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
AMF20 55.0 55.0 80.0 80.0 80.0 90.0 95.0 95.0 100.0
MMD23 47.8 47.8 73.9 73.9 73.9 87.0 95.7 100.0 100.0
RCM25 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
AMF15 46.7 46.7 66.7 66.7 66.7 66.7 86.7 93.3 93.3
MMD23 43.5 43.5 60.9 60.9 60.9 78.3 87.0 91.3 95.7
RCM25 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
AMF20 60.0 70.0 75.0 80.0 85.0 95.0 95.0 95.0 95.0
MMD23 52.2 60.9 60.9 65.2 65.2 87.0 91.3 95.7 95.7
RCM25 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
AMF20 50.0 65.0 65.0 70.0 70.0 75.0 85.0 100.0 100.0
MMD23 43.5 52.2 56.5 60.9 60.9 69.6 87.0 100.0 100.0
RCM25 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
AMF20 80.0 85.0 85.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 78.9 78.9 84.2 89.5 89.5 89.5 89.5 89.5 89.5
RCM17 88.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 92.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 75.0 80.0 85.0 90.0 95.0 95.0 100.0 100.0 100.0
MMD19 78.9 78.9 84.2 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 71.4 76.2 90.5 95.2 95.2 95.2 100.0 100.0 100.0
PQ25 68.0 68.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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
AMF20 80.0 85.0 85.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 78.9 78.9 84.2 89.5 89.5 89.5 89.5 89.5 89.5
RCM17 88.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 92.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 75.0 80.0 85.0 90.0 95.0 95.0 100.0 100.0 100.0
MMD19 78.9 78.9 84.2 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 71.4 76.2 90.5 95.2 95.2 95.2 100.0 100.0 100.0
PQ25 68.0 68.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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
AMF20 85.0 95.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 84.2 84.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 88.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 88.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 75.0 80.0 85.0 90.0 95.0 100.0 100.0 100.0 100.0
MMD19 78.9 84.2 84.2 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 71.4 85.7 95.2 95.2 95.2 100.0 100.0 100.0 100.0
PQ25 68.0 68.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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
AMF20 85.0 95.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 84.2 84.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 88.2 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 88.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 75.0 80.0 85.0 90.0 95.0 100.0 100.0 100.0 100.0
MMD19 78.9 84.2 84.2 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 71.4 85.7 95.2 95.2 95.2 100.0 100.0 100.0 100.0
PQ25 68.0 68.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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
AMF20 95.0 95.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 89.5 89.5 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 88.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 75.0 80.0 85.0 90.0 95.0 95.0 100.0 100.0 100.0
MMD19 78.9 84.2 84.2 94.7 100.0 100.0 100.0 100.0 100.0
RCM21 76.2 90.5 95.2 95.2 95.2 100.0 100.0 100.0 100.0
PQ25 68.0 72.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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
AMF20 95.0 95.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 89.5 89.5 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 88.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 75.0 80.0 85.0 90.0 95.0 95.0 100.0 100.0 100.0
MMD19 78.9 84.2 84.2 94.7 100.0 100.0 100.0 100.0 100.0
RCM21 76.2 90.5 95.2 95.2 95.2 100.0 100.0 100.0 100.0
PQ25 68.0 72.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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
AMF20 95.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 84.2 94.7 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 88.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 80.0 80.0 90.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 84.2 84.2 89.5 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 81.0 95.2 95.2 95.2 95.2 100.0 100.0 100.0 100.0
PQ25 72.0 72.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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
AMF20 95.0 95.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 84.2 94.7 100.0 100.0 100.0 100.0 100.0 100.0 100.0
RCM17 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
PQ25 80.0 88.0 92.0 96.0 96.0 100.0 100.0 100.0 100.0
ND6 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
AMF20 80.0 80.0 90.0 100.0 100.0 100.0 100.0 100.0 100.0
MMD19 84.2 84.2 89.5 100.0 100.0 100.0 100.0 100.0 100.0
RCM21 81.0 95.2 95.2 95.2 95.2 100.0 100.0 100.0 100.0
PQ25 72.0 72.0 76.0 84.0 84.0 88.0 88.0 92.0 96.0
ND12 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