Overall statistics

The following statistics is based on the number test problems that could be solved using a prescribed drop tolerance. "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, DEFAULT version, kappa=10

ILUPACK, SIMPLE version, kappa=25

ILUPACK, DEFAULT version, kappa=25

ILUPACK, SIMPLE version, kappa=50

ILUPACK, DEFAULT version, kappa=50

ILUPACK, SIMPLE version, kappa=100

ILUPACK, DEFAULT version, kappa=100

Performance statistics for circuit simulation (in tables)

ILUTP, percentage of successfully solved systems

ILUTP
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	55.0	55.0	80.0	80.0	80.0	90.0	95.0	95.0	100.0
MMD	23	47.8	47.8	73.9	73.9	73.9	87.0	95.7	100.0	100.0
RCM	25	52.0	52.0	76.0	76.0	76.0	84.0	96.0	100.0	100.0

ILUTP + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	15	46.7	46.7	66.7	66.7	66.7	66.7	86.7	93.3	93.3
MMD	23	43.5	43.5	60.9	60.9	60.9	78.3	87.0	91.3	95.7
RCM	25	40.0	40.0	56.0	56.0	56.0	68.0	88.0	92.0	96.0

IB-ILUC, percentage of successfully solved systems

IB-ILUC
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	60.0	70.0	75.0	80.0	85.0	95.0	95.0	95.0	95.0
MMD	23	52.2	60.9	60.9	65.2	65.2	87.0	91.3	95.7	95.7
RCM	25	52.0	64.0	72.0	72.0	72.0	88.0	100.0	100.0	100.0

IB-ILUC + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	50.0	65.0	65.0	70.0	70.0	75.0	85.0	100.0	100.0
MMD	23	43.5	52.2	56.5	60.9	60.9	69.6	87.0	100.0	100.0
RCM	25	40.0	52.0	60.0	60.0	64.0	72.0	96.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	80.0	85.0	85.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	78.9	78.9	84.2	89.5	89.5	89.5	89.5	89.5	89.5
RCM	17	88.2	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	92.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	75.0	80.0	85.0	90.0	95.0	95.0	100.0	100.0	100.0
MMD	19	78.9	78.9	84.2	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	71.4	76.2	90.5	95.2	95.2	95.2	100.0	100.0	100.0
PQ	25	68.0	68.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	75.0	75.0	75.0	75.0	75.0	100.0	100.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	80.0	85.0	85.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	78.9	78.9	84.2	89.5	89.5	89.5	89.5	89.5	89.5
RCM	17	88.2	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	92.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	75.0	80.0	85.0	90.0	95.0	95.0	100.0	100.0	100.0
MMD	19	78.9	78.9	84.2	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	71.4	76.2	90.5	95.2	95.2	95.2	100.0	100.0	100.0
PQ	25	68.0	68.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	75.0	75.0	75.0	75.0	75.0	100.0	100.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	85.0	95.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	84.2	84.2	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	88.2	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	88.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	83.3	83.3	83.3	83.3	83.3	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	75.0	80.0	85.0	90.0	95.0	100.0	100.0	100.0	100.0
MMD	19	78.9	84.2	84.2	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	71.4	85.7	95.2	95.2	95.2	100.0	100.0	100.0	100.0
PQ	25	68.0	68.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	75.0	75.0	75.0	83.3	100.0	100.0	100.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	85.0	95.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	84.2	84.2	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	88.2	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	88.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	83.3	83.3	83.3	83.3	83.3	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	75.0	80.0	85.0	90.0	95.0	100.0	100.0	100.0	100.0
MMD	19	78.9	84.2	84.2	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	71.4	85.7	95.2	95.2	95.2	100.0	100.0	100.0	100.0
PQ	25	68.0	68.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	75.0	75.0	75.0	83.3	100.0	100.0	100.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	95.0	95.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	89.5	89.5	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	88.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	83.3	83.3	83.3	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	75.0	80.0	85.0	90.0	95.0	95.0	100.0	100.0	100.0
MMD	19	78.9	84.2	84.2	94.7	100.0	100.0	100.0	100.0	100.0
RCM	21	76.2	90.5	95.2	95.2	95.2	100.0	100.0	100.0	100.0
PQ	25	68.0	72.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	66.7	66.7	75.0	100.0	100.0	100.0	100.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	95.0	95.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	89.5	89.5	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	88.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	83.3	83.3	83.3	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	75.0	80.0	85.0	90.0	95.0	95.0	100.0	100.0	100.0
MMD	19	78.9	84.2	84.2	94.7	100.0	100.0	100.0	100.0	100.0
RCM	21	76.2	90.5	95.2	95.2	95.2	100.0	100.0	100.0	100.0
PQ	25	68.0	72.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	66.7	66.7	75.0	100.0	100.0	100.0	100.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	95.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	84.2	94.7	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	88.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	66.7	83.3	100.0	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	80.0	80.0	90.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	84.2	84.2	89.5	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	81.0	95.2	95.2	95.2	95.2	100.0	100.0	100.0	100.0
PQ	25	72.0	72.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	66.7	66.7	91.7	100.0	100.0	100.0	100.0	100.0	100.0

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

ILUPACK
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	95.0	95.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	84.2	94.7	100.0	100.0	100.0	100.0	100.0	100.0	100.0
RCM	17	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0
PQ	25	80.0	88.0	92.0	96.0	96.0	100.0	100.0	100.0	100.0
ND	6	66.7	83.3	100.0	100.0	100.0	100.0	100.0	100.0	100.0

ILUPACK + MC64
ordering	#matrices	drop tolerance
		5e-01	2e-01	1e-01	5e-02	3e-02	1e-02	1e-03	1e-04	1e-05
AMF	20	80.0	80.0	90.0	100.0	100.0	100.0	100.0	100.0	100.0
MMD	19	84.2	84.2	89.5	100.0	100.0	100.0	100.0	100.0	100.0
RCM	21	81.0	95.2	95.2	95.2	95.2	100.0	100.0	100.0	100.0
PQ	25	72.0	72.0	76.0	84.0	84.0	88.0	88.0	92.0	96.0
ND	12	66.7	66.7	91.7	100.0	100.0	100.0	100.0	100.0	100.0

m.bollhoefer@tu-bs.de

Last modified: October 11, 2011