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 device 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 device 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
AMF28 0.0 0.0 17.9 17.9 17.9 32.1 67.9 78.6 89.3
MMD28 3.6 3.6 32.1 32.1 32.1 71.4 71.4 89.3 100.0
RCM28 7.1 7.1 53.6 53.6 53.6 71.4 71.4 92.9 100.0
ILUTP + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 16.7
MMD6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 16.7 50.0
RCM28 0.0 0.0 7.1 7.1 7.1 17.9 28.6 39.3 57.1

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
AMF28 0.0 0.0 17.9 57.1 60.7 67.9 67.9 67.9 67.9
MMD28 0.0 21.4 46.4 64.3 71.4 71.4 71.4 89.3 89.3
RCM28 3.6 32.1 53.6 60.7 67.9 67.9 71.4 78.6 89.3
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
AMF8 12.5 12.5 12.5 12.5 25.0 37.5 50.0 50.0 75.0
MMD7 14.3 14.3 14.3 14.3 42.9 57.1 71.4 100.0 100.0
RCM28 3.6 17.9 46.4 53.6 67.9 75.0 78.6 89.3 100.0

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
AMF15 13.3 26.7 26.7 26.7 26.7 26.7 40.0 40.0 40.0
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 0.0 0.0 18.2 18.2 18.2 18.2 18.2
PQ28 25.0 35.7 46.4 46.4 78.6 82.1 100.0 100.0 100.0
ND19 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 33.3 40.0 53.3 53.3 66.7 66.7 93.3 100.0 100.0
MMD3 0.0 0.0 33.3 33.3 33.3 33.3 100.0 100.0 100.0
RCM15 26.7 40.0 53.3 73.3 73.3 80.0 86.7 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 63.2 78.9
ND22 50.0 54.5 63.6 68.2 68.2 77.3 95.5 100.0 100.0

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
AMF15 13.3 26.7 26.7 26.7 26.7 26.7 40.0 40.0 40.0
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 0.0 0.0 18.2 18.2 18.2 18.2 18.2
PQ28 25.0 35.7 46.4 46.4 78.6 82.1 100.0 100.0 100.0
ND19 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5 10.5
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 33.3 40.0 53.3 53.3 66.7 66.7 93.3 100.0 100.0
MMD3 0.0 0.0 33.3 33.3 33.3 33.3 100.0 100.0 100.0
RCM15 26.7 40.0 53.3 73.3 73.3 80.0 86.7 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 63.2 78.9
ND22 50.0 54.5 63.6 68.2 68.2 77.3 95.5 100.0 100.0

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
AMF15 26.7 26.7 26.7 26.7 26.7 26.7 40.0 40.0 40.0
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 9.1 18.2 36.4 36.4 36.4 36.4 36.4
PQ28 32.1 46.4 46.4 57.1 82.1 82.1 100.0 100.0 100.0
ND19 15.8 15.8 15.8 15.8 15.8 15.8 15.8 15.8 15.8
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 46.7 53.3 60.0 60.0 73.3 80.0 93.3 100.0 100.0
MMD3 0.0 33.3 33.3 33.3 100.0 100.0 100.0 100.0 100.0
RCM15 40.0 53.3 60.0 73.3 80.0 80.0 93.3 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 63.2 78.9
ND22 63.6 68.2 68.2 72.7 77.3 77.3 100.0 100.0 100.0

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
AMF15 26.7 26.7 26.7 26.7 26.7 26.7 40.0 40.0 40.0
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 9.1 18.2 36.4 36.4 36.4 36.4 36.4
PQ28 32.1 46.4 46.4 57.1 82.1 82.1 100.0 100.0 100.0
ND19 15.8 15.8 15.8 15.8 15.8 15.8 15.8 15.8 15.8
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 46.7 53.3 60.0 60.0 73.3 80.0 93.3 100.0 100.0
MMD3 0.0 33.3 33.3 33.3 100.0 100.0 100.0 100.0 100.0
RCM15 40.0 53.3 60.0 73.3 80.0 80.0 93.3 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 63.2 78.9
ND22 63.6 68.2 68.2 72.7 77.3 77.3 100.0 100.0 100.0

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
AMF15 26.7 26.7 26.7 26.7 26.7 26.7 40.0 40.0 40.0
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 0.0 9.1 27.3 45.5 54.5 54.5 54.5
PQ28 39.3 46.4 46.4 50.0 82.1 82.1 100.0 100.0 100.0
ND19 15.8 21.1 31.6 63.2 68.4 73.7 78.9 78.9 78.9
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 46.7 53.3 53.3 73.3 80.0 80.0 93.3 100.0 100.0
MMD3 0.0 33.3 33.3 100.0 100.0 100.0 100.0 100.0 100.0
RCM15 46.7 46.7 60.0 80.0 80.0 80.0 93.3 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 63.2 78.9
ND22 63.6 68.2 77.3 77.3 77.3 95.5 100.0 100.0 100.0

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
AMF15 26.7 26.7 26.7 26.7 26.7 26.7 40.0 40.0 40.0
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 0.0 9.1 27.3 45.5 54.5 54.5 54.5
PQ28 39.3 46.4 46.4 50.0 82.1 82.1 100.0 100.0 100.0
ND19 15.8 21.1 31.6 63.2 68.4 73.7 78.9 78.9 78.9
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 46.7 53.3 53.3 73.3 80.0 80.0 93.3 100.0 100.0
MMD3 0.0 33.3 33.3 100.0 100.0 100.0 100.0 100.0 100.0
RCM15 46.7 46.7 60.0 80.0 80.0 80.0 93.3 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 63.2 78.9
ND22 63.6 68.2 77.3 77.3 77.3 95.5 100.0 100.0 100.0

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
AMF15 26.7 33.3 33.3 33.3 33.3 40.0 53.3 53.3 53.3
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 18.2 27.3 45.5 63.6 72.7 72.7 72.7
PQ27 37.0 44.4 44.4 48.1 81.5 81.5 100.0 100.0 100.0
ND19 15.8 68.4 68.4 68.4 73.7 73.7 94.7 94.7 94.7
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 53.3 60.0 66.7 73.3 73.3 73.3 86.7 100.0 100.0
MMD3 0.0 33.3 33.3 66.7 100.0 100.0 100.0 100.0 100.0
RCM15 46.7 53.3 80.0 80.0 80.0 80.0 100.0 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 73.7 89.5
ND22 68.2 68.2 72.7 77.3 81.8 95.5 100.0 100.0 100.0

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
AMF15 26.7 33.3 33.3 33.3 33.3 40.0 53.3 53.3 53.3
MMD3 0.0 0.0 0.0 0.0 0.0 0.0 66.7 66.7 66.7
RCM11 0.0 0.0 18.2 27.3 45.5 63.6 72.7 72.7 72.7
PQ27 37.0 44.4 44.4 48.1 81.5 81.5 100.0 100.0 100.0
ND19 15.8 68.4 68.4 68.4 73.7 73.7 94.7 94.7 94.7
ILUPACK + MC64
ordering#matrices drop tolerance
5e-01 2e-01 1e-01 5e-02 3e-02 1e-02 1e-03 1e-04 1e-05
AMF15 53.3 60.0 66.7 73.3 73.3 73.3 86.7 100.0 100.0
MMD3 0.0 33.3 33.3 66.7 100.0 100.0 100.0 100.0 100.0
RCM15 46.7 53.3 80.0 80.0 80.0 80.0 100.0 100.0 100.0
PQ19 0.0 0.0 5.3 5.3 21.1 36.8 52.6 73.7 89.5
ND22 68.2 68.2 72.7 77.3 81.8 95.5 100.0 100.0 100.0


m.bollhoefer@tu-bs.de

Last modified: October 11, 2011