Overall statistics with respect to the fill-in

The following statistics is based on the number test problems that could be solved using a prescribed fill-in factor. "Solved" in this context means that restarted GMRES(30) converged within 500 steps of iteration (using a relative tolerance of sqrt(eps)~10^-8

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 statistics for circuit simulation(real unsymmetric case)
ILUTP

ILUC

ILUPACK, SIMPLE version, kappa=10

ILUPACK, MEDIUM version, kappa=10

ILUPACK, SIMPLE version, kappa=25

ILUPACK, MEDIUM version, kappa=25

ILUPACK, SIMPLE version, kappa=50

ILUPACK, MEDIUM version, kappa=50

ILUPACK, SIMPLE version, kappa=100

ILUPACK, MEDIUM version, kappa=100

PARDISO

Performance statistics for circuit simulation(in tables)

ILUTP, percentage of successfully solved systems

ILUTP
ordering	#matrices	fill-in factor
		5e-01	1e+00	2e+00	2e+00	3e+00	4e+00	6e+00	8e+00	1e+01
AMF	15	8.0	13.0	14.0	15.0	15.0	15.0	15.0	15.0	15.0
MMD	23	15.0	21.0	22.0	23.0	23.0	23.0	23.0	23.0	23.0
RCM	25	14.0	18.0	20.0	21.0	23.0	23.0	23.0	24.0	24.0
ND	25	15.0	22.0	24.0	25.0	25.0	25.0	25.0	25.0	25.0

ILUTP + MC64
ordering	#matrices	fill-in factor
		5e-01	1e+00	2e+00	2e+00	3e+00	4e+00	6e+00	8e+00	1e+01
AMF	15	53.3	86.7	93.3	100.0	100.0	100.0	100.0	100.0	100.0
MMD	23	65.2	91.3	95.7	100.0	100.0	100.0	100.0	100.0	100.0
RCM	25	56.0	72.0	80.0	84.0	92.0	92.0	92.0	96.0	96.0
ND	25	60.0	88.0	96.0	100.0	100.0	100.0	100.0	100.0	100.0

IB-ILUC, percentage of successfully solved systems

IB-ILUC
ordering	#matrices	fill-in factor
		5e-01	1e+00	2e+00	2e+00	3e+00	4e+00	6e+00	8e+00	1e+01
AMF	20	14.0	17.0	20.0	20.0	20.0	20.0	20.0	20.0	20.0
MMD	23	17.0	23.0	23.0	23.0	23.0	23.0	23.0	23.0	23.0
RCM	25	17.0	21.0	23.0	24.0	25.0	25.0	25.0	25.0	25.0
ND	19	11.0	18.0	19.0	19.0	19.0	19.0	19.0	19.0	19.0

IB-ILUC + MC64
ordering	#matrices	fill-in factor
		5e-01	1e+00	2e+00	2e+00	3e+00	4e+00	6e+00	8e+00	1e+01
AMF	20	70.0	85.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	23	73.9	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	25	68.0	84.0	92.0	96.0	100.0	100.0	100.0	100.0	100.0
ND	19	57.9	94.7	100.0	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK, SIMPLE version, percentage of successfully solved systems, kappa= 10

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	40.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	42.1	89.5	89.5	89.5	89.5	89.5	89.5	89.5	89.5
RCM	17	11.8	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	8.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0
ND	6	116.7	333.3	333.3	333.3	333.3	333.3	333.3	333.3	333.3

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	40.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	42.1	94.7	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	9.5	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	28.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0
ND	12	75.0	166.7	166.7	166.7	166.7	166.7	166.7	166.7	166.7

ILUPACK, MEDIUM version, percentage of successfully solved systems, kappa= 10

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	27.3	86.4	95.5	95.5	95.5	95.5	95.5	95.5	95.5
MMD	16	31.2	68.8	93.8	93.8	93.8	93.8	93.8	93.8	93.8
RCM	18	5.6	83.3	94.4	94.4	94.4	94.4	94.4	94.4	94.4
PQ	22	18.2	86.4	90.9	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	40.9	86.4	95.5	95.5	100.0	100.0	100.0	100.0	100.0
MMD	22	40.9	81.8	90.9	95.5	100.0	100.0	100.0	100.0	100.0
RCM	22	9.1	86.4	95.5	95.5	95.5	95.5	100.0	100.0	100.0
PQ	22	22.7	86.4	95.5	95.5	100.0	100.0	100.0	100.0	100.0

ILUPACK, SIMPLE version, percentage of successfully solved systems, kappa= 25

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	30.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	26.3	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	11.8	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	12.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0
ND	6	100.0	333.3	333.3	333.3	333.3	333.3	333.3	333.3	333.3

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	35.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	36.8	94.7	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	9.5	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	20.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0
ND	12	75.0	158.3	166.7	166.7	166.7	166.7	166.7	166.7	166.7

ILUPACK, MEDIUM version, percentage of successfully solved systems, kappa= 25

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	22.7	86.4	95.5	95.5	95.5	95.5	95.5	95.5	95.5
MMD	16	12.5	81.2	93.8	93.8	93.8	93.8	93.8	93.8	93.8
RCM	18	5.6	83.3	94.4	94.4	94.4	94.4	94.4	94.4	94.4
PQ	22	18.2	86.4	90.9	95.5	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	36.4	81.8	90.9	95.5	100.0	100.0	100.0	100.0	100.0
MMD	22	31.8	81.8	95.5	95.5	100.0	100.0	100.0	100.0	100.0
RCM	22	9.1	81.8	90.9	95.5	95.5	100.0	100.0	100.0	100.0
PQ	22	22.7	86.4	95.5	95.5	100.0	100.0	100.0	100.0	100.0

ILUPACK, SIMPLE version, percentage of successfully solved systems, kappa= 50

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	25.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	26.3	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	11.8	88.2	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	12.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0
ND	6	83.3	300.0	333.3	333.3	333.3	333.3	333.3	333.3	333.3

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	35.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	36.8	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	9.5	90.5	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	28.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0
ND	12	58.3	166.7	166.7	166.7	166.7	166.7	166.7	166.7	166.7

ILUPACK, MEDIUM version, percentage of successfully solved systems, kappa= 50

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	18.2	77.3	95.5	95.5	95.5	95.5	95.5	95.5	95.5
MMD	16	12.5	81.2	93.8	93.8	93.8	93.8	93.8	93.8	93.8
RCM	18	5.6	72.2	94.4	94.4	94.4	94.4	94.4	94.4	94.4
PQ	22	13.6	86.4	90.9	95.5	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	31.8	86.4	95.5	95.5	100.0	100.0	100.0	100.0	100.0
MMD	22	31.8	86.4	95.5	95.5	100.0	100.0	100.0	100.0	100.0
RCM	22	9.1	77.3	90.9	95.5	95.5	95.5	95.5	100.0	100.0
PQ	22	18.2	86.4	95.5	95.5	100.0	100.0	100.0	100.0	100.0

ILUPACK, SIMPLE version, percentage of successfully solved systems, kappa= 100

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	25.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	26.3	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	5.9	82.4	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	8.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0	24.0
ND	6	83.3	300.0	333.3	333.3	333.3	333.3	333.3	333.3	333.3

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	20	35.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	36.8	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	9.5	81.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	24.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0	48.0
ND	12	66.7	166.7	166.7	166.7	166.7	166.7	166.7	166.7	166.7

ILUPACK, MEDIUM version, percentage of successfully solved systems, kappa= 100

ILUPACK
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	18.2	77.3	95.5	95.5	95.5	95.5	95.5	95.5	95.5
MMD	16	12.5	81.2	93.8	93.8	93.8	93.8	93.8	93.8	93.8
RCM	18	5.6	66.7	94.4	94.4	94.4	94.4	94.4	94.4	94.4
PQ	22	13.6	86.4	90.9	95.5	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	fill-in factor
		0.5	1.0	1.5	2.0	3.0	4.0	6.0	8.0	10.0
AMF	22	31.8	86.4	95.5	95.5	95.5	95.5	100.0	100.0	100.0
MMD	22	31.8	86.4	90.9	95.5	95.5	95.5	100.0	100.0	100.0
RCM	22	9.1	63.6	90.9	95.5	95.5	95.5	100.0	100.0	100.0
PQ	22	18.2	86.4	95.5	95.5	100.0	100.0	100.0	100.0	100.0

PARDISO, percentage of successfully solved systems

PARDISO
ordering	#matrices	fill-in factor
		5e-01	1e+00	2e+00	2e+00	3e+00	4e+00	6e+00	8e+00	1e+01
	25	0.0	1.0	8.0	12.0	19.0	22.0	24.0	24.0	25.0

PARDISO + MC64
ordering	#matrices	fill-in factor
		5e-01	1e+00	2e+00	2e+00	3e+00	4e+00	6e+00	8e+00	1e+01
	25	0.0	4.0	32.0	48.0	76.0	88.0	96.0	96.0	100.0

m.bollhoefer@tu-bs.de

Last modified: October 11, 2011