Parallelization of a 3-Dimensional Hydrodynamics Model Using a Hybrid Method with MPI and OpenMP

Fast and Accurate Solution of Integral Formulations of Large MQS Problems Based on Hybrid OpenMP–MPI Parallelization

This paper proposes an optimal strategy to parallelize the solution of large 3D magneto-quasi-static (MQS) problems, by combining the MPI and OpenMP approaches. The studied numerical problem comes from a weak-form integral formulation of a MQS problem and is finally cast in terms of a large linear system to be solved by means of a direct method. For this purpose, two main tasks are identified: the assembly and the inversion of the matrices. The paper focuses on the optimization of the resources required for assembling the matrices, by exploiting the feature of a hybrid OpenMP–MPI approach. Specifically, the job is shared between clusters of nodes in parallel by adopting an OpenMP paradigm at the node level and a MPI one at the process level between nodes. Compared with other solutions, such as pure MPI, this hybrid parallelization optimizes the available resources, with respect to the speed, allocated memory, and the communication between nodes. These advantages are clearly observed in the case studies analyzed in this paper, coming from the study of large plasma fusion machines, such as the fusion reactor ITER. Indeed, the MQS problems associated with such applications are characterized by a huge computational cost that requires parallel computing approaches.

A Hybrid MPI-OpenMP Parallel Algorithm for the Assessment of the Multifractal Spectrum of River Networks

The possibility to create a flood wave in a river network depends on the geometric properties of the river basin. Among the models that try to forecast the Instantaneous Unit Hydrograph (IUH) of rainfall precipitation, the so-called Multifractal Instantaneous Unit Hydrograph (MIUH) rather successfully connects the multifractal properties of the river basin to the observed IUH. Such properties can be assessed through different types of analysis (fixed-size algorithm, correlation integral, fixed-mass algorithm, sandbox algorithm, and so on). The fixed-mass algorithm is the one that produces the most precise estimate of the properties of the multifractal spectrum that are relevant for the MIUH model. However, a disadvantage of this method is that it requires very long computational times to produce the best possible results. In a previous work, we proposed a parallel version of the fixed-mass algorithm, which drastically reduced the computational times almost proportionally to the number of Central Processing Unit (CPU) cores available on the computational machine by using the Message Passing Interface (MPI), which is a standard for distributed memory clusters. In the present work, we further improved the code in order to include the use of the Open Multi-Processing (OpenMP) paradigm to facilitate the execution and improve the computational speed-up on single processor, multi-core workstations, which are much more common than multi-node clusters. Moreover, the assessment of the multifractal spectrum has also been improved through a direct computation method. Currently, to the best of our knowledge, this code represents the state-of-the-art for a fast evaluation of the multifractal properties of a river basin, and it opens up a new scenario for an effective flood forecast in reasonable computational times.