Matrix para-6

matrix size	155,924
number of nonzeros	5,416,358 (34.7 per row on the average)
type	real unsymmetric matrix, right hand side provided
application area	Semiconductor device simulation
provided by	Olaf Schenk, University of Basel

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-02	1.0e+01	0.5	8.5e+01	1.1e+02	1.95e+02	339
2.5e-02	2.5e+01	0.6	1.1e+02	5.5e+00	1.16e+02	18
2.5e-02	5.0e+01	0.6	1.2e+02	5.2e+00	1.25e+02	17
2.5e-02	1.0e+02	0.6	1.2e+02	5.2e+00	1.25e+02	17
1.0e-02	1.0e+01	0.6	1.3e+02	4.6e+00	1.35e+02	15
1.0e-02	2.5e+01	0.6	2.4e+02	4.1e+00	2.44e+02	13
1.0e-02	5.0e+01	0.6	2.5e+02	3.8e+00	2.54e+02	12
1.0e-02	1.0e+02	0.6	2.5e+02	3.9e+00	2.54e+02	12
5.0e-03	1.0e+01	0.6	2.1e+02	3.9e+00	2.14e+02	12
5.0e-03	2.5e+01	0.7	4.9e+02	3.4e+00	4.93e+02	10
5.0e-03	5.0e+01	0.7	5.0e+02	3.4e+00	5.03e+02	10
5.0e-03	1.0e+02	0.7	5.0e+02	3.4e+00	5.03e+02	10
2.5e-03	1.0e+01	0.7	5.8e+02	3.4e+00	5.83e+02	10
2.5e-03	2.5e+01	0.8	7.9e+02	3.4e+00	7.93e+02	9

ILUPACK - MEDIUM VERSION + PQ + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - MEDIUM VERSION + RCM
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - MEDIUM VERSION + RCM + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

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

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

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
2.5e-02	2.5e+01	0.6	3.4e+01	5.5e+01	8.90e+01	153
2.5e-02	5.0e+01	0.6	3.3e+01	9.4e+01	1.27e+02	270
2.5e-02	1.0e+02	0.6	3.4e+01	1.2e+02	1.54e+02	341
1.0e-02	1.0e+01	0.6	3.6e+01	6.5e+00	4.25e+01	19
1.0e-02	2.5e+01	0.6	3.9e+01	6.3e+00	4.53e+01	18
1.0e-02	5.0e+01	0.6	4.0e+01	6.4e+00	4.64e+01	18
1.0e-02	1.0e+02	0.6	4.1e+01	6.5e+00	4.75e+01	18
5.0e-03	1.0e+01	0.6	4.0e+01	4.5e+00	4.45e+01	13
5.0e-03	2.5e+01	0.7	5.2e+01	4.5e+00	5.65e+01	12
5.0e-03	5.0e+01	0.7	5.3e+01	4.1e+00	5.71e+01	11
5.0e-03	1.0e+02	0.7	5.2e+01	4.1e+00	5.61e+01	11
2.5e-03	1.0e+01	0.7	5.9e+01	3.8e+00	6.28e+01	10
2.5e-03	2.5e+01	0.8	6.9e+01	3.7e+00	7.27e+01	9

ILUPACK - SIMPLE VERSION + PQ + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-04	1.0e+02	2.0	6.3e+02	2.3e+02	8.60e+02	340

ILUPACK - SIMPLE VERSION + RCM
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - SIMPLE VERSION + RCM + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - SIMPLE VERSION + MMD
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - SIMPLE VERSION + MMD + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - SIMPLE VERSION + AMF
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - SIMPLE VERSION + AMF + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUPACK - SIMPLE VERSION + Multilevel ND
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
2.5e-01	1.0e+02	1.2	1.1e+02	5.5e+01	1.65e+02	116
1.0e-01	1.0e+02	1.4	1.4e+02	2.1e+01	1.61e+02	39
5.0e-02	5.0e+01	1.3	1.2e+02	1.5e+02	2.70e+02	300
5.0e-02	1.0e+02	1.6	1.7e+02	2.2e+01	1.92e+02	37
2.5e-02	5.0e+01	1.5	1.5e+02	3.1e+01	1.81e+02	57
2.5e-02	1.0e+02	1.9	2.0e+02	1.2e+01	2.12e+02	18
1.0e-02	5.0e+01	1.8	1.8e+02	1.0e+01	1.90e+02	17
1.0e-02	1.0e+02	2.3	2.6e+02	1.0e+01	2.70e+02	14
5.0e-03	5.0e+01	2.1	2.3e+02	1.3e+01	2.43e+02	20
5.0e-03	1.0e+02	2.6	3.1e+02	1.0e+01	3.20e+02	13
2.5e-03	5.0e+01	2.3	2.7e+02	1.3e+01	2.83e+02	18
2.5e-03	1.0e+02	3.0	3.7e+02	9.6e+00	3.80e+02	11
1.0e-03	5.0e+01	2.8	3.4e+02	1.1e+01	3.51e+02	14
1.0e-03	1.0e+02	3.4	4.5e+02	9.5e+00	4.60e+02	10
1.0e-04	1.0e+02	5.0	8.0e+02	1.1e+01	8.11e+02	9

ILUPACK - SIMPLE VERSION + Multilevel ND + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-01	1.0e+01	0.3	2.7e+01	5.4e+01	8.10e+01	214
5.0e-01	2.5e+01	0.3	2.8e+01	3.2e+01	6.00e+01	122
5.0e-01	5.0e+01	0.3	2.8e+01	2.4e+01	5.20e+01	88
5.0e-01	1.0e+02	0.4	2.9e+01	2.7e+01	5.60e+01	92
2.5e-01	1.0e+01	0.4	2.8e+01	3.6e+01	6.40e+01	138
2.5e-01	2.5e+01	0.4	2.9e+01	2.4e+01	5.30e+01	87
2.5e-01	5.0e+01	0.4	2.9e+01	2.7e+01	5.60e+01	91
2.5e-01	1.0e+02	0.5	3.1e+01	2.7e+01	5.80e+01	84
1.0e-01	1.0e+01	0.4	2.9e+01	2.3e+01	5.20e+01	85
1.0e-01	2.5e+01	0.4	3.0e+01	2.7e+01	5.70e+01	91
1.0e-01	5.0e+01	0.5	3.2e+01	2.1e+01	5.30e+01	66
1.0e-01	1.0e+02	0.6	3.4e+01	1.9e+01	5.30e+01	53
5.0e-02	1.0e+01	0.5	3.1e+01	2.8e+01	5.90e+01	97
5.0e-02	2.5e+01	0.5	3.2e+01	2.2e+01	5.40e+01	71
5.0e-02	5.0e+01	0.6	3.4e+01	1.9e+01	5.30e+01	54
5.0e-02	1.0e+02	0.7	3.7e+01	1.3e+01	5.00e+01	33
2.5e-02	1.0e+01	0.5	3.3e+01	2.5e+01	5.80e+01	84
2.5e-02	2.5e+01	0.6	3.5e+01	1.6e+01	5.10e+01	48
2.5e-02	5.0e+01	0.7	3.7e+01	1.2e+01	4.90e+01	31
2.5e-02	1.0e+02	0.8	4.1e+01	1.0e+01	5.10e+01	25
1.0e-02	1.0e+01	0.6	3.6e+01	1.5e+01	5.10e+01	49
1.0e-02	2.5e+01	0.7	3.9e+01	1.1e+01	5.00e+01	29
1.0e-02	5.0e+01	0.8	4.3e+01	9.1e+00	5.21e+01	22
1.0e-02	1.0e+02	0.9	4.7e+01	8.7e+00	5.57e+01	19
5.0e-03	1.0e+01	0.7	4.0e+01	1.1e+01	5.10e+01	31
5.0e-03	2.5e+01	0.8	4.4e+01	8.5e+00	5.25e+01	22
5.0e-03	5.0e+01	0.9	4.8e+01	8.4e+00	5.64e+01	19
5.0e-03	1.0e+02	1.1	5.3e+01	7.9e+00	6.09e+01	16
2.5e-03	1.0e+01	0.8	4.5e+01	8.9e+00	5.39e+01	25
2.5e-03	2.5e+01	0.9	4.9e+01	7.4e+00	5.64e+01	18
2.5e-03	5.0e+01	1.0	5.4e+01	7.5e+00	6.15e+01	16
2.5e-03	1.0e+02	1.2	5.9e+01	6.9e+00	6.59e+01	13
1.0e-03	1.0e+01	0.9	5.2e+01	6.8e+00	5.88e+01	18
1.0e-03	2.5e+01	1.0	5.7e+01	6.3e+00	6.33e+01	14
1.0e-03	5.0e+01	1.2	6.3e+01	6.8e+00	6.98e+01	13
1.0e-03	1.0e+02	1.4	7.0e+01	6.4e+00	7.64e+01	11
1.0e-04	1.0e+01	1.3	7.7e+01	4.6e+00	8.16e+01	10
1.0e-04	2.5e+01	1.5	8.5e+01	5.1e+00	9.01e+01	9

ILUTP

ILUTP + RCM
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-01		0.2	4.6e+00	3.0e+01	3.46e+01	89
1.0e-02		0.3	5.9e+00	7.9e+01	8.49e+01	236
1.0e-03		0.8	1.0e+01	5.7e+00	1.57e+01	14
1.0e-04		1.8	3.2e+01	2.9e+00	3.49e+01	5

ILUTP + RCM + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-07		22.4	3.2e+03	6.5e+01	3.26e+03	25

ILUTP + MMD
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-02		0.4	1.8e+02	1.4e+01	1.94e+02	35
1.0e-03		0.7	1.8e+02	9.2e+00	1.89e+02	20
1.0e-04		1.4	1.9e+02	3.8e+00	1.94e+02	7

ILUTP + MMD + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUTP + AMF
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-03		4.1	5.6e+02	4.5e+01	6.05e+02	38
1.0e-04		8.0	2.0e+03	1.8e+01	2.02e+03	10
1.0e-05		13.9	4.8e+03	1.4e+01	4.81e+03	5
1.0e-06		-0.0	9.1e+03	-	-	failure

ILUTP + AMF + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUTP + Multilevel ND
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUTP + Mutilevel ND + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUC

ILUC + RCM
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
2.5e-01		0.2	7.5e+00	1.5e+02	1.58e+02	463
1.0e-01		0.3	8.6e+00	5.1e+01	5.96e+01	133
5.0e-02		0.4	9.7e+00	4.4e+01	5.37e+01	108
2.5e-02		0.6	1.1e+01	3.1e+01	4.20e+01	70
1.0e-02		0.8	1.5e+01	2.6e+01	4.10e+01	57
1.0e-03		2.4	5.5e+01	1.7e+01	7.20e+01	23
1.0e-04		7.3	4.6e+02	1.2e+01	4.72e+02	10
1.0e-05		17.8	2.0e+03	1.5e+01	2.02e+03	6

ILUC + RCM + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-01		0.2	7.7e+00	8.4e+01	9.17e+01	235
5.0e-02		0.2	8.6e+00	6.3e+01	7.16e+01	168
2.5e-02		0.3	1.0e+01	4.8e+01	5.80e+01	121
1.0e-02		0.5	1.4e+01	3.8e+01	5.20e+01	88
1.0e-03		1.6	4.2e+01	2.2e+01	6.40e+01	35
1.0e-04		4.6	2.3e+02	1.6e+01	2.46e+02	16
1.0e-05		11.8	1.4e+03	1.3e+01	1.41e+03	8

ILUC + MMD
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-01		0.3	1.9e+02	7.1e+01	2.61e+02	162
5.0e-02		0.4	1.9e+02	5.1e+01	2.41e+02	111
2.5e-02		0.6	1.8e+02	4.0e+01	2.20e+02	87
1.0e-02		0.8	1.9e+02	2.7e+01	2.17e+02	54
1.0e-03		1.7	2.1e+02	1.8e+01	2.28e+02	29
1.0e-04		3.4	2.9e+02	6.7e+00	2.97e+02	8

ILUC + MMD + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUC + AMF
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
5.0e-02		5.8	5.1e+02	3.9e+02	9.00e+02	332
2.5e-02		11.0	1.3e+03	3.0e+02	1.60e+03	169
1.0e-02		-0.0	3.0e+03	-	-	failure

ILUC + AMF + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter

ILUC + Multilevel ND
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-02		1.0	3.2e+01	2.3e+01	5.50e+01	74
1.0e-03		2.4	6.4e+01	1.4e+01	7.80e+01	29
1.0e-04		4.6	1.6e+02	7.4e+00	1.67e+02	11
1.0e-05		6.7	2.9e+02	5.2e+00	2.95e+02	6

ILUC + Multilevel ND + MC64
parameters			time [sec]
drop tol	condest	fill-in	ILU	GMRES(30)	total	iter
1.0e-02		0.4	2.6e+01	2.9e+01	5.50e+01	108
1.0e-03		1.1	3.7e+01	1.8e+01	5.50e+01	54
1.0e-04		2.2	7.5e+01	7.4e+00	8.24e+01	16
1.0e-05		3.6	1.4e+02	6.0e+00	1.46e+02	9

PARDISO

PARDISO
parameters			time [sec]
		fill-in	LU fac.	LU solve	total	iter

PARDISO + MC64
parameters		time [sec]
	fill-in	LU fac.	LU solve	total	iter
	33.0	7.3e+03	7.3e+00	7.3e+03	0

m.bollhoefer@tu-bs.de

Last modified: October 11, 2011