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
AMF33 14.0 19.0 22.0 24.0 27.0 28.0 30.0 31.0 32.0
MMD33 17.0 21.0 25.0 28.0 28.0 30.0 33.0 33.0 33.0
RCM33 15.0 23.0 25.0 28.0 28.0 31.0 33.0 33.0 33.0
ND33 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
AMF33 42.4 57.6 66.7 72.7 81.8 84.8 90.9 93.9 97.0
MMD33 51.5 63.6 75.8 84.8 84.8 90.9 100.0 100.0 100.0
RCM33 45.5 69.7 75.8 84.8 84.8 93.9 100.0 100.0 100.0
ND33 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
AMF33 16.0 19.0 25.0 25.0 27.0 27.0 28.0 28.0 28.0
MMD33 18.0 22.0 27.0 28.0 28.0 33.0 33.0 33.0 33.0
RCM33 14.0 22.0 24.0 28.0 29.0 32.0 33.0 33.0 33.0
ND33 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
AMF33 48.5 57.6 75.8 75.8 81.8 81.8 84.8 84.8 84.8
MMD33 54.5 66.7 81.8 84.8 84.8 100.0 100.0 100.0 100.0
RCM33 42.4 66.7 72.7 84.8 87.9 97.0 100.0 100.0 100.0
ND33 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
AMF33 9.1 66.7 75.8 87.9 90.9 93.9 97.0 97.0 97.0
MMD33 9.1 66.7 75.8 81.8 90.9 90.9 97.0 97.0 100.0
RCM33 9.1 63.6 75.8 84.8 90.9 93.9 100.0 100.0 100.0
PQ33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ND0 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
AMF33 36.4 78.8 84.8 87.9 90.9 90.9 90.9 90.9 90.9
MMD33 45.5 78.8 84.8 84.8 90.9 90.9 90.9 90.9 90.9
RCM33 27.3 72.7 84.8 90.9 90.9 90.9 90.9 90.9 90.9
PQ33 33.3 63.6 81.8 87.9 87.9 87.9 87.9 87.9 87.9
ND32 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
AMF28 10.7 78.6 82.1 82.1 89.3 89.3 96.4 96.4 96.4
MMD2 0.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM33 9.1 69.7 84.8 90.9 90.9 97.0 97.0 100.0 100.0
PQ33 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
AMF33 39.4 78.8 84.8 90.9 90.9 90.9 90.9 90.9 90.9
MMD33 51.5 78.8 90.9 90.9 90.9 90.9 93.9 93.9 93.9
RCM33 27.3 72.7 87.9 87.9 90.9 90.9 93.9 93.9 93.9
PQ33 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
AMF33 9.1 60.6 75.8 87.9 90.9 90.9 97.0 97.0 97.0
MMD33 9.1 57.6 75.8 84.8 87.9 87.9 93.9 97.0 97.0
RCM33 9.1 60.6 75.8 84.8 90.9 90.9 97.0 100.0 100.0
PQ33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ND0 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
AMF33 36.4 75.8 84.8 87.9 90.9 90.9 93.9 93.9 93.9
MMD33 45.5 78.8 84.8 84.8 90.9 90.9 93.9 93.9 93.9
RCM33 15.2 69.7 81.8 87.9 90.9 90.9 93.9 93.9 93.9
PQ33 30.3 63.6 72.7 87.9 87.9 87.9 90.9 90.9 90.9
ND32 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
AMF28 10.7 71.4 82.1 89.3 89.3 89.3 100.0 100.0 100.0
MMD2 0.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM33 9.1 63.6 84.8 90.9 90.9 93.9 97.0 100.0 100.0
PQ33 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
AMF33 42.4 78.8 84.8 90.9 90.9 90.9 93.9 93.9 93.9
MMD33 48.5 78.8 87.9 90.9 90.9 93.9 93.9 97.0 97.0
RCM33 24.2 66.7 84.8 90.9 90.9 90.9 93.9 93.9 97.0
PQ33 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
AMF33 9.1 60.6 75.8 84.8 90.9 93.9 97.0 100.0 100.0
MMD33 9.1 57.6 75.8 84.8 87.9 87.9 93.9 97.0 97.0
RCM33 9.1 57.6 69.7 81.8 87.9 87.9 93.9 97.0 97.0
PQ33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ND0 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
AMF33 27.3 69.7 81.8 87.9 90.9 90.9 93.9 93.9 93.9
MMD33 33.3 72.7 81.8 84.8 90.9 90.9 93.9 93.9 93.9
RCM33 15.2 63.6 78.8 87.9 90.9 90.9 93.9 93.9 93.9
PQ33 21.2 60.6 69.7 84.8 87.9 87.9 90.9 90.9 90.9
ND32 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
AMF28 10.7 71.4 82.1 89.3 89.3 92.9 96.4 100.0 100.0
MMD2 0.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM33 9.1 60.6 78.8 90.9 90.9 97.0 100.0 100.0 100.0
PQ33 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
AMF33 33.3 72.7 84.8 90.9 90.9 90.9 93.9 93.9 93.9
MMD33 36.4 75.8 84.8 90.9 90.9 93.9 93.9 97.0 97.0
RCM33 15.2 63.6 78.8 90.9 90.9 90.9 93.9 97.0 97.0
PQ33 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
AMF33 9.1 57.6 75.8 87.9 90.9 93.9 97.0 100.0 100.0
MMD33 9.1 57.6 75.8 87.9 87.9 87.9 93.9 93.9 97.0
RCM33 9.1 57.6 69.7 78.8 87.9 87.9 93.9 97.0 97.0
PQ33 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ND0 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
AMF33 21.2 66.7 81.8 84.8 90.9 90.9 93.9 93.9 93.9
MMD33 33.3 66.7 81.8 84.8 90.9 90.9 93.9 93.9 93.9
RCM33 12.1 54.5 75.8 81.8 90.9 93.9 93.9 93.9 93.9
PQ33 21.2 42.4 66.7 84.8 87.9 87.9 90.9 90.9 90.9
ND32 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
AMF28 10.7 67.9 82.1 89.3 89.3 92.9 96.4 100.0 100.0
MMD2 0.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM33 9.1 60.6 78.8 87.9 90.9 93.9 97.0 100.0 100.0
PQ33 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
AMF33 21.2 72.7 81.8 90.9 90.9 90.9 93.9 93.9 93.9
MMD33 33.3 75.8 81.8 87.9 90.9 93.9 93.9 97.0 97.0
RCM33 12.1 51.5 75.8 84.8 90.9 93.9 93.9 97.0 97.0
PQ33 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