Speaker
Prof.
Neki Frasheri
(Polytechnic University of Tirana, Faculty of Information Technology)
Description
In the paper there is presented a summary of results obtained for the parallelization of 3D gravity inversion using the principle of algorithm CLEAN [Hogborn 1974], undertaken in framework o f FP7 project HP-SEE. The problem is “ill posed” with the definition of [Hadamard 1902].
The core of our algorithm consists in cross-calculation of the effect of 3D array of underground nodes to each of 2D array ground surface points. The process is iterative, updating at each iteration the mass density of one node with a predefined step in order to decrease of the least squares error. The volume of calculations for each iteration was calculated of the order O (N^5). The number of iterations to obtain the same anomalous body resulted of the order O (N^3), leading to an order of calculations O (N^8).
Experiments were carried out in two HPC systems – the HPCG system of IICT-BAS in Sofia, Bulgaria, and in the SGE system of NIIFI at University of Pécs, Hungary, using both OpenMP and MPI. Obtained results confirmed the order of calculations of O (N^8). The absolute user-time and wall-time was obtained. For moderate sized models with geosection 4000m*4000m*2000m using 3D arrays of 101*101*51 nodes, using up to 1,000 parallel cores, the run-time reached the level of 100,000 seconds (27 hours).
Tests with models and field data resulted with clear mass density contrasts between the anomalous bodies and the medium where they were situated, in the same way as in real geological structures. Tests with multi-bodies geosections indicated the tendency of the algorithm to converge towards single body solutions.
MPI tests carried out in HPCG system of IICT-BAS showed a systematic time overhead when the number of parallel processes increased from 8 to 32. Hypothesizing that this was caused because of inter-process communication between computer nodes, a prediction of potential run-time in multi-cluster MPI grid platforms was undertaken, taking into consideration the relative low bandwidth of campus and metropolitan links (compared with the bandwidth of the BUS connecting cores of a computer node). The extrapolation of data led to the hypothesis that the increase in cores using multi-cluster grids may not result in reduction of the run-time.
Primary author
Prof.
Neki Frasheri
(Polytechnic University of Tirana, Faculty of Information Technology)
Co-author
Prof.
Betim Cico
(Polytechnic University of Tirana)
