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 chemical engineering (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 chemical engineering (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	33	14.0	19.0	22.0	24.0	27.0	28.0	30.0	31.0	32.0
MMD	33	17.0	21.0	25.0	28.0	28.0	30.0	33.0	33.0	33.0
RCM	33	15.0	23.0	25.0	28.0	28.0	31.0	33.0	33.0	33.0
ND	33	17.0	20.0	26.0	28.0	29.0	32.0	33.0	33.0	33.0

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	33	42.4	57.6	66.7	72.7	81.8	84.8	90.9	93.9	97.0
MMD	33	51.5	63.6	75.8	84.8	84.8	90.9	100.0	100.0	100.0
RCM	33	45.5	69.7	75.8	84.8	84.8	93.9	100.0	100.0	100.0
ND	33	51.5	60.6	78.8	84.8	87.9	97.0	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	33	16.0	19.0	25.0	25.0	27.0	27.0	28.0	28.0	28.0
MMD	33	18.0	22.0	27.0	28.0	28.0	33.0	33.0	33.0	33.0
RCM	33	14.0	22.0	24.0	28.0	29.0	32.0	33.0	33.0	33.0
ND	33	17.0	20.0	26.0	28.0	32.0	33.0	33.0	33.0	33.0

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	33	48.5	57.6	75.8	75.8	81.8	81.8	84.8	84.8	84.8
MMD	33	54.5	66.7	81.8	84.8	84.8	100.0	100.0	100.0	100.0
RCM	33	42.4	66.7	72.7	84.8	87.9	97.0	100.0	100.0	100.0
ND	33	51.5	60.6	78.8	84.8	97.0	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	33	9.1	66.7	75.8	87.9	90.9	93.9	97.0	97.0	97.0
MMD	33	9.1	66.7	75.8	81.8	90.9	90.9	97.0	97.0	100.0
RCM	33	9.1	63.6	75.8	84.8	90.9	93.9	100.0	100.0	100.0
PQ	33	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
ND	0	300.0	2200.0	2300.0	2300.0	2500.0	2500.0	2700.0	2700.0	2700.0

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	33	36.4	78.8	84.8	87.9	90.9	90.9	90.9	90.9	90.9
MMD	33	45.5	78.8	84.8	84.8	90.9	90.9	90.9	90.9	90.9
RCM	33	27.3	72.7	84.8	90.9	90.9	90.9	90.9	90.9	90.9
PQ	33	33.3	63.6	81.8	87.9	87.9	87.9	87.9	87.9	87.9
ND	32	40.6	81.2	87.5	93.8	93.8	93.8	93.8	93.8	93.8

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	28	10.7	78.6	82.1	82.1	89.3	89.3	96.4	96.4	96.4
MMD	2	0.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	33	9.1	69.7	84.8	90.9	90.9	97.0	97.0	100.0	100.0
PQ	33	3.0	66.7	81.8	90.9	90.9	93.9	97.0	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	33	39.4	78.8	84.8	90.9	90.9	90.9	90.9	90.9	90.9
MMD	33	51.5	78.8	90.9	90.9	90.9	90.9	93.9	93.9	93.9
RCM	33	27.3	72.7	87.9	87.9	90.9	90.9	93.9	93.9	93.9
PQ	33	15.2	75.8	87.9	90.9	93.9	93.9	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	33	9.1	60.6	75.8	87.9	90.9	90.9	97.0	97.0	97.0
MMD	33	9.1	57.6	75.8	84.8	87.9	87.9	93.9	97.0	97.0
RCM	33	9.1	60.6	75.8	84.8	90.9	90.9	97.0	100.0	100.0
PQ	33	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
ND	0	300.0	2000.0	2300.0	2500.0	2500.0	2500.0	2800.0	2800.0	2800.0

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	33	36.4	75.8	84.8	87.9	90.9	90.9	93.9	93.9	93.9
MMD	33	45.5	78.8	84.8	84.8	90.9	90.9	93.9	93.9	93.9
RCM	33	15.2	69.7	81.8	87.9	90.9	90.9	93.9	93.9	93.9
PQ	33	30.3	63.6	72.7	87.9	87.9	87.9	90.9	90.9	90.9
ND	32	43.8	81.2	87.5	93.8	93.8	93.8	96.9	96.9	96.9

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	28	10.7	71.4	82.1	89.3	89.3	89.3	100.0	100.0	100.0
MMD	2	0.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	33	9.1	63.6	84.8	90.9	90.9	93.9	97.0	100.0	100.0
PQ	33	3.0	60.6	78.8	90.9	90.9	90.9	97.0	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	33	42.4	78.8	84.8	90.9	90.9	90.9	93.9	93.9	93.9
MMD	33	48.5	78.8	87.9	90.9	90.9	93.9	93.9	97.0	97.0
RCM	33	24.2	66.7	84.8	90.9	90.9	90.9	93.9	93.9	97.0
PQ	33	15.2	69.7	87.9	90.9	90.9	97.0	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	33	9.1	60.6	75.8	84.8	90.9	93.9	97.0	100.0	100.0
MMD	33	9.1	57.6	75.8	84.8	87.9	87.9	93.9	97.0	97.0
RCM	33	9.1	57.6	69.7	81.8	87.9	87.9	93.9	97.0	97.0
PQ	33	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
ND	0	300.0	2000.0	2300.0	2500.0	2500.0	2600.0	2700.0	2800.0	2800.0

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	33	27.3	69.7	81.8	87.9	90.9	90.9	93.9	93.9	93.9
MMD	33	33.3	72.7	81.8	84.8	90.9	90.9	93.9	93.9	93.9
RCM	33	15.2	63.6	78.8	87.9	90.9	90.9	93.9	93.9	93.9
PQ	33	21.2	60.6	69.7	84.8	87.9	87.9	90.9	90.9	90.9
ND	32	34.4	75.0	87.5	93.8	93.8	93.8	96.9	96.9	96.9

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	28	10.7	71.4	82.1	89.3	89.3	92.9	96.4	100.0	100.0
MMD	2	0.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	33	9.1	60.6	78.8	90.9	90.9	97.0	100.0	100.0	100.0
PQ	33	3.0	57.6	78.8	87.9	90.9	93.9	97.0	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	33	33.3	72.7	84.8	90.9	90.9	90.9	93.9	93.9	93.9
MMD	33	36.4	75.8	84.8	90.9	90.9	93.9	93.9	97.0	97.0
RCM	33	15.2	63.6	78.8	90.9	90.9	90.9	93.9	97.0	97.0
PQ	33	15.2	69.7	87.9	90.9	90.9	93.9	97.0	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	33	9.1	57.6	75.8	87.9	90.9	93.9	97.0	100.0	100.0
MMD	33	9.1	57.6	75.8	87.9	87.9	87.9	93.9	93.9	97.0
RCM	33	9.1	57.6	69.7	78.8	87.9	87.9	93.9	97.0	97.0
PQ	33	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
ND	0	300.0	1900.0	2300.0	2500.0	2500.0	2600.0	2700.0	2800.0	2800.0

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	33	21.2	66.7	81.8	84.8	90.9	90.9	93.9	93.9	93.9
MMD	33	33.3	66.7	81.8	84.8	90.9	90.9	93.9	93.9	93.9
RCM	33	12.1	54.5	75.8	81.8	90.9	93.9	93.9	93.9	93.9
PQ	33	21.2	42.4	66.7	84.8	87.9	87.9	90.9	90.9	90.9
ND	32	21.9	75.0	84.4	93.8	93.8	93.8	96.9	96.9	96.9

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	28	10.7	67.9	82.1	89.3	89.3	92.9	96.4	100.0	100.0
MMD	2	0.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	33	9.1	60.6	78.8	87.9	90.9	93.9	97.0	100.0	100.0
PQ	33	3.0	57.6	78.8	87.9	90.9	93.9	97.0	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	33	21.2	72.7	81.8	90.9	90.9	90.9	93.9	93.9	93.9
MMD	33	33.3	75.8	81.8	87.9	90.9	93.9	93.9	97.0	97.0
RCM	33	12.1	51.5	75.8	84.8	90.9	93.9	93.9	97.0	97.0
PQ	33	15.2	66.7	87.9	90.9	90.9	93.9	97.0	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
	33	0.0	0.0	0.0	0.0	3.0	6.0	11.0	24.0	29.0

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
	33	0.0	0.0	0.0	0.0	9.1	18.2	33.3	72.7	87.9

m.bollhoefer@tu-bs.de

Last modified: October 11, 2011