Wyniki 1-1 spośród 1 dla zapytania: authorDesc:"Marek MACHACZEK"

Parallel computing of two-parameter bifurcation diagrams of an electric arc model with chaotic dynamics using Nvidia CUDA and OpenMP technologies DOI:10.15199/48.2019.03.31

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This paper presents two-parameter bifurcation diagrams for a simple electric arc model. The bifurcation diagrams are understood as changes in the oscillatory solutions when two parameters of the analyzed electric arc model vary simultaneously. The goal is to obtain high resolution color diagrams showing various oscillatory and chaotic responses. However, obtaining such two-parameter diagrams requires solving the underlying system of ordinary differential equations (ODEs) many hundreds of thousands (or millions) of times. In each solution, in addition to solving the system of ODEs, it is necessary to find the local maxima, identify period of oscillation, or determine that the solution is chaotic or unstable. The final graphical representation of the identified solutions is the bifurcation diagram. Such a process of solving ODEs, identifying the type of response (i.e. period-n, chaotic or unstable) would be very time and memory consuming for large size of the two-parameter matrix values and, for those reasons, its sequential execution would not be obtainable in practice. The answer to this problem is the use of parallel programming. Parallel programming is an increasingly popular way of solving complicated problems. Parallel designed and implemented program code is characterized by a better use of resources and shorter computation time. Parallelization usually aims to shorten computation time by using more computing units, e.g. multiple cores and graphical processing units (GPUs). Many calculation problems have a sequential nature, that is, instructions are to be executed one by one and the next instruction depends on the previous one. Such difficulties are a serious limitation for the possibility of parallelizing the code. The code parallelization process can be further complicated by the specific hardware architecture, for example the GPU. Another limiting factor, when using a GPU, may be the amount of available memory. [...]

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