Recent Progress on ISAT

Stephen B. Pope

January 25, 2007

Research Group Meetings

• Practice talks– e.g. for upcoming Combustion Institute

meeting

• Report and discussion of recent research

In Situ Adaptive Tabulation

• Particle methods– 1010 particle steps– Reaction sub-step: direct integration 104 s– 108 s = 3.2 years– X 1,000 speed-up -> 28 hrs

• ISAT– Tabulate results of ODE integration

ISAT-CK 5.1• Primary retrieve

– BT, MRU, MFU

• Secondary retrieve– EBT in affine space – can afford to be complete

• Grow– EOA/EOI– EBT

• Add– EOI initialized to exclude existing points

Very Recent Additions

• de_nearby– Location (x) of direct evaluation may be

slightly different from the query location– Needed for ICE-PIC/ISAT

• “Slow progress”– Query time > DE time– Reduce growing– Worst case: query time = 2 x DE time

Preliminary Testing of ISAT-CK 5.1

• Systematic testing to be performed by Liuyan

• Study performance as function of parameters– Error tolerance– Available storage

Test YF: varying error tolerance

• Skeletal mechanism (16 species)– CPU for DI =5,000 s

• Premixed

• Storage = 1.2 Gbytes

• Idites=1000 (affects performance)

• Q=107

• Etol=2-p, p=1,2,…,32

CDF of error for etol=1.2e-4

Test YF: observations

• Error well controlled down to 1e-8: confirmed that errors due to ODE

• Timing affected by error testing

• Speed-up on table filling

Test YH: varying number of leaves

• Skeletal mechanism (16 species)– CPU for DI =5,000 s

• Premixed

• Q=107

• Etol=10-4

• Leaves = 16, 32, 64,…,2048.

Test YH: observations

• As storage decreases, query time tends to DE time

• “Slow progress” avoids excessive CPU time– “slow progress” if query time > DE time– Ret_frac set to ½– Grow_frac set to ½– EOIs not shrunk

Test YA: varying error tolerance

• GRI 3.0 mechanism (53 species)– CPU for DI =80,000 s (x16 cf skeletal)

• Premixed

• Storage = 1.2 Gbytes

• Idites=1000 (affects performance)

• Q=108

• Etol=2-p, p=1,2,…,19

Test YA: Observations

• Error well controlled

• Even for smallest etol, retrieves dominate in the end; but it takes longer to reach retrieving asymptote

Test K: Dim. Of Affine Space

• Skeletal mechanism (16 species)

• Premixed

• Storage = 1.0 Gbytes

• Idites=1000 (affects performance)

• Q=1e7

• Etol=1e-3

• Affine space, na=1,2,3,…15

Test M: Pair Cover

• Skeletal mechanism (16 species)• Premixed• Storage = 2.5 Gbytes• Idites=1000 (affects performance)• Q=1e7• Etol=1e-4• Pair_cover: type of ellipsoid used to cover two

other ellipsoids (in EBT)– 1 – spheroid (no shrinking)– 2 – ellipsoid (covariance algorithm)– 3 – ellipsoid (iterative algorithm)– 4 – spheroid (with shrinking)

Test YJ: storage and etol

• Skeletal mechanism (16 species)

• Premixed

• Idites=10,000 Q=1e7

• Etol = 4-p = 1, ¼, 1/16,…,1.5e-5

• Leaves = 4q = 16, 64, 256,…,16,384

Test YI: varying etol

• Skeletal mechanism (16 species)– CPU for DI =5e3 s

• Non-premixed, variable time step

• Idites=10,000 Q=1e8

• Storage = 1.2 Gbytes

• etola = 1, 1/2,...3e-5

Future Plans: ISATAB

• Single precision for ellipsoids

• x2f_mpi

• ISAT/ANN

Future Plans: ISAT-CK

• ICE-PIC

• CEQ in place of Stanjan

• ADIFOR for Jacobians

• LP for realizability

• Conservation correction for sensitivity matrix

Future Plans: papers

• Pope (2007) – new algorithms

• Lu & Pope (2007) – performance of ISAT

• Lu, Lantz, Ren, Pope (2007) – x2f_mpi

• Ren & Pope (2007) – ICE-PIC/ISAT