Recent Progress on ISAT

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 104ms • 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 ms • 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 ms • 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 ms (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 ms • 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

Recent Progress on ISAT

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