |
|
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 | 18 | 50.0 | 72.2 | 77.8 | 94.4 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 38.9 | 66.7 | 77.8 | 88.9 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 60.0 | 83.3 | 83.3 | 90.0 | 93.3 | 96.7 | 100.0 | 100.0 |
---|
PP | 24 | 16.7 | 54.2 | 66.7 | 75.0 | 75.0 | 91.7 | 95.8 | 95.8 | 95.8 |
---|
| |
|
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 | 18 | 50.0 | 72.2 | 77.8 | 94.4 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 38.9 | 66.7 | 77.8 | 88.9 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 60.0 | 83.3 | 83.3 | 90.0 | 93.3 | 93.3 | 93.3 | 93.3 |
---|
PP | 24 | 16.7 | 50.0 | 62.5 | 75.0 | 75.0 | 75.0 | 95.8 | 95.8 | 95.8 |
---|
| |
|
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 | 18 | 50.0 | 72.2 | 77.8 | 94.4 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 38.9 | 66.7 | 77.8 | 88.9 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 60.0 | 83.3 | 83.3 | 90.0 | 93.3 | 93.3 | 96.7 | 100.0 |
---|
PP | 24 | 16.7 | 54.2 | 66.7 | 75.0 | 75.0 | 91.7 | 95.8 | 95.8 | 95.8 |
---|
| |
|
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 | 18 | 50.0 | 72.2 | 77.8 | 94.4 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 38.9 | 66.7 | 77.8 | 88.9 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 60.0 | 83.3 | 83.3 | 90.0 | 93.3 | 93.3 | 93.3 | 93.3 |
---|
PP | 24 | 16.7 | 50.0 | 62.5 | 75.0 | 75.0 | 75.0 | 95.8 | 95.8 | 95.8 |
---|
| |
|
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 | 18 | 50.0 | 72.2 | 77.8 | 94.4 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 38.9 | 66.7 | 77.8 | 88.9 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 56.7 | 83.3 | 83.3 | 90.0 | 93.3 | 93.3 | 93.3 | 93.3 |
---|
PP | 24 | 16.7 | 54.2 | 66.7 | 75.0 | 75.0 | 91.7 | 95.8 | 95.8 | 95.8 |
---|
| |
|
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 | 18 | 50.0 | 72.2 | 77.8 | 94.4 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
MMD | 18 | 38.9 | 66.7 | 77.8 | 88.9 | 94.4 | 100.0 | 100.0 | 100.0 | 100.0 |
---|
RCM | 30 | 33.3 | 56.7 | 83.3 | 83.3 | 90.0 | 93.3 | 93.3 | 93.3 | 93.3 |
---|
PP | 24 | 16.7 | 50.0 | 62.5 | 75.0 | 75.0 | 75.0 | 95.8 | 95.8 | 95.8 |
---|
| |
|
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|