Matrix fidap007

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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
5.0e-021.0e+01 1.94.2e-012.9e-017.10e-0162
2.5e-021.0e+01 1.83.9e-012.2e-016.10e-0156
2.5e-022.5e+01 2.14.5e-012.7e-017.20e-0156
2.5e-025.0e+01 2.14.2e-011.4e-015.60e-0131
2.5e-021.0e+02 1.83.7e-011.2e-014.90e-0128
1.0e-021.0e+01 1.94.5e-019.0e-025.40e-0122
1.0e-022.5e+01 2.14.5e-012.6e-017.10e-0158
1.0e-025.0e+01 2.14.9e-012.7e-017.60e-0158
1.0e-021.0e+02 2.14.0e-011.3e-015.30e-0126
5.0e-031.0e+01 2.34.8e-011.2e-016.00e-0122
5.0e-032.5e+01 2.35.0e-019.0e-025.90e-0120
5.0e-035.0e+01 2.34.8e-019.0e-025.70e-0120
5.0e-031.0e+02 2.34.9e-019.0e-025.80e-0120
2.5e-031.0e+01 2.25.3e-017.0e-026.00e-0116
2.5e-032.5e+01 2.64.9e-011.3e-016.20e-0121
2.5e-035.0e+01 2.64.6e-011.4e-016.00e-0121
2.5e-031.0e+02 2.65.2e-011.3e-016.50e-0121
1.0e-031.0e+01 2.46.4e-016.0e-027.00e-0113
1.0e-032.5e+01 2.85.4e-011.1e-016.50e-0114
1.0e-035.0e+01 2.95.5e-011.1e-016.60e-0117
1.0e-031.0e+02 2.85.2e-018.0e-026.00e-0116
1.0e-041.0e+01 2.99.0e-013.0e-029.30e-015
ILUPACK - MEDIUM VERSION + PQ + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
2.5e-031.0e+01 2.61.1e+003.2e+004.30e+00480
2.5e-032.5e+01 3.92.1e+007.8e-012.88e+0085
2.5e-035.0e+01 3.92.4e+001.0e+003.40e+0082
2.5e-031.0e+02 3.92.6e+001.1e+003.70e+0082
1.0e-031.0e+01 2.91.4e+006.0e-012.00e+0073
1.0e-032.5e+01 4.02.7e+003.8e-013.08e+0030
1.0e-035.0e+01 4.23.0e+002.9e-013.29e+0020
1.0e-031.0e+02 4.22.9e+002.7e-013.17e+0020
1.0e-041.0e+01 4.62.6e+008.0e-022.68e+009
ILUPACK - MEDIUM VERSION + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-041.0e+01 6.33.8e+002.9e-014.09e+0025
1.0e-051.0e+01 5.94.0e+003.1e-014.31e+0028
1.0e-052.5e+01 4.44.3e+002.4e-014.54e+0030
1.0e-055.0e+01 3.74.4e+006.1e-015.01e+0093
1.0e-051.0e+02 3.23.9e+001.6e-014.06e+0026
ILUPACK - MEDIUM VERSION + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-041.0e+01 6.95.9e+003.5e+009.40e+00149
1.0e-051.0e+01 6.85.8e+005.1e-016.31e+0031
1.0e-052.5e+01 6.31.0e+013.5e-011.03e+0123
1.0e-055.0e+01 6.01.0e+013.1e-011.03e+0121
1.0e-051.0e+02 5.71.1e+014.2e-011.14e+0130
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
2.5e-021.0e+02 1.71.2e+004.7e-011.67e+00112
1.0e-021.0e+01 1.42.0e+001.3e+003.30e+00401
1.0e-025.0e+01 1.61.3e+003.0e-011.60e+0073
1.0e-021.0e+02 1.71.4e+002.3e-011.63e+0059
5.0e-031.0e+01 2.02.0e+004.5e-012.45e+00108
5.0e-032.5e+01 1.92.2e+003.0e-012.50e+0074
5.0e-035.0e+01 1.71.7e+001.6e-011.86e+0041
5.0e-031.0e+02 1.81.5e+002.5e-011.75e+0056
2.5e-031.0e+01 2.12.1e+001.6e-012.26e+0044
2.5e-032.5e+01 2.22.6e+001.1e-012.71e+0024
2.5e-035.0e+01 1.81.7e+009.0e-021.79e+0024
2.5e-031.0e+02 1.91.7e+002.3e-011.93e+0051
1.0e-031.0e+01 2.32.5e+008.0e-022.58e+0021
1.0e-032.5e+01 2.01.8e+008.0e-021.88e+0018
1.0e-035.0e+01 1.92.0e+001.0e-012.10e+0020
1.0e-031.0e+02 2.02.0e+001.1e-012.11e+0020
1.0e-041.0e+01 2.73.5e+005.0e-023.55e+009
ILUPACK - MEDIUM VERSION + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
ILUPACK - MEDIUM VERSION + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-021.0e+02 1.69.6e-014.9e-011.45e+00113
1.0e-025.0e+01 1.71.3e+005.2e-011.82e+00140
1.0e-021.0e+02 1.61.2e+003.6e-011.56e+0087
5.0e-031.0e+01 2.11.0e+001.0e+002.00e+00216
5.0e-032.5e+01 2.01.3e+002.5e-011.55e+0061
5.0e-035.0e+01 1.81.7e+001.4e-011.84e+0031
5.0e-031.0e+02 1.81.6e+001.2e-011.72e+0031
2.5e-031.0e+01 2.31.1e+002.1e-011.31e+0045
2.5e-032.5e+01 2.11.6e+001.2e-011.72e+0027
2.5e-035.0e+01 1.91.7e+001.2e-011.82e+0023
2.5e-031.0e+02 1.91.4e+001.3e-011.53e+0025
1.0e-031.0e+01 2.61.4e+001.0e-011.50e+0021
1.0e-032.5e+01 2.21.6e+008.0e-021.68e+0018
1.0e-035.0e+01 2.01.8e+008.0e-021.88e+0020
1.0e-031.0e+02 2.21.6e+001.0e-011.70e+0020
1.0e-041.0e+01 2.81.8e+006.0e-021.86e+0012
1.0e-042.5e+01 2.62.1e+005.0e-022.15e+009
1.0e-045.0e+01 2.32.3e+004.0e-022.34e+0010
1.0e-041.0e+02 3.92.4e+001.1e-012.51e+0011
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
5.0e-021.0e+01 1.42.8e-012.0e-014.80e-0158
5.0e-022.5e+01 1.73.1e-014.2e-017.30e-0188
5.0e-025.0e+01 1.73.0e-014.3e-017.30e-0188
5.0e-021.0e+02 1.73.1e-014.3e-017.40e-0188
2.5e-021.0e+01 1.52.8e-011.2e-014.00e-0128
2.5e-021.0e+02 1.83.0e-012.6e-015.60e-0158
1.0e-022.5e+01 1.93.1e-012.8e-015.90e-0158
1.0e-025.0e+01 1.93.1e-012.1e-015.20e-0156
1.0e-021.0e+02 1.93.0e-011.3e-014.30e-0130
5.0e-031.0e+01 1.63.1e-017.0e-023.80e-0116
5.0e-035.0e+01 1.93.0e-019.0e-023.90e-0116
5.0e-031.0e+02 2.03.7e-015.0e-024.20e-0112
2.5e-031.0e+01 1.63.3e-018.0e-024.10e-0118
2.5e-032.5e+01 2.03.1e-019.0e-024.00e-0117
2.5e-035.0e+01 2.03.2e-017.0e-023.90e-0113
2.5e-031.0e+02 2.03.1e-018.0e-023.90e-0118
1.0e-031.0e+01 1.83.4e-015.0e-023.90e-0114
1.0e-032.5e+01 2.13.2e-017.0e-023.90e-0115
1.0e-035.0e+01 2.13.4e-014.0e-023.80e-0111
1.0e-031.0e+02 2.13.3e-018.0e-024.10e-0114
1.0e-041.0e+01 1.73.4e-013.0e-023.70e-017
ILUPACK - SIMPLE VERSION + PQ + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-052.5e+01 3.69.1e-011.7e+002.61e+00185
ILUPACK - SIMPLE VERSION + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-025.0e+01 4.91.5e+001.1e+002.60e+00124
5.0e-021.0e+02 4.81.5e+003.5e+005.00e+00432
2.5e-021.0e+02 4.11.2e+006.7e-011.87e+0093
1.0e-022.5e+01 5.11.6e+005.5e-012.15e+0060
5.0e-031.0e+01 4.21.4e+002.0e-011.60e+0028
5.0e-032.5e+01 5.31.6e+002.4e-011.84e+0027
5.0e-031.0e+02 4.01.0e+006.3e-011.63e+0091
2.5e-031.0e+01 3.91.3e+002.0e-011.50e+0029
2.5e-031.0e+02 4.11.1e+004.5e-011.55e+0061
1.0e-031.0e+01 6.12.1e+002.0e-012.30e+0017
1.0e-031.0e+02 3.91.2e+002.0e-011.40e+0028
1.0e-041.0e+01 6.32.2e+002.9e-012.49e+0024
1.0e-042.5e+01 4.71.3e+002.4e-011.54e+0029
1.0e-045.0e+01 3.59.3e-011.3e-011.06e+0022
1.0e-041.0e+02 3.61.1e+001.1e-011.21e+0020
1.0e-051.0e+01 5.92.0e+001.3e-012.13e+0012
1.0e-052.5e+01 4.41.3e+001.3e-011.43e+0017
1.0e-055.0e+01 3.71.2e+001.3e-011.33e+0022
1.0e-051.0e+02 3.29.3e-011.5e-011.08e+0025
ILUPACK - SIMPLE VERSION + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-051.0e+02 5.72.9e+00infInfinf
ILUPACK - SIMPLE VERSION + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-011.0e+01 0.92.6e-015.2e-017.80e-01183
5.0e-021.0e+01 1.02.4e-011.8e-014.20e-0158
5.0e-022.5e+01 0.71.9e-011.8e-013.70e-0157
5.0e-025.0e+01 0.71.6e-011.6e-013.20e-0160
5.0e-021.0e+02 0.71.6e-011.6e-013.20e-0158
2.5e-021.0e+01 1.02.6e-015.0e-023.10e-0120
2.5e-022.5e+01 0.91.9e-015.0e-022.40e-0124
2.5e-025.0e+01 0.81.8e-017.0e-022.50e-0124
2.5e-021.0e+02 0.71.7e-017.0e-022.40e-0124
1.0e-021.0e+01 1.12.5e-014.0e-022.90e-0117
1.0e-022.5e+01 0.91.7e-014.0e-022.10e-0117
1.0e-025.0e+01 0.81.9e-013.0e-022.20e-0113
1.0e-021.0e+02 0.71.8e-016.0e-022.40e-0119
5.0e-031.0e+01 1.12.6e-013.0e-022.90e-0111
5.0e-032.5e+01 0.92.2e-014.0e-022.60e-0116
5.0e-035.0e+01 0.81.9e-014.0e-022.30e-0113
5.0e-031.0e+02 0.71.9e-013.0e-022.20e-0113
2.5e-031.0e+01 1.12.5e-013.0e-022.80e-0112
2.5e-032.5e+01 0.91.9e-015.0e-022.40e-0114
2.5e-035.0e+01 0.82.1e-013.0e-022.40e-0111
2.5e-031.0e+02 0.82.0e-013.0e-022.30e-0112
1.0e-031.0e+01 1.12.5e-013.0e-022.80e-0110
1.0e-032.5e+01 0.91.9e-013.0e-022.20e-0113
1.0e-035.0e+01 0.81.9e-014.0e-022.30e-0111
1.0e-031.0e+02 0.81.8e-013.0e-022.10e-0112
1.0e-041.0e+01 1.12.6e-011.0e-022.70e-016
ILUPACK - SIMPLE VERSION + MMD + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-021.0e+01 1.08.1e-011.1e+001.91e+00357
2.5e-032.5e+01 1.21.4e+008.7e-012.27e+00272
1.0e-052.5e+01 2.01.3e+002.2e-011.52e+0059
1.0e-055.0e+01 1.99.2e-012.4e-011.16e+0061
1.0e-051.0e+02 1.86.8e-012.4e-019.20e-0161
ILUPACK - SIMPLE VERSION + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-015.0e+01 0.81.6e-011.6e-013.20e-0161
5.0e-022.5e+01 0.81.6e-012.5e-014.10e-0192
5.0e-025.0e+01 1.01.8e-011.7e-013.50e-0159
5.0e-021.0e+02 0.71.4e-013.7e-015.10e-01120
2.5e-022.5e+01 0.71.6e-018.0e-022.40e-0130
2.5e-025.0e+01 0.81.4e-017.0e-022.10e-0120
2.5e-021.0e+02 0.71.5e-015.0e-022.00e-0118
1.0e-021.0e+01 1.02.0e-015.0e-022.50e-0120
1.0e-022.5e+01 0.71.5e-016.0e-022.10e-0125
1.0e-025.0e+01 0.81.3e-013.0e-021.60e-0113
1.0e-021.0e+02 0.71.4e-016.0e-022.00e-0112
5.0e-031.0e+01 1.01.8e-014.0e-022.20e-0117
5.0e-032.5e+01 0.81.6e-015.0e-022.10e-0120
5.0e-035.0e+01 0.81.6e-015.0e-022.10e-0112
5.0e-031.0e+02 0.71.3e-013.0e-021.60e-019
2.5e-031.0e+01 1.01.9e-014.0e-022.30e-0115
2.5e-032.5e+01 0.81.5e-015.0e-022.00e-0118
1.0e-031.0e+01 1.02.0e-013.0e-022.30e-0111
1.0e-032.5e+01 0.81.6e-013.0e-021.90e-0110
ILUPACK - SIMPLE VERSION + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-052.5e+01 2.16.1e-014.2e-011.03e+0091
1.0e-055.0e+01 1.95.7e-012.4e-018.10e-0159
1.0e-051.0e+02 4.08.6e-016.2e-011.48e+0082
ILUPACK - SIMPLE VERSION + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-022.5e+01 0.72.1e-011.2e-013.30e-0159
5.0e-025.0e+01 0.82.0e-016.1e-018.10e-01279
5.0e-021.0e+02 0.71.8e-011.3e-013.10e-0160
2.5e-022.5e+01 0.82.1e-016.0e-022.70e-0128
2.5e-025.0e+01 0.82.0e-011.3e-013.30e-0160
2.5e-021.0e+02 0.71.9e-011.2e-013.10e-0156
1.0e-021.0e+01 0.92.7e-016.0e-023.30e-0127
1.0e-022.5e+01 0.82.1e-014.0e-022.50e-0118
1.0e-025.0e+01 0.82.0e-016.0e-022.60e-0127
1.0e-021.0e+02 0.72.0e-015.0e-022.50e-0123
5.0e-031.0e+01 1.02.4e-014.0e-022.80e-0118
5.0e-032.5e+01 0.82.3e-015.0e-022.80e-0123
5.0e-035.0e+01 0.81.9e-015.0e-022.40e-0122
5.0e-031.0e+02 0.81.8e-014.0e-022.20e-0117
2.5e-031.0e+01 1.02.5e-013.0e-022.80e-0116
2.5e-032.5e+01 0.82.2e-015.0e-022.70e-0121
2.5e-035.0e+01 0.82.0e-015.0e-022.50e-0122
2.5e-031.0e+02 0.81.9e-013.0e-022.20e-0116
1.0e-031.0e+01 0.92.6e-013.0e-022.90e-0113
1.0e-032.5e+01 0.82.3e-013.0e-022.60e-0114
1.0e-035.0e+01 0.82.1e-011.0e-022.20e-016
1.0e-031.0e+02 0.81.8e-012.0e-022.00e-0112
1.0e-041.0e+02 0.82.2e-013.0e-022.50e-0110
ILUPACK - SIMPLE VERSION + Multilevel ND + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-052.5e+01 2.05.2e-011.6e-016.80e-0155
1.0e-055.0e+01 1.84.8e-018.0e-025.60e-0124
1.0e-051.0e+02 1.84.5e-018.0e-025.30e-0126

ILUTP

ILUTP + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-06 2.72.5e-013.0e-022.80e-018
ILUTP + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-07 6.51.2e+00infInfinf
ILUTP + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-02 0.79.0e-022.0e-021.10e-0113
1.0e-03 0.89.0e-022.0e-021.10e-016
ILUTP + MMD + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-07 6.41.9e+001.3e+003.20e+00123
ILUTP + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-01 5.11.4e+002.3e+003.70e+00341
1.0e-02 6.31.9e+003.4e-012.24e+0043
1.0e-05 7.62.3e+009.0e-022.39e+0010
1.0e-06 7.92.4e+004.0e-022.44e+004
ILUTP + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-07 6.21.8e+005.4e-012.34e+0060
ILUTP + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-02 0.71.2e-011.0e-021.30e-0110
1.0e-03 0.81.4e-010.0e+001.40e-015
ILUTP + Mutilevel ND + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-07 4.26.3e-014.6e-011.09e+0058

ILUC

ILUC + RCM
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 2.11.9e-011.1e-013.00e-0127
1.0e-05 2.42.3e-013.0e-022.60e-015
ILUC + RCM + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-05 3.43.4e-01infInfinf
ILUC + MMD
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
5.0e-02 0.91.3e-011.1e-012.40e-0148
2.5e-02 1.01.4e-014.0e-021.80e-0116
1.0e-02 1.21.5e-012.0e-021.70e-0111
1.0e-03 1.41.5e-011.0e-021.60e-016
ILUC + MMD + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-02 1.51.8e-014.4e-016.20e-01132
1.0e-03 1.92.3e-012.0e-014.30e-0152
1.0e-04 2.12.3e-011.4e-013.70e-0140
1.0e-05 2.12.1e-018.0e-022.90e-0121
ILUC + AMF
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-05 10.22.3e+00infInfinf
ILUC + AMF + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-03 1.82.1e-012.3e-014.40e-0156
1.0e-04 2.02.2e-012.2e-014.40e-0150
1.0e-05 2.02.4e-011.0e-013.40e-0122
ILUC + Multilevel ND
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-02 1.11.6e-013.0e-021.90e-0115
1.0e-03 1.41.9e-012.0e-022.10e-0110
1.0e-04 1.51.8e-012.0e-022.00e-016
ILUC + Multilevel ND + MC64
parameters time [sec]
drop tol condest fill-in ILU GMRES(30) total iter
1.0e-02 1.42.0e-011.2e-013.20e-0156
1.0e-03 1.82.2e-011.4e-013.60e-0149
1.0e-04 1.92.2e-011.4e-013.60e-0143
1.0e-05 2.02.3e-017.0e-023.00e-0123
1.0e-06 2.02.2e-014.0e-022.60e-0113
1.0e-07 2.12.4e-011.0e-022.50e-013

PARDISO

PARDISO
parameters time [sec]
fill-in LU fac. LU solve total iter
2.92.0e-011.0e-022.1e-010
PARDISO + MC64
parameters time [sec]
fill-in LU fac. LU solve total iter
2.92.0e-011.0e-022.1e-010
m.bollhoefer@tu-bs.de

Last modified: October 11, 2011