Matrix xenon1

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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 - 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
Abbreviations for Orderings
PQ new PQ ordering for multilevel ILU
RCM Reverse Cuthill-McKee
MMD minimum degree
AMF approximate inverse fill
ND MeTiS multilevel (node) nested dissection

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 + PQ
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-021.0e+01 3.97.3e+021.8e+017.48e+0268
1.0e-021.0e+01 5.71.3e+039.2e+001.31e+0328
2.5e-011.0e+01 2.01.2e+027.4e+011.94e+02458
1.0e-011.0e+01 4.02.5e+023.8e+012.88e+02178
5.0e-021.0e+01 8.57.6e+022.4e+017.84e+0254
ILUPACK - MEDIUM VERSION + PQ + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-011.0e+01 1.43.4e+013.0e+016.40e+01229
1.0e-011.0e+01 2.91.2e+022.2e+011.42e+02128
1.0e-012.5e+01 2.91.2e+022.6e+011.46e+02128
1.0e-015.0e+01 2.91.2e+022.5e+011.45e+02128
1.0e-011.0e+02 2.91.2e+022.3e+011.43e+02128
5.0e-021.0e+01 5.73.1e+021.3e+013.23e+0249
5.0e-022.5e+01 5.83.1e+021.3e+013.23e+0249
5.0e-025.0e+01 5.83.1e+021.2e+013.22e+0249
5.0e-021.0e+02 5.82.8e+021.2e+012.92e+0249
2.5e-021.0e+01 9.44.9e+021.0e+015.00e+0227
2.5e-022.5e+01 9.75.2e+028.9e+005.29e+0226
2.5e-025.0e+01 9.75.1e+028.4e+005.18e+0226
2.5e-021.0e+02 9.75.4e+029.0e+005.49e+0226
1.0e-021.0e+01 18.31.1e+038.1e+001.11e+0314
1.0e-022.5e+01 18.01.1e+037.6e+001.11e+0314
1.0e-025.0e+01 18.01.0e+037.1e+001.01e+0314
1.0e-021.0e+02 18.01.1e+038.6e+001.11e+0314
5.0e-031.0e+01 28.11.9e+037.9e+001.91e+039
ILUPACK - MEDIUM VERSION + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-011.0e+01 1.23.1e+014.4e+017.50e+01296
1.0e-011.0e+01 1.78.4e+013.9e+011.23e+02177
5.0e-021.0e+01 2.61.7e+021.4e+011.84e+0253
2.5e-021.0e+01 4.23.4e+029.2e+003.49e+0226
ILUPACK - MEDIUM VERSION + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-011.0e+01 1.13.1e+016.0e+019.10e+01434
1.0e-011.0e+01 1.77.5e+013.6e+011.11e+02173
5.0e-021.0e+01 2.81.7e+021.8e+011.88e+0270
2.5e-021.0e+01 4.23.3e+029.1e+003.39e+0226
ILUPACK - MEDIUM VERSION + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
ILUPACK - MEDIUM VERSION + MMD + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 1.91.1e+023.5e+011.45e+02191
5.0e-021.0e+01 3.02.1e+021.2e+012.22e+0248
2.5e-021.0e+01 4.64.0e+027.7e+004.08e+0225
ILUPACK - MEDIUM VERSION + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 1.77.5e+012.9e+011.04e+02146
5.0e-021.0e+01 2.31.5e+021.4e+011.64e+0261
2.5e-021.0e+01 2.92.7e+027.2e+002.77e+0227
ILUPACK - MEDIUM VERSION + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 1.77.3e+013.8e+011.11e+02210
5.0e-021.0e+01 2.31.7e+021.5e+011.85e+0259
2.5e-021.0e+01 3.02.9e+028.4e+002.98e+0227
ILUPACK - MEDIUM VERSION + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
ILUPACK - MEDIUM VERSION + Multilevel ND + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter

ILUPACK - SIMPLE VERSION

ILUPACK - SIMPLE VERSION + PQ
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-021.0e+01 5.69.1e+013.1e+011.22e+0290
1.0e-022.5e+01 7.71.5e+023.9e+011.89e+0297
1.0e-025.0e+01 8.61.4e+023.8e+011.78e+0293
1.0e-021.0e+02 8.51.4e+024.8e+011.88e+02118
5.0e-031.0e+01 8.62.3e+021.2e+012.42e+0228
5.0e-032.5e+01 10.01.9e+021.4e+012.04e+0230
5.0e-035.0e+01 12.02.5e+022.0e+012.70e+0238
5.0e-031.0e+02 12.42.8e+021.6e+012.96e+0230
2.5e-031.0e+01 10.22.0e+027.6e+002.08e+0217
2.5e-032.5e+01 13.62.9e+021.1e+013.01e+0218
2.5e-031.0e+02 17.04.2e+021.5e+014.35e+0219
1.0e-031.0e+01 14.53.4e+027.6e+003.48e+0211
ILUPACK - SIMPLE VERSION + PQ + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-052.5e+01 38.21.3e+034.2e+001.30e+034
5.0e-031.0e+01 5.77.7e+017.8e+008.48e+0124
5.0e-032.5e+01 5.77.6e+018.5e+008.45e+0125
5.0e-035.0e+01 5.77.4e+018.5e+008.25e+0125
5.0e-031.0e+02 5.77.6e+018.6e+008.46e+0125
2.5e-031.0e+01 7.41.0e+021.1e+011.11e+0227
2.5e-032.5e+01 7.51.1e+021.1e+011.21e+0227
2.5e-035.0e+01 7.51.1e+021.1e+011.21e+0227
2.5e-031.0e+02 7.51.1e+021.1e+011.21e+0227
1.0e-031.0e+01 10.42.3e+025.8e+002.36e+0211
1.0e-032.5e+01 10.01.6e+025.2e+001.65e+0211
1.0e-035.0e+01 10.01.6e+025.5e+001.66e+0211
1.0e-031.0e+02 10.01.6e+025.5e+001.66e+0211
ILUPACK - SIMPLE VERSION + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-025.0e+01 4.63.4e+011.2e+021.54e+02247
5.0e-021.0e+02 6.44.3e+017.0e+011.13e+02123
2.5e-022.5e+01 4.24.2e+011.8e+016.00e+0145
2.5e-025.0e+01 6.25.3e+011.6e+016.90e+0130
2.5e-021.0e+02 9.07.6e+011.8e+019.40e+0127
1.0e-021.0e+01 4.26.0e+019.2e+006.92e+0126
1.0e-022.5e+01 6.07.5e+019.9e+008.49e+0120
1.0e-025.0e+01 8.71.0e+021.3e+011.13e+0218
1.0e-021.0e+02 12.71.3e+021.3e+011.43e+0217
5.0e-031.0e+01 5.49.1e+016.8e+009.78e+0116
5.0e-032.5e+01 7.91.2e+026.8e+001.27e+0212
5.0e-035.0e+01 11.51.6e+028.5e+001.68e+0212
5.0e-031.0e+02 17.22.1e+029.2e+002.19e+0210
2.5e-031.0e+01 6.91.4e+024.7e+001.45e+0210
2.5e-032.5e+01 10.02.0e+026.1e+002.06e+029
ILUPACK - SIMPLE VERSION + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-025.0e+01 4.43.8e+016.3e+011.01e+02124
5.0e-021.0e+02 6.44.5e+013.1e+017.60e+0153
2.5e-022.5e+01 4.24.7e+012.3e+017.00e+0148
2.5e-025.0e+01 6.06.6e+011.6e+018.20e+0128
2.5e-021.0e+02 8.78.8e+012.0e+011.08e+0229
1.0e-021.0e+01 4.26.7e+019.0e+007.60e+0124
1.0e-022.5e+01 6.08.3e+011.0e+019.30e+0119
1.0e-025.0e+01 9.01.1e+021.1e+011.21e+0217
1.0e-021.0e+02 13.01.5e+021.4e+011.64e+0215
5.0e-031.0e+01 5.41.1e+026.2e+001.16e+0214
5.0e-032.5e+01 7.91.4e+027.4e+001.47e+0212
5.0e-035.0e+01 11.71.8e+028.0e+001.88e+0211
5.0e-031.0e+02 17.02.6e+021.0e+012.70e+0210
2.5e-031.0e+01 6.91.6e+025.3e+001.65e+0210
2.5e-032.5e+01 10.12.3e+025.8e+002.36e+028
ILUPACK - SIMPLE VERSION + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-022.5e+01 4.55.1e+011.2e+021.71e+02299
2.5e-025.0e+01 5.65.6e+011.1e+021.66e+02240
1.0e-021.0e+01 4.39.0e+013.0e+011.20e+0284
1.0e-022.5e+01 5.97.6e+011.4e+019.00e+0130
1.0e-025.0e+01 7.69.0e+011.4e+011.04e+0227
1.0e-021.0e+02 9.21.1e+021.8e+011.28e+0227
5.0e-031.0e+01 5.41.3e+029.7e+001.40e+0224
5.0e-032.5e+01 7.11.1e+021.0e+011.20e+0220
5.0e-035.0e+01 9.61.3e+021.1e+011.41e+0219
5.0e-031.0e+02 11.31.4e+021.2e+011.52e+0218
2.5e-031.0e+01 6.91.9e+024.4e+001.94e+0210
2.5e-032.5e+01 8.51.5e+025.1e+001.55e+029
ILUPACK - SIMPLE VERSION + MMD + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-021.0e+01 4.39.0e+012.5e+011.15e+0270
1.0e-022.5e+01 5.98.4e+011.4e+019.80e+0130
1.0e-025.0e+01 7.49.1e+011.5e+011.06e+0229
1.0e-021.0e+02 8.81.0e+021.7e+011.17e+0229
5.0e-031.0e+01 5.31.3e+029.5e+001.40e+0224
5.0e-032.5e+01 7.11.1e+021.0e+011.20e+0220
5.0e-035.0e+01 8.21.4e+021.0e+011.50e+0219
5.0e-031.0e+02 10.51.4e+021.1e+011.51e+0218
2.5e-031.0e+01 6.31.8e+025.3e+001.85e+0212
2.5e-032.5e+01 8.31.5e+026.4e+001.56e+0210
2.5e-035.0e+01 10.81.8e+026.6e+001.87e+029
ILUPACK - SIMPLE VERSION + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-022.5e+01 4.23.9e+011.9e+022.29e+02459
2.5e-025.0e+01 5.44.3e+014.3e+018.60e+0193
2.5e-021.0e+02 6.55.6e+016.3e+011.19e+02116
1.0e-021.0e+01 4.15.6e+013.0e+018.60e+0183
1.0e-022.5e+01 5.35.2e+011.0e+016.20e+0121
1.0e-025.0e+01 6.86.6e+011.1e+017.70e+0120
1.0e-021.0e+02 8.38.1e+011.1e+019.20e+0118
5.0e-031.0e+01 5.08.0e+016.2e+008.62e+0115
5.0e-032.5e+01 6.48.5e+016.2e+009.12e+0112
5.0e-035.0e+01 8.41.0e+026.7e+001.07e+0211
5.0e-031.0e+02 9.41.0e+026.5e+001.06e+0210
2.5e-031.0e+01 6.31.2e+024.3e+001.24e+029
ILUPACK - SIMPLE VERSION + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-025.0e+01 5.23.9e+014.1e+018.00e+0192
2.5e-021.0e+02 6.45.6e+019.6e+011.52e+02180
1.0e-021.0e+01 4.04.9e+011.9e+016.80e+0158
1.0e-022.5e+01 5.44.8e+011.0e+015.80e+0121
1.0e-025.0e+01 6.76.0e+019.2e+006.92e+0119
1.0e-021.0e+02 8.88.2e+019.8e+009.18e+0117
5.0e-031.0e+01 4.97.1e+015.6e+007.66e+0115
5.0e-032.5e+01 6.56.9e+016.2e+007.52e+0113
5.0e-035.0e+01 8.48.4e+016.1e+009.01e+0111
5.0e-031.0e+02 9.79.8e+016.7e+001.05e+0211
2.5e-031.0e+01 6.21.2e+023.8e+001.24e+029
ILUPACK - SIMPLE VERSION + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
ILUPACK - SIMPLE VERSION + Multilevel ND + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+02 4.62.2e+011.6e+021.82e+02433
5.0e-025.0e+01 4.52.5e+012.0e+014.50e+0154
5.0e-021.0e+02 5.62.8e+011.3e+014.10e+0131
2.5e-022.5e+01 4.22.9e+011.5e+014.40e+0144
2.5e-025.0e+01 5.53.3e+011.0e+014.30e+0125
2.5e-021.0e+02 7.04.0e+019.6e+004.96e+0121
1.0e-021.0e+01 4.14.4e+016.8e+005.08e+0122
1.0e-022.5e+01 5.34.1e+016.4e+004.74e+0116
1.0e-025.0e+01 6.94.8e+016.5e+005.45e+0114
1.0e-021.0e+02 8.65.9e+015.6e+006.46e+0111
5.0e-031.0e+01 4.96.0e+014.1e+006.41e+0112
5.0e-032.5e+01 6.45.8e+014.3e+006.23e+0110
5.0e-035.0e+01 8.36.8e+014.5e+007.25e+019

ILUTP

ILUTP + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-01 -0.04.1e+02--failure
1.0e-02 2.55.5e+006.5e+017.05e+01369
1.0e-03 7.73.4e+016.2e+004.02e+0120
1.0e-04 22.22.2e+025.8e+002.26e+0210
ILUTP + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-01 -0.04.2e+02--failure
1.0e-02 2.45.7e+006.9e+017.47e+01344
1.0e-03 7.73.6e+016.7e+004.27e+0119
1.0e-04 22.12.4e+026.2e+002.46e+029
ILUTP + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 7.55.6e+015.6e+006.16e+0119
1.0e-04 14.62.0e+022.6e+002.03e+026
ILUTP + MMD + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 7.56.0e+015.6e+006.56e+0117
1.0e-04 14.62.1e+023.1e+002.13e+026
ILUTP + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 9.46.9e+014.9e+007.39e+0115
1.0e-04 21.13.6e+023.9e+003.64e+027
1.0e-06 -0.01.7e+03--failure
ILUTP + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 6.93.7e+014.3e+004.13e+0116
1.0e-04 13.11.5e+022.3e+001.52e+026
ILUTP + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 7.13.9e+014.3e+004.33e+0115
1.0e-04 12.01.3e+023.0e+001.33e+026
ILUTP + Mutilevel ND + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 7.03.9e+015.0e+004.40e+0115
1.0e-04 12.01.3e+022.7e+001.33e+026

ILUC

ILUC + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-01 -0.02.2e+02--failure
1.0e-02 9.95.0e+011.0e+021.50e+02267
1.0e-03 21.21.4e+027.1e+001.47e+0212
ILUC + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-01 -0.02.4e+02--failure
1.0e-02 9.24.7e+011.0e+021.47e+02277
1.0e-03 21.01.5e+027.6e+001.58e+0212
ILUC + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 13.91.4e+029.0e+001.49e+0222
1.0e-04 20.52.5e+022.6e+002.53e+025
ILUC + MMD + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 13.71.5e+028.9e+001.59e+0219
1.0e-04 20.42.8e+023.3e+002.83e+025
ILUC + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-01 -0.03.1e+02--failure
1.0e-03 18.12.3e+029.6e+002.40e+0219
ILUC + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 13.41.2e+025.9e+001.26e+0214
1.0e-04 18.32.0e+022.6e+002.03e+025
ILUC + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 11.08.2e+016.9e+008.89e+0118
1.0e-04 14.51.3e+022.3e+001.32e+025
ILUC + Multilevel ND + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 11.08.7e+017.0e+009.40e+0117
1.0e-04 14.61.6e+023.1e+001.63e+025

PARDISO

PARDISO
parameters time [sec]
fill-in LU fac. LU solve total iter
17.62.1e+029.4e-012.1e+020
PARDISO + MC64
parameters time [sec]
fill-in LU fac. LU solve total iter
17.62.1e+029.4e-012.1e+020
m.bollhoefer@tu-bs.de

Last modified: October 11, 2011