1 / 11

Multi-Processing Least Squares Collocation: Applications to Gravity Field Analysis.

Multi-Processing Least Squares Collocation: Applications to Gravity Field Analysis. Kaas . E., B. Sørensen , C. C. Tscherning, M. Veicherts. Introduction. LSC is used for gravity field modeling. This includes the determination of parameters and the estimation of errors.

gizi
Download Presentation

Multi-Processing Least Squares Collocation: Applications to Gravity Field Analysis.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multi-Processing Least Squares Collocation: Applications to Gravity Field Analysis. Kaas. E., B. Sørensen, C. C. Tscherning, M. Veicherts

  2. Introduction • LSC is used for gravity field modeling. • This includes the determination of parameters and the estimation of errors. • The quantity to be modeled is the so-called anomalous potential T.

  3. Remove-Restore • An EGM is removed and laterrestored: • The change of summationorder enables the use of multiprocessing of a sum for eachorder.

  4. Timing Results Summation times for EGM2008 for 26 points (at different latitude) including read overhead of coefficients.

  5. Covariancecomputation, C, CP Computation of N*(N+1)/2 covariances. Time in seconds as a function of number of processors and of block-size k*k. N 37971 22464 22464 22464 Processors 22 22 4 4 Blocksize, k. s sss 05 8486 32044 31341 10 3737 1101 3703 4784 15 4623 1268 3159 4430 20 3547 895 2847 3851 25 3600 1047 2974 3694 30 3621 1031 3101 3804

  6. Solution of EquationsUpper triangular part divided in blocks, collected in ”Chunks” Cij

  7. CholeskyreductionRow-wise Inner sum over block k, Outer sum over all blocksm/b in a column of blocks of size b.

  8. Timing of Choleskyreduction: OMP N 37971 22464 22464 22464 Processors 22 22 4 4 Blocksize, k. 05 369 5157 1698 10 440 136 421 639 15 966 208 419 612 20 1013 238 391 591 25 1307 346 538 755 30 1542 411 668 1060

  9. Time depends on block-size and number of working processors

  10. MPI timing ???

  11. Conclusion Standard software for Choleskyreductioncan not beused in the general setting, wherealso parameters areunknowns: Summation in the reduction must bechanged from positive accumulation to negative accumulation. Use of OMP and MPI makes LSC feasibleeven for very large number of data. Bothcovariancecomputation and Choleskyreductionbecomesmuch faster.

More Related