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

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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. The quantity to be modeled is the so-called anomalous potential T. (A2)

Remove-Restore An EGM is removed and later restored: The change of summation order enables the use of multiprocessing of a sum for each order. (1)

Timing Results N – max. degree Number of processors Time (s) Summation times for EGM2008 for 26 points (at different latitude) including read overhead of coefficients.

Covariance computation, C, C P Computation of N*(N+1)/2 covariances. Time in seconds as a function of number of processors and of block-size k*k. N Processors Blocksize, k. s s s s

Solution of Equations Upper triangular part divided in blocks, collected in ”Chunks” C ij

Cholesky reduction Row-wise Inner sum over block k, Outer sum over all blocks m/b in a column of blocks of size b.

Timing of Cholesky reduction: OMP N Processors Blocksize, k

Time depends on block-size and number of working processors

MPI timing ???

Conclusion Standard software for Cholesky reduction can not be used in the general setting, where also parameters are unknowns: Summation in the reduction must be changed from positive accumulation to negative accumulation. Use of OMP and MPI makes LSC feasible even for very large number of data. Both covariance computation and Cholesky reduction becomes much faster.