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 circuit simulation(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 circuit simulation(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
AMF15 8.0 13.0 14.0 15.0 15.0 15.0 15.0 15.0 15.0
MMD23 15.0 21.0 22.0 23.0 23.0 23.0 23.0 23.0 23.0
RCM25 14.0 18.0 20.0 21.0 23.0 23.0 23.0 24.0 24.0
ND25 15.0 22.0 24.0 25.0 25.0 25.0 25.0 25.0 25.0
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
AMF15 53.3 86.7 93.3 100.0 100.0 100.0 100.0 100.0 100.0
MMD23 65.2 91.3 95.7 100.0 100.0 100.0 100.0 100.0 100.0
RCM25 56.0 72.0 80.0 84.0 92.0 92.0 92.0 96.0 96.0
ND25 60.0 88.0 96.0 100.0 100.0 100.0 100.0 100.0 100.0

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
AMF20 14.0 17.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0
MMD23 17.0 23.0 23.0 23.0 23.0 23.0 23.0 23.0 23.0
RCM25 17.0 21.0 23.0 24.0 25.0 25.0 25.0 25.0 25.0
ND19 11.0 18.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0
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
AMF20 70.0 85.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD23 73.9 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM25 68.0 84.0 92.0 96.0 100.0 100.0 100.0 100.0 100.0
ND19 57.9 94.7 100.0 100.0 100.0 100.0 100.0 100.0 100.0

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
AMF20 40.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 42.1 89.5 89.5 89.5 89.5 89.5 89.5 89.5 89.5
RCM17 11.8 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 8.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0
ND6 116.7 333.3 333.3 333.3 333.3 333.3 333.3 333.3 333.3
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
AMF20 40.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 42.1 94.7 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 9.5 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 28.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0
ND12 75.0 166.7 166.7 166.7 166.7 166.7 166.7 166.7 166.7

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
AMF22 27.3 86.4 95.5 95.5 95.5 95.5 95.5 95.5 95.5
MMD16 31.2 68.8 93.8 93.8 93.8 93.8 93.8 93.8 93.8
RCM18 5.6 83.3 94.4 94.4 94.4 94.4 94.4 94.4 94.4
PQ22 18.2 86.4 90.9 100.0 100.0 100.0 100.0 100.0 100.0
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
AMF22 40.9 86.4 95.5 95.5 100.0 100.0 100.0 100.0 100.0
MMD22 40.9 81.8 90.9 95.5 100.0 100.0 100.0 100.0 100.0
RCM22 9.1 86.4 95.5 95.5 95.5 95.5 100.0 100.0 100.0
PQ22 22.7 86.4 95.5 95.5 100.0 100.0 100.0 100.0 100.0

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
AMF20 30.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 26.3 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 11.8 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 12.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0
ND6 100.0 333.3 333.3 333.3 333.3 333.3 333.3 333.3 333.3
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
AMF20 35.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 36.8 94.7 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 9.5 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 20.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0
ND12 75.0 158.3 166.7 166.7 166.7 166.7 166.7 166.7 166.7

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
AMF22 22.7 86.4 95.5 95.5 95.5 95.5 95.5 95.5 95.5
MMD16 12.5 81.2 93.8 93.8 93.8 93.8 93.8 93.8 93.8
RCM18 5.6 83.3 94.4 94.4 94.4 94.4 94.4 94.4 94.4
PQ22 18.2 86.4 90.9 95.5 100.0 100.0 100.0 100.0 100.0
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
AMF22 36.4 81.8 90.9 95.5 100.0 100.0 100.0 100.0 100.0
MMD22 31.8 81.8 95.5 95.5 100.0 100.0 100.0 100.0 100.0
RCM22 9.1 81.8 90.9 95.5 95.5 100.0 100.0 100.0 100.0
PQ22 22.7 86.4 95.5 95.5 100.0 100.0 100.0 100.0 100.0

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
AMF20 25.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 26.3 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 11.8 88.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 12.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0
ND6 83.3 300.0 333.3 333.3 333.3 333.3 333.3 333.3 333.3
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
AMF20 35.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 36.8 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 9.5 90.5 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 28.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0
ND12 58.3 166.7 166.7 166.7 166.7 166.7 166.7 166.7 166.7

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
AMF22 18.2 77.3 95.5 95.5 95.5 95.5 95.5 95.5 95.5
MMD16 12.5 81.2 93.8 93.8 93.8 93.8 93.8 93.8 93.8
RCM18 5.6 72.2 94.4 94.4 94.4 94.4 94.4 94.4 94.4
PQ22 13.6 86.4 90.9 95.5 100.0 100.0 100.0 100.0 100.0
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
AMF22 31.8 86.4 95.5 95.5 100.0 100.0 100.0 100.0 100.0
MMD22 31.8 86.4 95.5 95.5 100.0 100.0 100.0 100.0 100.0
RCM22 9.1 77.3 90.9 95.5 95.5 95.5 95.5 100.0 100.0
PQ22 18.2 86.4 95.5 95.5 100.0 100.0 100.0 100.0 100.0

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
AMF20 25.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 26.3 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 5.9 82.4 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 8.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0 24.0
ND6 83.3 300.0 333.3 333.3 333.3 333.3 333.3 333.3 333.3
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
AMF20 35.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 36.8 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 9.5 81.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 24.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0
ND12 66.7 166.7 166.7 166.7 166.7 166.7 166.7 166.7 166.7

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
AMF22 18.2 77.3 95.5 95.5 95.5 95.5 95.5 95.5 95.5
MMD16 12.5 81.2 93.8 93.8 93.8 93.8 93.8 93.8 93.8
RCM18 5.6 66.7 94.4 94.4 94.4 94.4 94.4 94.4 94.4
PQ22 13.6 86.4 90.9 95.5 100.0 100.0 100.0 100.0 100.0
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
AMF22 31.8 86.4 95.5 95.5 95.5 95.5 100.0 100.0 100.0
MMD22 31.8 86.4 90.9 95.5 95.5 95.5 100.0 100.0 100.0
RCM22 9.1 63.6 90.9 95.5 95.5 95.5 100.0 100.0 100.0
PQ22 18.2 86.4 95.5 95.5 100.0 100.0 100.0 100.0 100.0

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
25 0.0 1.0 8.0 12.0 19.0 22.0 24.0 24.0 25.0
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
25 0.0 4.0 32.0 48.0 76.0 88.0 96.0 96.0 100.0





m.bollhoefer@tu-bs.de

Last modified: October 11, 2011