Matrix bcsstk23

???

performance of incomplete LU preconditioners

Abbreviations for Preconditioners
ILUPACK inverse-based Multilevel ILU. Uses the concept of ARMS and an inverse based partial ILUC
ILUPACK - DEFAULT 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
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
Abbreviations for Orderings
PP new PP ordering for multilevel ILU
RCM Reverse Cuthill-McKee
MMD minimum degree
AMF approximate inverse fill

Performance - Best Computation Time

Computation Time

time
[sec]
drop tolerance

Memory Requirement

nz(L+U)
----------
nz(A)
drop tolerance

Performance - Best Memory Requirement

Computation Time

time
[sec]
drop tolerance

Memory Requirement

nz(L+U)
----------
nz(A)
drop tolerance

Performance - Most Robust Method

Computation Time

time
[sec]
drop tolerance

Memory Requirement

nz(L+U)
----------
nz(A)
drop tolerance

ILUPACK - MEDIUM VERSION

ILUPACK - MEDIUM VERSION + PP
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-021.0e+01 1.21.8e-018.0e-019.80e-01256
5.0e-022.5e+01 1.21.6e-018.2e-019.80e-01256
5.0e-025.0e+01 1.21.8e-018.1e-019.90e-01256
5.0e-021.0e+02 1.21.9e-018.0e-019.90e-01256
2.5e-021.0e+01 1.52.9e-016.4e-019.30e-01191
2.5e-022.5e+01 1.52.9e-016.4e-019.30e-01191
2.5e-025.0e+01 1.52.7e-016.4e-019.10e-01191
2.5e-021.0e+02 1.53.0e-016.5e-019.50e-01191
1.0e-021.0e+01 2.15.0e-014.8e-019.80e-01115
1.0e-022.5e+01 2.14.9e-014.8e-019.70e-01115
1.0e-025.0e+01 2.14.7e-014.9e-019.60e-01115
1.0e-021.0e+02 2.15.1e-014.8e-019.90e-01115
5.0e-031.0e+01 3.49.2e-015.3e-011.45e+0070
5.0e-032.5e+01 3.48.9e-015.3e-011.42e+0070
5.0e-035.0e+01 3.49.3e-015.2e-011.45e+0070
5.0e-031.0e+02 3.49.9e-015.4e-011.53e+0070
2.5e-031.0e+01 4.11.2e+004.4e-011.64e+0054
2.5e-032.5e+01 4.11.3e+004.3e-011.73e+0054
2.5e-035.0e+01 4.11.3e+004.3e-011.73e+0054
2.5e-031.0e+02 4.11.3e+004.8e-011.78e+0054
1.0e-031.0e+01 5.12.0e+003.1e-012.31e+0034
1.0e-032.5e+01 5.12.0e+003.2e-012.32e+0034
1.0e-035.0e+01 5.12.1e+003.1e-012.41e+0034
1.0e-031.0e+02 5.11.9e+003.0e-012.20e+0034
1.0e-041.0e+01 11.86.5e+005.4e-017.04e+0013
1.0e-042.5e+01 11.86.4e+005.3e-016.93e+0013
1.0e-045.0e+01 11.86.4e+005.4e-016.94e+0013
1.0e-041.0e+02 11.86.4e+005.0e-016.90e+0013
ILUPACK - MEDIUM VERSION + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-031.0e+01 2.21.2e+008.2e-012.02e+00139
1.0e-031.0e+01 2.92.5e+006.4e-013.14e+0088
1.0e-041.0e+01 5.04.5e+003.9e-014.89e+0037
1.0e-042.5e+01 6.02.2e+005.7e-012.77e+0047
1.0e-045.0e+01 7.11.2e+006.8e-011.88e+0052
1.0e-051.0e+01 7.97.8e+002.0e-018.00e+0012
1.0e-052.5e+01 10.03.0e+003.4e-013.34e+0017
1.0e-055.0e+01 11.52.7e+004.9e-013.19e+0021
1.0e-051.0e+02 13.11.7e+006.5e-012.35e+0024
1.0e-011.0e+01 0.65.0e-021.3e+001.35e+00480
1.0e-012.5e+01 0.66.0e-021.1e+001.16e+00441
1.0e-015.0e+01 0.65.0e-021.1e+001.15e+00441
1.0e-011.0e+02 0.65.0e-021.1e+001.15e+00441
5.0e-021.0e+01 0.76.0e-021.1e+001.16e+00400
5.0e-022.5e+01 0.75.0e-021.1e+001.15e+00387
5.0e-025.0e+01 0.76.0e-021.1e+001.16e+00387
5.0e-021.0e+02 0.75.0e-021.1e+001.15e+00387
2.5e-021.0e+01 1.09.0e-028.0e-018.90e-01261
2.5e-022.5e+01 1.07.0e-028.7e-019.40e-01290
2.5e-025.0e+01 1.06.0e-028.7e-019.30e-01290
2.5e-021.0e+02 1.07.0e-028.7e-019.40e-01290
1.0e-021.0e+01 1.42.5e-018.9e-011.14e+00242
1.0e-022.5e+01 1.48.0e-027.8e-018.60e-01229
1.0e-025.0e+01 1.48.0e-028.0e-018.80e-01229
1.0e-021.0e+02 1.48.0e-027.8e-018.60e-01229
5.0e-031.0e+01 1.87.4e-018.2e-011.56e+00177
5.0e-032.5e+01 1.91.3e-016.6e-017.90e-01160
5.0e-035.0e+01 1.91.2e-016.6e-017.80e-01160
5.0e-031.0e+02 1.91.3e-016.7e-018.00e-01160
2.5e-032.5e+01 2.32.1e-016.2e-018.30e-01134
2.5e-035.0e+01 2.41.5e-016.2e-017.70e-01126
2.5e-031.0e+02 2.41.4e-016.1e-017.50e-01126
1.0e-032.5e+01 3.36.6e-015.2e-011.18e+0092
1.0e-035.0e+01 3.52.2e-015.8e-018.00e-0188
1.0e-031.0e+02 3.52.1e-016.2e-018.30e-0188
1.0e-041.0e+02 7.64.7e-017.2e-011.19e+0041
ILUPACK - MEDIUM VERSION + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 0.82.7e-011.2e+001.47e+00412
1.0e-012.5e+01 0.82.5e-018.2e-011.07e+00373
1.0e-015.0e+01 0.82.6e-018.1e-011.07e+00373
1.0e-011.0e+02 0.82.6e-018.4e-011.10e+00373
5.0e-021.0e+01 1.02.8e-011.0e+001.28e+00320
5.0e-022.5e+01 1.12.6e-016.8e-019.40e-01282
5.0e-025.0e+01 1.12.6e-016.7e-019.30e-01282
5.0e-021.0e+02 1.12.8e-016.6e-019.40e-01282
2.5e-021.0e+01 1.33.2e-018.5e-011.17e+00242
2.5e-022.5e+01 1.42.8e-015.3e-018.10e-01212
2.5e-025.0e+01 1.42.8e-015.2e-018.00e-01212
2.5e-021.0e+02 1.42.8e-015.5e-018.30e-01212
1.0e-021.0e+01 1.86.2e-018.0e-011.42e+00196
1.0e-022.5e+01 2.03.0e-014.5e-017.50e-01162
1.0e-025.0e+01 2.03.2e-014.9e-018.10e-01162
1.0e-021.0e+02 2.03.3e-014.8e-018.10e-01162
5.0e-031.0e+01 2.39.5e-017.5e-011.70e+00150
5.0e-032.5e+01 2.73.8e-017.2e-011.10e+00127
5.0e-035.0e+01 2.73.6e-014.0e-017.60e-01126
5.0e-031.0e+02 2.73.6e-014.0e-017.60e-01126
2.5e-031.0e+01 2.81.5e+006.2e-012.12e+0098
2.5e-032.5e+01 3.54.4e-016.9e-011.13e+0096
2.5e-035.0e+01 3.64.2e-014.4e-018.60e-01101
2.5e-031.0e+02 3.64.0e-013.9e-017.90e-01101
1.0e-031.0e+01 3.52.1e+004.2e-012.52e+0066
1.0e-032.5e+01 4.75.8e-015.7e-011.15e+0069
1.0e-035.0e+01 5.14.9e-013.0e-017.90e-0163
1.0e-031.0e+02 5.15.3e-013.9e-019.20e-0163
1.0e-041.0e+01 5.53.8e+001.9e-013.99e+0021
1.0e-042.5e+01 7.61.0e+003.9e-011.39e+0029
1.0e-045.0e+01 8.18.1e-013.7e-011.18e+0027
1.0e-041.0e+02 8.56.9e-013.8e-011.07e+0026
1.0e-051.0e+01 7.94.4e+001.1e-014.51e+008
1.0e-055.0e+01 10.61.1e+001.8e-011.28e+0011
1.0e-051.0e+02 10.91.1e+002.3e-011.33e+0012
ILUPACK - MEDIUM VERSION + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 0.71.0e-011.2e+001.30e+00419
1.0e-012.5e+01 0.88.0e-028.3e-019.10e-01396
1.0e-015.0e+01 0.89.0e-028.7e-019.60e-01396
1.0e-011.0e+02 0.89.0e-028.7e-019.60e-01396
5.0e-021.0e+01 0.91.2e-019.4e-011.06e+00312
5.0e-022.5e+01 1.01.1e-016.5e-017.60e-01298
5.0e-025.0e+01 1.08.0e-026.6e-017.40e-01298
5.0e-021.0e+02 1.01.0e-016.5e-017.50e-01298
2.5e-021.0e+01 1.21.8e-017.9e-019.70e-01251
2.5e-022.5e+01 1.31.0e-014.9e-015.90e-01219
2.5e-025.0e+01 1.31.0e-015.1e-016.10e-01219
2.5e-021.0e+02 1.31.1e-015.0e-016.10e-01219
1.0e-021.0e+01 1.74.2e-018.0e-011.22e+00205
1.0e-022.5e+01 1.81.3e-016.7e-018.00e-01163
1.0e-025.0e+01 1.81.4e-014.1e-015.50e-01153
1.0e-021.0e+02 1.81.4e-013.9e-015.30e-01153
5.0e-031.0e+01 2.17.3e-017.9e-011.52e+00165
5.0e-032.5e+01 2.41.7e-015.9e-017.60e-01123
5.0e-035.0e+01 2.41.8e-013.9e-015.70e-01130
5.0e-031.0e+02 2.41.6e-014.0e-015.60e-01130
2.5e-031.0e+01 2.51.1e+005.4e-011.64e+00106
2.5e-032.5e+01 3.22.3e-015.3e-017.60e-0189
2.5e-035.0e+01 3.22.1e-012.8e-014.90e-0181
2.5e-031.0e+02 3.22.2e-013.0e-015.20e-0181
1.0e-031.0e+01 3.11.9e+004.4e-012.34e+0065
1.0e-032.5e+01 4.04.5e-015.1e-019.60e-0171
1.0e-035.0e+01 4.42.7e-012.4e-015.10e-0155
1.0e-031.0e+02 4.42.7e-012.8e-015.50e-0155
1.0e-041.0e+01 4.74.2e+001.7e-014.37e+0020
1.0e-042.5e+01 6.31.1e+003.3e-011.43e+0028
1.0e-045.0e+01 7.15.6e-014.0e-019.60e-0132
1.0e-041.0e+02 7.44.3e-013.6e-017.90e-0125
1.0e-051.0e+01 6.55.1e+009.0e-025.19e+008
1.0e-055.0e+01 9.37.3e-011.6e-018.90e-0111
1.0e-051.0e+02 9.76.7e-012.0e-018.70e-0112
ILUPACK - MEDIUM VERSION + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter

ILUPACK - SIMPLE VERSION

ILUPACK - SIMPLE VERSION + PP
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-021.0e+01 1.17.0e-021.3e+001.37e+00406
2.5e-022.5e+01 1.17.0e-021.3e+001.37e+00406
2.5e-025.0e+01 1.15.0e-021.3e+001.35e+00406
2.5e-021.0e+02 1.17.0e-021.3e+001.37e+00406
1.0e-021.0e+01 1.39.0e-028.7e-019.60e-01263
1.0e-022.5e+01 1.38.0e-028.7e-019.50e-01263
1.0e-025.0e+01 1.31.0e-018.8e-019.80e-01263
1.0e-021.0e+02 1.39.0e-028.6e-019.50e-01263
5.0e-031.0e+01 1.51.1e-017.2e-018.30e-01206
5.0e-032.5e+01 1.51.0e-017.3e-018.30e-01206
5.0e-035.0e+01 1.51.1e-017.2e-018.30e-01206
5.0e-031.0e+02 1.51.1e-017.2e-018.30e-01206
2.5e-031.0e+01 1.71.4e-015.4e-016.80e-01147
2.5e-032.5e+01 1.71.4e-015.3e-016.70e-01147
2.5e-035.0e+01 1.71.4e-015.4e-016.80e-01147
2.5e-031.0e+02 1.71.3e-015.4e-016.70e-01147
1.0e-031.0e+01 2.11.8e-014.6e-016.40e-01119
1.0e-032.5e+01 2.11.7e-014.7e-016.40e-01119
1.0e-035.0e+01 2.11.7e-014.5e-016.20e-01119
1.0e-031.0e+02 2.11.8e-014.7e-016.50e-01119
1.0e-041.0e+01 3.44.0e-013.4e-017.40e-0159
1.0e-042.5e+01 3.44.0e-013.4e-017.40e-0159
1.0e-045.0e+01 3.43.9e-013.2e-017.10e-0159
1.0e-041.0e+02 3.44.0e-013.1e-017.10e-0159
1.0e-051.0e+01 5.99.2e-012.5e-011.17e+0024
1.0e-052.5e+01 5.99.2e-012.6e-011.18e+0024
1.0e-055.0e+01 5.99.3e-012.6e-011.19e+0024
1.0e-051.0e+02 5.99.3e-012.5e-011.18e+0024
ILUPACK - SIMPLE VERSION + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-051.0e+01 7.91.1e+003.3e-011.43e+0020
1.0e-052.5e+01 10.09.6e-014.1e-011.37e+0022
1.0e-055.0e+01 11.59.8e-013.5e-011.33e+0018
1.0e-051.0e+02 13.19.2e-015.3e-011.45e+0021
1.0e-011.0e+01 0.63.0e-021.2e+001.23e+00447
1.0e-012.5e+01 0.64.0e-021.1e+001.14e+00425
1.0e-015.0e+01 0.64.0e-021.1e+001.14e+00425
1.0e-011.0e+02 0.64.0e-021.1e+001.14e+00425
5.0e-021.0e+01 0.75.0e-021.0e+001.05e+00365
5.0e-022.5e+01 0.74.0e-021.0e+001.04e+00372
5.0e-025.0e+01 0.76.0e-021.0e+001.06e+00372
5.0e-021.0e+02 0.76.0e-021.1e+001.16e+00372
2.5e-021.0e+01 1.07.0e-029.4e-011.01e+00295
2.5e-022.5e+01 1.09.0e-027.9e-018.80e-01249
2.5e-025.0e+01 1.06.0e-027.4e-018.00e-01249
2.5e-021.0e+02 1.06.0e-027.6e-018.20e-01249
1.0e-021.0e+01 1.37.0e-028.1e-018.80e-01223
1.0e-022.5e+01 1.48.0e-027.4e-018.20e-01222
1.0e-025.0e+01 1.47.0e-027.6e-018.30e-01222
1.0e-021.0e+02 1.48.0e-027.6e-018.40e-01222
5.0e-031.0e+01 1.71.1e-016.2e-017.30e-01168
5.0e-032.5e+01 1.91.0e-016.4e-017.40e-01156
5.0e-035.0e+01 1.99.0e-026.4e-017.30e-01156
5.0e-031.0e+02 1.91.0e-016.1e-017.10e-01156
2.5e-031.0e+01 2.01.6e-015.5e-017.10e-01129
2.5e-032.5e+01 2.31.3e-015.9e-017.20e-01123
2.5e-035.0e+01 2.41.4e-015.8e-017.20e-01123
2.5e-031.0e+02 2.41.2e-015.7e-016.90e-01123
1.0e-031.0e+01 2.92.8e-015.9e-018.70e-0192
1.0e-032.5e+01 3.32.1e-015.5e-017.60e-0185
1.0e-035.0e+01 3.51.8e-015.4e-017.20e-0186
1.0e-031.0e+02 3.52.0e-015.5e-017.50e-0186
1.0e-041.0e+01 5.05.7e-014.9e-011.06e+0046
1.0e-042.5e+01 6.04.7e-015.0e-019.70e-0143
1.0e-045.0e+01 7.14.6e-015.4e-011.00e+0040
1.0e-041.0e+02 7.64.2e-017.0e-011.12e+0041
ILUPACK - SIMPLE VERSION + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 0.82.6e-011.1e+001.36e+00378
1.0e-012.5e+01 0.82.6e-017.9e-011.05e+00373
1.0e-015.0e+01 0.82.4e-017.9e-011.03e+00373
1.0e-011.0e+02 0.82.6e-017.9e-011.05e+00373
5.0e-021.0e+01 1.02.5e-018.9e-011.14e+00290
5.0e-022.5e+01 1.12.6e-016.3e-018.90e-01282
5.0e-025.0e+01 1.12.6e-016.3e-018.90e-01282
5.0e-021.0e+02 1.12.6e-016.4e-019.00e-01282
2.5e-021.0e+01 1.22.7e-018.2e-011.09e+00238
2.5e-022.5e+01 1.42.7e-015.2e-017.90e-01212
2.5e-025.0e+01 1.42.7e-015.2e-017.90e-01212
2.5e-021.0e+02 1.42.8e-015.3e-018.10e-01212
1.0e-021.0e+01 1.73.6e-017.2e-011.08e+00182
1.0e-022.5e+01 2.03.3e-014.9e-018.20e-01162
1.0e-025.0e+01 2.03.4e-014.9e-018.30e-01162
1.0e-021.0e+02 2.03.2e-014.6e-017.80e-01162
5.0e-031.0e+01 2.33.8e-017.4e-011.12e+00132
5.0e-032.5e+01 2.73.6e-016.7e-011.03e+00126
5.0e-035.0e+01 2.73.4e-014.5e-017.90e-01126
5.0e-031.0e+02 2.73.6e-014.5e-018.10e-01126
2.5e-031.0e+01 2.84.3e-016.1e-011.04e+0099
2.5e-032.5e+01 3.54.1e-017.6e-011.17e+00101
2.5e-035.0e+01 3.64.0e-014.3e-018.30e-01101
2.5e-031.0e+02 3.63.8e-014.7e-018.50e-01101
1.0e-031.0e+01 3.55.3e-014.8e-011.01e+0070
1.0e-032.5e+01 4.74.8e-015.9e-011.07e+0063
1.0e-035.0e+01 5.15.0e-013.5e-018.50e-0163
1.0e-031.0e+02 5.14.8e-012.9e-017.70e-0163
1.0e-041.0e+01 5.56.7e-012.8e-019.50e-0129
1.0e-042.5e+01 7.66.6e-013.3e-019.90e-0125
1.0e-045.0e+01 8.16.9e-013.5e-011.04e+0024
1.0e-041.0e+02 8.56.8e-013.8e-011.06e+0024
1.0e-051.0e+01 7.99.5e-011.7e-011.12e+0011
1.0e-052.5e+01 10.19.2e-011.6e-011.08e+0010
1.0e-055.0e+01 10.69.8e-012.1e-011.19e+0010
1.0e-051.0e+02 10.91.0e+002.4e-011.24e+0010
ILUPACK - SIMPLE VERSION + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 0.78.0e-021.1e+001.18e+00399
1.0e-012.5e+01 0.88.0e-028.7e-019.50e-01396
1.0e-015.0e+01 0.88.0e-028.7e-019.50e-01396
1.0e-011.0e+02 0.89.0e-028.7e-019.60e-01396
5.0e-021.0e+01 0.98.0e-029.0e-019.80e-01286
5.0e-022.5e+01 1.08.0e-026.8e-017.60e-01298
5.0e-025.0e+01 1.01.0e-016.7e-017.70e-01298
5.0e-021.0e+02 1.08.0e-027.0e-017.80e-01298
2.5e-021.0e+01 1.21.1e-017.2e-018.30e-01211
2.5e-022.5e+01 1.31.1e-015.5e-016.60e-01219
2.5e-025.0e+01 1.31.0e-015.5e-016.50e-01219
2.5e-021.0e+02 1.31.0e-015.0e-016.00e-01219
1.0e-021.0e+01 1.71.3e-017.1e-018.40e-01171
1.0e-022.5e+01 1.81.3e-016.2e-017.50e-01160
1.0e-025.0e+01 1.81.4e-014.2e-015.60e-01153
1.0e-021.0e+02 1.81.4e-014.2e-015.60e-01153
5.0e-031.0e+01 2.11.7e-015.4e-017.10e-01121
5.0e-032.5e+01 2.41.7e-016.2e-017.90e-01130
5.0e-035.0e+01 2.41.7e-014.0e-015.70e-01130
5.0e-031.0e+02 2.41.8e-013.8e-015.60e-01130
2.5e-031.0e+01 2.52.2e-014.4e-016.60e-0187
2.5e-032.5e+01 3.22.2e-014.4e-016.60e-0180
2.5e-035.0e+01 3.22.0e-013.0e-015.00e-0181
2.5e-031.0e+02 3.22.0e-013.1e-015.10e-0181
1.0e-031.0e+01 3.12.8e-014.3e-017.10e-0170
1.0e-032.5e+01 4.02.5e-013.7e-016.20e-0156
1.0e-035.0e+01 4.42.7e-012.5e-015.20e-0155
1.0e-031.0e+02 4.42.4e-012.7e-015.10e-0155
1.0e-041.0e+01 4.74.4e-012.1e-016.50e-0124
1.0e-042.5e+01 6.34.1e-012.7e-016.80e-0126
1.0e-045.0e+01 7.14.1e-012.9e-017.00e-0125
1.0e-041.0e+02 7.44.2e-013.1e-017.30e-0125
1.0e-051.0e+01 6.56.2e-011.0e-017.20e-019
1.0e-052.5e+01 8.55.6e-011.4e-017.00e-0110
ILUPACK - SIMPLE VERSION + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
???
m.bollhoefer@tu-bs.de

Last modified: October 11, 2011