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 Chemical engineering (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 chemical engineering (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
AMF33 12.1 12.1 24.2 24.2 24.2 36.4 39.4 60.6 63.6
MMD33 12.1 12.1 21.2 21.2 21.2 36.4 42.4 60.6 66.7
RCM33 12.1 12.1 21.2 21.2 21.2 36.4 39.4 54.5 63.6
ILUTP + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 42.4 42.4 63.6 63.6 63.6 75.8 84.8 84.8 90.9
MMD33 42.4 42.4 69.7 69.7 69.7 75.8 84.8 84.8 90.9
RCM33 42.4 42.4 69.7 69.7 69.7 78.8 84.8 84.8 90.9

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
AMF33 12.1 15.2 21.2 21.2 21.2 21.2 21.2 21.2 21.2
MMD33 12.1 18.2 21.2 21.2 21.2 21.2 21.2 21.2 21.2
RCM33 12.1 18.2 21.2 21.2 21.2 21.2 21.2 21.2 21.2
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
AMF33 42.4 54.5 72.7 72.7 75.8 78.8 84.8 84.8 84.8
MMD33 48.5 54.5 75.8 75.8 75.8 81.8 84.8 84.8 100.0
RCM33 42.4 54.5 63.6 72.7 78.8 78.8 84.8 87.9 100.0

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
AMF33 45.5 54.5 63.6 69.7 75.8 78.8 87.9 90.9 97.0
MMD33 36.4 48.5 54.5 57.6 66.7 72.7 78.8 84.8 100.0
RCM33 48.5 63.6 72.7 81.8 84.8 90.9 100.0 100.0 100.0
PQ33 45.5 51.5 69.7 78.8 78.8 87.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 75.8 75.8 84.8 84.8 84.8 84.8 90.9 90.9 90.9
MMD33 75.8 81.8 84.8 90.9 90.9 90.9 90.9 93.9 93.9
RCM33 72.7 84.8 84.8 87.9 90.9 90.9 90.9 93.9 93.9
PQ33 72.7 75.8 84.8 84.8 90.9 90.9 100.0 100.0 100.0
ND32 75.0 75.0 78.1 81.2 84.4 84.4 90.6 90.6 90.6

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
AMF33 45.5 54.5 63.6 69.7 75.8 78.8 87.9 90.9 97.0
MMD33 36.4 48.5 54.5 57.6 66.7 72.7 78.8 84.8 100.0
RCM33 48.5 63.6 72.7 81.8 84.8 90.9 100.0 100.0 100.0
PQ33 45.5 51.5 69.7 78.8 78.8 87.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 75.8 75.8 84.8 84.8 84.8 84.8 90.9 90.9 90.9
MMD33 75.8 81.8 84.8 90.9 90.9 90.9 90.9 93.9 93.9
RCM33 72.7 84.8 84.8 87.9 90.9 90.9 90.9 93.9 93.9
PQ33 72.7 75.8 84.8 84.8 90.9 90.9 100.0 100.0 100.0
ND32 75.0 75.0 78.1 81.2 84.4 84.4 90.6 90.6 90.6

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
AMF33 45.5 54.5 63.6 69.7 75.8 78.8 90.9 90.9 100.0
MMD33 36.4 45.5 57.6 57.6 66.7 72.7 81.8 84.8 97.0
RCM33 48.5 63.6 75.8 78.8 84.8 90.9 100.0 100.0 100.0
PQ33 48.5 54.5 69.7 78.8 84.8 90.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 75.8 81.8 84.8 84.8 84.8 90.9 90.9 90.9 93.9
MMD33 78.8 84.8 84.8 90.9 90.9 90.9 93.9 93.9 97.0
RCM33 81.8 84.8 87.9 90.9 90.9 90.9 93.9 93.9 97.0
PQ33 72.7 75.8 84.8 84.8 90.9 90.9 100.0 100.0 100.0
ND32 78.1 78.1 84.4 84.4 84.4 90.6 90.6 90.6 93.8

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
AMF33 45.5 54.5 63.6 69.7 75.8 78.8 90.9 90.9 100.0
MMD33 36.4 45.5 57.6 57.6 66.7 72.7 81.8 84.8 97.0
RCM33 48.5 63.6 75.8 78.8 84.8 90.9 100.0 100.0 100.0
PQ33 48.5 54.5 69.7 78.8 84.8 90.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 75.8 81.8 84.8 84.8 84.8 90.9 90.9 90.9 93.9
MMD33 78.8 84.8 84.8 90.9 90.9 90.9 93.9 93.9 97.0
RCM33 81.8 84.8 87.9 90.9 90.9 90.9 93.9 93.9 97.0
PQ33 72.7 75.8 84.8 84.8 90.9 90.9 100.0 100.0 100.0
ND32 78.1 78.1 84.4 84.4 84.4 90.6 90.6 90.6 93.8

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
AMF33 45.5 54.5 63.6 69.7 75.8 78.8 90.9 93.9 100.0
MMD33 42.4 48.5 57.6 57.6 63.6 72.7 81.8 84.8 97.0
RCM33 48.5 63.6 72.7 81.8 84.8 90.9 100.0 100.0 100.0
PQ33 45.5 54.5 69.7 78.8 84.8 90.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 75.8 81.8 84.8 87.9 90.9 90.9 90.9 93.9 93.9
MMD33 78.8 84.8 87.9 90.9 93.9 93.9 93.9 97.0 100.0
RCM33 81.8 84.8 90.9 90.9 90.9 90.9 93.9 97.0 97.0
PQ33 72.7 75.8 84.8 84.8 87.9 90.9 100.0 100.0 100.0
ND32 78.1 81.2 84.4 84.4 87.5 90.6 90.6 93.8 93.8

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
AMF33 45.5 54.5 63.6 69.7 75.8 78.8 90.9 93.9 100.0
MMD33 42.4 48.5 57.6 57.6 63.6 72.7 81.8 84.8 97.0
RCM33 48.5 63.6 72.7 81.8 84.8 90.9 100.0 100.0 100.0
PQ33 45.5 54.5 69.7 78.8 84.8 90.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 75.8 81.8 84.8 87.9 90.9 90.9 90.9 93.9 93.9
MMD33 78.8 84.8 87.9 90.9 93.9 93.9 93.9 97.0 100.0
RCM33 81.8 84.8 90.9 90.9 90.9 90.9 93.9 97.0 97.0
PQ33 72.7 75.8 84.8 84.8 87.9 90.9 100.0 100.0 100.0
ND32 78.1 81.2 84.4 84.4 87.5 90.6 90.6 93.8 93.8

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
AMF33 48.5 54.5 63.6 69.7 75.8 78.8 90.9 93.9 100.0
MMD33 39.4 48.5 57.6 57.6 66.7 72.7 84.8 87.9 97.0
RCM33 48.5 63.6 72.7 81.8 84.8 93.9 100.0 100.0 100.0
PQ33 48.5 54.5 69.7 78.8 84.8 93.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 78.8 84.8 84.8 90.9 90.9 90.9 93.9 93.9 93.9
MMD33 78.8 84.8 87.9 90.9 93.9 93.9 97.0 100.0 100.0
RCM33 81.8 84.8 90.9 90.9 93.9 93.9 93.9 97.0 97.0
PQ33 72.7 75.8 84.8 84.8 87.9 90.9 100.0 100.0 100.0
ND32 78.1 84.4 84.4 84.4 90.6 90.6 93.8 93.8 93.8

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
AMF33 48.5 54.5 63.6 69.7 75.8 78.8 90.9 93.9 100.0
MMD33 39.4 48.5 57.6 57.6 66.7 72.7 84.8 87.9 97.0
RCM33 48.5 63.6 72.7 81.8 84.8 93.9 100.0 100.0 100.0
PQ33 48.5 54.5 69.7 78.8 84.8 93.9 100.0 100.0 100.0
ND0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF33 78.8 84.8 84.8 90.9 90.9 90.9 93.9 93.9 93.9
MMD33 78.8 84.8 87.9 90.9 93.9 93.9 97.0 100.0 100.0
RCM33 81.8 84.8 90.9 90.9 93.9 93.9 93.9 97.0 97.0
PQ33 72.7 75.8 84.8 84.8 87.9 90.9 100.0 100.0 100.0
ND32 78.1 84.4 84.4 84.4 90.6 90.6 93.8 93.8 93.8


m.bollhoefer@tu-bs.de

Last modified: October 11, 2011