Fragmented Algorithm for Construction of Adapted Structured Computational Grids Based on Inverted Beltrami Equation
Olzhas Nurkonysuly Turar, D. Akhmed-Zaki, G. S. Khakimzyanov, Beimbet Daribayev, D. Lebedev · ECMOR XVII · 2020
Summary The paper describes implementation of Language for Numerical Algorithms (LuNA), which is the system aimed at automatic generation of parallel programs for the large-scale numerical modeling, for construction of structured computational grids adapted to the field of values and gradients. This system is based on operating with data fragments and operation fragments as separate objects with their call and use order and hierarchy. As any automated system generation of parallel programs may show less efficiency comparing to straight implementation of parallelization for computational programs. But benefit of automatization is in optimization of resource spent for development both in terms of funding in human resources. So, when the time loss of automated program is not too large, i.e. in cases of comparable speed of operation automated approach is counted as effective. Grid construction method is based on solving border problem for inverted Beltrami equation. Adaptation of the grid is managed by control metric that is different from the metric of the space volume where the computations take place. The behavior of such model close to diffuse equation problems considering that metric of the domain is different from flat metric of cartesian grid. Parallelization is based on algorithm of 3D decomposition for the computational area. The equation is solved on each subdomain of the initial domain using alternating directions implicit (ADI) method in 3D. This parallel algorithm does not exactly parallelize similar ADI method for whole domain. It rather performs adaptation of whole domain as connected patches of lesser domains each of which adapts to control metric and changes border values on each iteration. Correctness of the approach is based on previous research of grid construction method where the correctness such technique for constructing of continuous adapted grids for patched domains are stated. The results and performance of computations on LuNA system were compared with straight parallel algorithm on the same machine.