In this paper, we consider a general conformal mapping function with complex constant coefficients, to solve the elasticity problems for an infinite plate weakened by a curvilinear hole. Conformal was used outside and inside of a unit circle in the presence of an initial heat flowing perpendicular to the plate. The use of the complex variable method gives convenient expressions of Goursat functions in applications, it also achieves the objective rapidly. Several previous works are considered as special cases of this work. The hole takes different shapes that make this study applicable to many cases, like tunnels, caves, excavations in soil or rock, etc. Stress and strain components have been obtained and plotted to investigate their physical meanings. With the aid of a computer, shapes of holes were received, and distribution of stresses obtained.

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An overview of concerns observed in allowing for reproducibility in parallel applications that heavily depend on the three dimensional distributed memory fast Fourier transform are summarized. Suggestions for reproducibility categories for benchmark results are given. CCS CONCEPTS• Mathematics of computing → Computation of transforms;• Theory of computation → Massively parallel algorithms;• Software and its engineering → Software performance; • Hardware → Testing with distributed and parallel systems.

We present mpi4py.futures, a lightweight, asynchronous task execution framework targeting the Python programming language and using the Message Passing Interface (MPI) for interprocess communication. mpi4py.futures follows the interface of the concurrent.futures package from the Python standard library and can be used as its drop-in replacement, while allowing applications to scale over multiple compute nodes. We discuss the design, implementation, and feature set of mpi4py.futures and compare its performance to other solutions on both shared and distributed memory architectures. On a shared-memory system, we show mpi4py.futures to consistently outperform Python's concurrent.futures with speedup ratios between 1.4X and 3.7X in throughput (tasks per second) and between 1.9X and 2.9X in bandwidth. On a Cray XC40 system, we compare mpi4py.futures to Dask -a well-known Python parallel computing package. Although we note more varied results, we show mpi4py.futures to outperform Dask in most scenarios.

The fast Fourier transform (FFT) has applications in almost every frequency related studies, e.g. in image and signal processing, and radio astronomy. It is also used to solve partial differential equations used in fluid flows, density functional theory, many-body theory, and others. Three-dimensional 3 FFT has large time complexity ( 3 log 2 ). Hence, parallel algorithms are made to compute such FFTs. Popular libraries perform slab division or pencil decomposition of 3 data. None of the existing libraries have achieved perfect inverse scaling of time with ( −1 ≈ ) cores because FFT requires all-to-all communication and clusters hitherto do not have physical all-to-all connections. Dragonfly, one of the popular topologies for the interconnect, supports hierarchical connections among the components. Thus, we show that if we align the all-to-all communication of FFT with the physical connections of Dragonfly topology we will achieve a better scaling and reduce communication time.