Matrix s2rmq4m1

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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 - 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-02	1.0e+01	1.5	2.7e+00	8.4e+00	1.11e+01	429
5.0e-02	2.5e+01	1.5	2.6e+00	7.3e+00	9.90e+00	429
5.0e-02	5.0e+01	1.5	2.6e+00	7.9e+00	1.05e+01	429
5.0e-02	1.0e+02	1.5	2.5e+00	8.2e+00	1.07e+01	429
2.5e-02	1.0e+01	2.5	5.6e+00	9.1e+00	1.47e+01	312
2.5e-02	2.5e+01	2.5	5.6e+00	8.3e+00	1.39e+01	312
2.5e-02	5.0e+01	2.5	5.4e+00	8.2e+00	1.36e+01	312
2.5e-02	1.0e+02	2.5	5.6e+00	9.2e+00	1.48e+01	312
1.0e-02	1.0e+01	5.2	1.8e+01	1.2e+01	3.00e+01	173
1.0e-02	2.5e+01	5.2	1.8e+01	1.2e+01	3.00e+01	173
1.0e-02	5.0e+01	5.2	1.7e+01	1.1e+01	2.80e+01	173
1.0e-02	1.0e+02	5.2	1.7e+01	1.2e+01	2.90e+01	173
5.0e-03	1.0e+01	8.3	6.7e+01	3.6e+01	1.03e+02	96
5.0e-03	2.5e+01	8.3	5.6e+01	3.1e+01	8.70e+01	96
5.0e-03	5.0e+01	8.3	5.5e+01	3.1e+01	8.60e+01	96
5.0e-03	1.0e+02	8.3	5.7e+01	2.8e+01	8.50e+01	96
2.5e-03	1.0e+01	12.9	1.8e+02	7.5e+01	2.55e+02	62
2.5e-03	2.5e+01	12.9	1.9e+02	7.2e+01	2.62e+02	62
2.5e-03	5.0e+01	12.9	1.8e+02	7.8e+01	2.58e+02	62
2.5e-03	1.0e+02	12.9	1.8e+02	7.7e+01	2.57e+02	62
1.0e-03	1.0e+01	13.9	2.2e+02	4.9e+01	2.69e+02	35
1.0e-03	2.5e+01	13.9	2.3e+02	4.2e+01	2.72e+02	35
1.0e-03	5.0e+01	13.9	2.2e+02	4.3e+01	2.63e+02	35
1.0e-03	1.0e+02	13.9	2.2e+02	4.3e+01	2.63e+02	35
1.0e-05	1.0e+02	30.2	1.1e+03	2.4e+01	1.12e+03	5

ILUPACK - MEDIUM VERSION + RCM
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-02	1.0e+01	0.7	3.3e-01	4.8e+00	5.13e+00	383
5.0e-02	2.5e+01	0.7	3.2e-01	4.8e+00	5.12e+00	383
5.0e-02	5.0e+01	0.7	3.1e-01	4.6e+00	4.91e+00	383
5.0e-02	1.0e+02	0.7	2.9e-01	4.6e+00	4.89e+00	383
2.5e-02	1.0e+01	1.1	4.5e-01	5.0e+00	5.45e+00	236
2.5e-02	2.5e+01	1.1	4.2e-01	3.3e+00	3.72e+00	230
2.5e-02	5.0e+01	1.1	4.2e-01	3.5e+00	3.92e+00	230
2.5e-02	1.0e+02	1.1	4.1e-01	3.4e+00	3.81e+00	230
1.0e-02	1.0e+01	1.6	2.9e+00	4.5e+00	7.40e+00	158
1.0e-02	2.5e+01	1.6	5.7e-01	2.6e+00	3.17e+00	139
1.0e-02	5.0e+01	1.6	5.9e-01	2.7e+00	3.29e+00	139
1.0e-02	1.0e+02	1.6	5.2e-01	2.6e+00	3.12e+00	139
5.0e-03	1.0e+01	2.0	8.3e+00	3.8e+00	1.21e+01	108
5.0e-03	2.5e+01	2.2	8.0e-01	3.4e+00	4.20e+00	94
5.0e-03	5.0e+01	2.2	7.7e-01	2.1e+00	2.87e+00	94
5.0e-03	1.0e+02	2.2	6.9e-01	2.1e+00	2.79e+00	94
2.5e-03	1.0e+01	2.5	1.3e+01	2.8e+00	1.58e+01	71
2.5e-03	2.5e+01	3.0	1.2e+00	2.8e+00	4.00e+00	62
2.5e-03	5.0e+01	3.0	1.1e+00	1.7e+00	2.80e+00	61
2.5e-03	1.0e+02	3.0	1.0e+00	1.7e+00	2.70e+00	61
1.0e-03	1.0e+01	2.9	2.0e+01	1.9e+00	2.19e+01	41
1.0e-03	2.5e+01	3.6	1.4e+01	2.0e+00	1.60e+01	40
1.0e-03	5.0e+01	4.1	3.5e+00	2.0e+00	5.50e+00	38
1.0e-03	1.0e+02	4.2	1.7e+00	1.9e+00	3.60e+00	36
1.0e-04	1.0e+01	4.1	5.0e+01	1.2e+00	5.12e+01	14
1.0e-04	2.5e+01	4.9	2.7e+01	8.6e-01	2.79e+01	14
1.0e-04	5.0e+01	5.2	2.2e+01	1.0e+00	2.30e+01	15
1.0e-04	1.0e+02	6.0	6.0e+00	1.0e+00	7.00e+00	15
1.0e-05	1.0e+01	4.9	6.4e+01	5.3e-01	6.45e+01	7

ILUPACK - MEDIUM VERSION + MMD
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-02	1.0e+01	0.9	6.9e-01	6.2e+00	6.89e+00	424
5.0e-02	2.5e+01	0.9	6.9e-01	5.9e+00	6.59e+00	424
5.0e-02	5.0e+01	0.9	6.8e-01	6.3e+00	6.98e+00	424
5.0e-02	1.0e+02	0.9	7.1e-01	6.2e+00	6.91e+00	424
2.5e-02	1.0e+01	1.5	8.7e-01	4.7e+00	5.57e+00	246
2.5e-02	2.5e+01	1.5	8.3e-01	4.0e+00	4.83e+00	246
2.5e-02	5.0e+01	1.5	8.1e-01	4.1e+00	4.91e+00	246
2.5e-02	1.0e+02	1.5	8.0e-01	3.9e+00	4.70e+00	246
1.0e-02	1.0e+01	2.0	7.3e+00	4.7e+00	1.20e+01	133
1.0e-02	2.5e+01	2.5	1.2e+00	4.3e+00	5.50e+00	113
1.0e-02	5.0e+01	2.5	1.1e+00	2.6e+00	3.70e+00	109
1.0e-02	1.0e+02	2.5	1.1e+00	2.9e+00	4.00e+00	109
5.0e-03	1.0e+01	2.4	1.2e+01	3.0e+00	1.50e+01	75
5.0e-03	2.5e+01	2.8	6.5e+00	2.9e+00	9.40e+00	65
5.0e-03	5.0e+01	3.1	1.8e+00	2.8e+00	4.60e+00	62
5.0e-03	1.0e+02	3.2	1.3e+00	1.9e+00	3.20e+00	59
2.5e-03	1.0e+01	2.7	1.9e+01	2.0e+00	2.10e+01	38
2.5e-03	2.5e+01	3.0	9.2e+00	1.6e+00	1.08e+01	36
2.5e-03	5.0e+01	3.3	6.0e+00	1.7e+00	7.70e+00	36
2.5e-03	1.0e+02	3.6	1.7e+00	1.7e+00	3.40e+00	37
1.0e-03	1.0e+01	2.9	2.3e+01	8.9e-01	2.39e+01	19
1.0e-03	2.5e+01	3.1	1.8e+01	8.7e-01	1.89e+01	18
1.0e-03	5.0e+01	3.6	7.6e+00	1.0e+00	8.60e+00	17
1.0e-03	1.0e+02	3.9	2.7e+00	9.8e-01	3.68e+00	18
1.0e-04	1.0e+01	3.2	4.1e+01	3.0e-01	4.13e+01	7

ILUPACK - MEDIUM VERSION + AMF
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-02	1.0e+01	0.9	3.7e-01	6.0e+00	6.37e+00	429
5.0e-02	2.5e+01	0.9	4.0e-01	6.2e+00	6.60e+00	429
5.0e-02	5.0e+01	0.9	3.9e-01	6.0e+00	6.39e+00	429
5.0e-02	1.0e+02	0.9	3.5e-01	6.2e+00	6.55e+00	429
2.5e-02	1.0e+01	1.5	6.9e-01	6.6e+00	7.29e+00	250
2.5e-02	2.5e+01	1.5	5.1e-01	3.8e+00	4.31e+00	235
2.5e-02	5.0e+01	1.5	4.8e-01	3.8e+00	4.28e+00	235
2.5e-02	1.0e+02	1.5	5.1e-01	4.0e+00	4.51e+00	235
1.0e-02	1.0e+01	2.0	6.6e+00	3.7e+00	1.03e+01	112
1.0e-02	2.5e+01	2.4	8.5e-01	3.6e+00	4.45e+00	104
1.0e-02	5.0e+01	2.4	6.9e-01	2.4e+00	3.09e+00	103
1.0e-02	1.0e+02	2.4	7.6e-01	2.7e+00	3.46e+00	103
5.0e-03	1.0e+01	2.3	1.2e+01	2.4e+00	1.44e+01	56
5.0e-03	2.5e+01	2.6	9.0e+00	2.2e+00	1.12e+01	56
5.0e-03	5.0e+01	3.1	1.2e+00	2.4e+00	3.60e+00	54
5.0e-03	1.0e+02	3.1	1.0e+00	2.6e+00	3.60e+00	52
2.5e-03	1.0e+01	2.5	1.6e+01	1.6e+00	1.76e+01	33
2.5e-03	2.5e+01	2.7	1.5e+01	1.2e+00	1.62e+01	29
2.5e-03	5.0e+01	3.1	7.0e+00	1.5e+00	8.50e+00	31
2.5e-03	1.0e+02	3.6	1.2e+00	1.6e+00	2.80e+00	30
1.0e-03	1.0e+01	2.8	2.3e+01	9.4e-01	2.39e+01	20
1.0e-03	2.5e+01	2.9	1.8e+01	7.9e-01	1.88e+01	16
1.0e-03	5.0e+01	3.1	1.2e+01	7.0e-01	1.27e+01	15
1.0e-03	1.0e+02	3.5	4.9e+00	9.5e-01	5.85e+00	17
1.0e-04	1.0e+01	3.1	4.3e+01	4.3e-01	4.34e+01	8

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
1.0e-02	1.0e+01	1.4	9.1e-01	7.1e+00	8.01e+00	363
1.0e-02	2.5e+01	1.4	9.6e-01	7.1e+00	8.06e+00	363
1.0e-02	5.0e+01	1.4	9.2e-01	7.3e+00	8.22e+00	363
1.0e-02	1.0e+02	1.4	9.0e-01	7.1e+00	8.00e+00	363
5.0e-03	1.0e+01	1.9	1.3e+00	6.5e+00	7.80e+00	289
5.0e-03	2.5e+01	1.9	1.1e+00	6.0e+00	7.10e+00	289
5.0e-03	5.0e+01	1.9	1.1e+00	5.9e+00	7.00e+00	289
5.0e-03	1.0e+02	1.9	1.2e+00	6.2e+00	7.40e+00	289
2.5e-03	1.0e+01	2.6	1.9e+00	5.6e+00	7.50e+00	212
2.5e-03	2.5e+01	2.6	1.9e+00	5.6e+00	7.50e+00	212
2.5e-03	5.0e+01	2.6	1.9e+00	5.9e+00	7.80e+00	212
2.5e-03	1.0e+02	2.6	1.9e+00	6.0e+00	7.90e+00	212
1.0e-03	1.0e+01	3.8	3.5e+00	6.0e+00	9.50e+00	148
1.0e-03	2.5e+01	3.8	3.5e+00	5.5e+00	9.00e+00	150
1.0e-03	5.0e+01	3.8	3.5e+00	5.6e+00	9.10e+00	150
1.0e-03	1.0e+02	3.8	3.1e+00	5.7e+00	8.80e+00	150
1.0e-04	1.0e+01	8.8	3.8e+01	1.9e+01	5.70e+01	43
1.0e-04	2.5e+01	8.8	3.8e+01	2.0e+01	5.80e+01	48
1.0e-04	5.0e+01	8.8	3.3e+01	1.5e+01	4.80e+01	48
1.0e-04	1.0e+02	8.8	3.4e+01	1.6e+01	5.00e+01	48
1.0e-05	1.0e+01	13.9	1.7e+02	2.4e+01	1.94e+02	18
1.0e-05	2.5e+01	14.0	1.7e+02	2.0e+01	1.90e+02	15
1.0e-05	5.0e+01	14.0	1.7e+02	1.9e+01	1.89e+02	15
1.0e-05	1.0e+02	14.0	1.8e+02	2.0e+01	2.00e+02	15

ILUPACK - SIMPLE VERSION + RCM
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-02	1.0e+01	0.7	3.5e-01	4.7e+00	5.05e+00	383
5.0e-02	2.5e+01	0.7	3.2e-01	4.8e+00	5.12e+00	383
5.0e-02	5.0e+01	0.7	3.0e-01	4.8e+00	5.10e+00	383
5.0e-02	1.0e+02	0.7	3.6e-01	4.8e+00	5.16e+00	383
2.5e-02	1.0e+01	1.1	4.6e-01	4.8e+00	5.26e+00	229
2.5e-02	2.5e+01	1.1	3.7e-01	3.4e+00	3.77e+00	230
2.5e-02	5.0e+01	1.1	4.4e-01	3.3e+00	3.74e+00	230
2.5e-02	1.0e+02	1.1	4.1e-01	3.4e+00	3.81e+00	230
1.0e-02	1.0e+01	1.6	5.4e-01	4.1e+00	4.64e+00	144
1.0e-02	2.5e+01	1.6	5.5e-01	2.6e+00	3.15e+00	139
1.0e-02	5.0e+01	1.6	5.6e-01	2.6e+00	3.16e+00	139
1.0e-02	1.0e+02	1.6	4.9e-01	2.5e+00	2.99e+00	139
5.0e-03	1.0e+01	1.9	9.8e-01	3.8e+00	4.78e+00	126
5.0e-03	2.5e+01	2.2	7.5e-01	3.3e+00	4.05e+00	94
5.0e-03	5.0e+01	2.2	6.9e-01	2.0e+00	2.69e+00	94
5.0e-03	1.0e+02	2.2	7.5e-01	2.0e+00	2.75e+00	94
2.5e-03	1.0e+01	2.2	1.5e+00	3.1e+00	4.60e+00	96
2.5e-03	2.5e+01	3.0	1.0e+00	2.7e+00	3.70e+00	61
2.5e-03	5.0e+01	3.0	1.0e+00	1.6e+00	2.60e+00	61
2.5e-03	1.0e+02	3.0	1.0e+00	1.6e+00	2.60e+00	61
1.0e-03	1.0e+01	2.9	2.7e+00	2.6e+00	5.30e+00	56
1.0e-03	2.5e+01	3.6	1.9e+00	2.0e+00	3.90e+00	39
1.0e-03	5.0e+01	4.1	1.5e+00	1.9e+00	3.40e+00	35
1.0e-03	1.0e+02	4.2	1.5e+00	1.9e+00	3.40e+00	35
1.0e-04	1.0e+01	4.1	7.0e+00	2.0e+00	9.00e+00	23
1.0e-04	2.5e+01	4.9	4.1e+00	1.2e+00	5.30e+00	16
1.0e-04	5.0e+01	5.2	3.9e+00	9.1e-01	4.81e+00	14
1.0e-04	1.0e+02	6.0	2.6e+00	9.8e-01	3.58e+00	14
1.0e-05	1.0e+01	4.9	8.2e+00	9.0e-01	9.10e+00	11
1.0e-05	2.5e+01	5.7	5.6e+00	4.9e-01	6.09e+00	8

ILUPACK - SIMPLE VERSION + MMD
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-02	1.0e+01	0.9	6.6e-01	5.4e+00	6.06e+00	424
5.0e-02	2.5e+01	0.9	6.6e-01	4.9e+00	5.56e+00	424
5.0e-02	5.0e+01	0.9	6.8e-01	5.2e+00	5.88e+00	424
5.0e-02	1.0e+02	0.9	6.6e-01	5.2e+00	5.86e+00	424
2.5e-02	1.0e+01	1.5	7.4e-01	3.5e+00	4.24e+00	246
2.5e-02	2.5e+01	1.5	7.3e-01	3.5e+00	4.23e+00	246
2.5e-02	5.0e+01	1.5	7.4e-01	3.5e+00	4.24e+00	246
2.5e-02	1.0e+02	1.5	7.5e-01	3.7e+00	4.45e+00	246
1.0e-02	1.0e+01	1.9	1.1e+00	3.9e+00	5.00e+00	153
1.0e-02	2.5e+01	2.5	1.0e+00	3.6e+00	4.60e+00	109
1.0e-02	5.0e+01	2.5	1.0e+00	2.3e+00	3.30e+00	109
1.0e-02	1.0e+02	2.5	1.0e+00	2.4e+00	3.40e+00	109
5.0e-03	1.0e+01	2.1	1.3e+00	2.9e+00	4.20e+00	105
5.0e-03	2.5e+01	2.8	1.3e+00	2.5e+00	3.80e+00	63
5.0e-03	5.0e+01	3.1	1.3e+00	2.4e+00	3.70e+00	59
5.0e-03	1.0e+02	3.2	1.2e+00	1.5e+00	2.70e+00	59
2.5e-03	1.0e+01	2.7	2.0e+00	2.3e+00	4.30e+00	57
2.5e-03	2.5e+01	3.0	1.4e+00	1.6e+00	3.00e+00	39
2.5e-03	5.0e+01	3.3	1.5e+00	1.5e+00	3.00e+00	35
2.5e-03	1.0e+02	3.6	1.4e+00	1.5e+00	2.90e+00	35
1.0e-03	1.0e+01	2.9	2.2e+00	1.5e+00	3.70e+00	34
1.0e-03	2.5e+01	3.1	1.8e+00	9.8e-01	2.78e+00	22
1.0e-03	5.0e+01	3.6	1.7e+00	8.7e-01	2.57e+00	19
1.0e-03	1.0e+02	3.9	1.6e+00	8.6e-01	2.46e+00	18
1.0e-04	1.0e+01	3.2	2.7e+00	5.9e-01	3.29e+00	13
1.0e-04	2.5e+01	3.4	2.0e+00	3.9e-01	2.39e+00	9

ILUPACK - SIMPLE VERSION + AMF
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-02	1.0e+01	0.9	3.9e-01	5.9e+00	6.29e+00	429
5.0e-02	2.5e+01	0.9	3.7e-01	5.2e+00	5.57e+00	429
5.0e-02	5.0e+01	0.9	3.6e-01	5.8e+00	6.16e+00	429
5.0e-02	1.0e+02	0.9	3.8e-01	5.7e+00	6.08e+00	429
2.5e-02	1.0e+01	1.5	4.8e-01	5.4e+00	5.88e+00	238
2.5e-02	2.5e+01	1.5	4.8e-01	3.6e+00	4.08e+00	235
2.5e-02	5.0e+01	1.5	4.9e-01	3.4e+00	3.89e+00	235
2.5e-02	1.0e+02	1.5	4.8e-01	3.8e+00	4.28e+00	235
1.0e-02	1.0e+01	1.8	7.4e-01	3.9e+00	4.64e+00	144
1.0e-02	2.5e+01	2.4	6.9e-01	3.7e+00	4.39e+00	103
1.0e-02	5.0e+01	2.4	7.0e-01	2.0e+00	2.70e+00	103
1.0e-02	1.0e+02	2.4	7.0e-01	2.1e+00	2.80e+00	103
5.0e-03	1.0e+01	2.0	9.9e-01	2.9e+00	3.89e+00	106
5.0e-03	2.5e+01	2.6	9.6e-01	2.2e+00	3.16e+00	56
5.0e-03	5.0e+01	3.1	8.6e-01	2.4e+00	3.26e+00	52
5.0e-03	1.0e+02	3.1	8.8e-01	2.2e+00	3.08e+00	50
2.5e-03	1.0e+01	2.5	1.6e+00	2.1e+00	3.70e+00	55
2.5e-03	2.5e+01	2.7	1.2e+00	1.4e+00	2.60e+00	36
2.5e-03	5.0e+01	3.1	1.1e+00	1.2e+00	2.30e+00	30
2.5e-03	1.0e+02	3.6	1.0e+00	1.3e+00	2.30e+00	28
1.0e-03	1.0e+01	2.8	2.6e+00	1.8e+00	4.40e+00	36
1.0e-03	2.5e+01	2.9	1.4e+00	9.5e-01	2.35e+00	22
1.0e-03	5.0e+01	3.1	1.3e+00	7.4e-01	2.04e+00	17
1.0e-03	1.0e+02	3.5	1.2e+00	6.9e-01	1.89e+00	17
1.0e-04	1.0e+01	3.1	3.0e+00	7.4e-01	3.74e+00	14
1.0e-04	2.5e+01	3.1	1.8e+00	3.5e-01	2.15e+00	9

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