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.

2D PROBLEM FOR A SPHERE IN THE FRACTIONAL ORDER THEORY THERMOELASTICITY TO AXISYMMETRIC TEMPERATURE DISTRIBUTION

In the present article, we implement the fractional thermoelasticity theory to a 2D issue for a sphere whose surface is free from traction, subject to a provided axisymmetric temperature distribution of heat. The medium is supposed to be quiescent initially. A direct method is used to get a solution and the Laplace transform technique is used. Mathematical models for copper material are designed as a particular instance. Numerical results are computed with help of Mathcad software and graphically represented and the fractional-order parameter effect has been explained.

Determination of probabilistic characteristics of random values of estimates of the Lyapunov function when describing a physical process

The applied application of the Lyapunov characteristic function is determined by the properties of its estimates. Probabilistic characteristics of estimates of the Lyapunov characteristic function are described for the first time. The probabilistic characteristics of random values of estimates of the Lyapunov function are empirically estimated using statistical methods. The Matlab package has developed a model of a special device for obtaining estimates of the characteristic function by a direct method. A quasi-deterministic signal is fed to the input of the model, the instantaneous values of which are distributed according to the arcsine law, and an array of values of estimates of the Lyapunov function is obtained at the output, which is used to estimate the probabilistic characteristics of these estimates. Statistical estimation was performed by an indirect method. It is established that the values of the estimates of the Lyapunov characteristic function are distributed according to the normal law. The results of the research will be useful in engineering calculations, for example, when detecting message transmission errors in modems with a modulated characteristic function.

PENDAMPINGAN BELAJAR SISWA MELALUI KEGIATAN BIMBINGAN BELAJAR DI DESA SONGAN DALAM MEMUTUS LAJU PENYEBARAN COVID 19

ABSTRAKPenyebaran virus covid 19 yang melanda dunia harus mengubah paradigma pendidikan yang sebelumnya di laksanakan secara tatap muka di sekolah berubah harus belajar secara mandiri dirumah. Tujuan belajar dirumah adalah untuk membatasi laju dan mencegah perkembangan virus covid 19. Kegiatan proses belajar di rumah memunculkan berbagai persoalan bagi anak-anak maupun orang tua, beberapa pelajaran yang harus diselesaikan oleh anak-anak tidak bisa dipahami secara baik. Harapan- anak-anak bisa dibantu belajar oleh orang tuanya masing-masing juga mengalami kendala akibat kurang pahamanya orang tua terhadap materi pembelajaran yang harus diselesaikan oleh anak-anak selama belajar di rumah. Masalah yang dihadapi oleh anak-anak maupun orang tua tim pecahkan dengan memberikan solusi melakukan pendampingan belajar dirumah. Tujuan dilaksanakan pendampingan belajar dirumah ialah untuk membantu anak-anak memahami materi serta membantu menyelesaikan tugas-tugas yang diberikan oleh gurunya untuk diselesaikan dirumah selama pembelajaran di lakukan dirumah. Pendampingan belajar dirumah disusun dengan metode secara langsung dilakukan ke rumah-rumah anak-anak yang berada di wilayah desa songan untuk memberiakan bantuan pembelajaran tambahan pada materi-materi yang tidak bisa di pahami oleh anak-anak. Pegabdian masyarakat berupa pendampingan belajar di rumah telah memberikan kontribusi yang positif kepada anak-anak yang berada di wilayah desa songan. Anak-anak maupun orang tuanya yang didampingi belajar oleh tim pegabdian sangat senang dengan ada kegiatan seperti ini serta merasa terbantu untuk memahami materi yang tidak bisa di pahami secara mandiri dirumah. Kata Kunci: sekolah dasar; pendampingan belajar;covid 19 ABSTRACTCovid-19 pandemic has drastically changed the education paradigm from face-to-face interaction at school to be learning independently at home. Learning at home is aimed at restricting the spread and rate of the Covid-19 virus. Learning at home has caused various problems for the students and parents. Some subjects could not be understood well by the students. The hope of the students being assisted by their parents could not also be realized since the parents did not understand the learning materials that should be learned by the students at home. This problem was overcome by the team with learning assistance at home. The goal of learning assistance at home was assisting the students to understand learning materials and finishing the assignments from the teachers during learning from home. Learning assistance at home was conducted with a direct method to be conducted at home in Songan Village to support additional learning sessions for the subjects that are not understood yet. This community service in form of learning assistance has positively contributed to the students in Songan Village. Both the students and parents were happy to get this learning assistance since they were helped to understand the learning materials from learning at home independently. Keywords: elementary school; learning assistance; covid-19

Organic Photoredox Catalyzed Direct Hydroamination of Ynamides with Azoles

Disclosed herein is a novel photoinduced selective hydroamination of ynamides with nitrogen heteroaromatic nucleophiles. By using an organocatalytic photoredox system, a direct method to construct a diverse of (Z)-α-azole enamides from ynamides and pyrazoles, as well as triazoles, benzotriazoles, indazoles, and tetrazoles, is developed, thus providing a concise route to heterocyclic motifs common in medicinal agents. Based on the mechanistic studies, the hydroamination is postulated to operate via a mechanism in which the single-electron oxidation of ynamide and the intermediacy of an alkyne radical cation, is responsible for the observed reactivity.

On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations

Multistaged crystallization systems are used in the production of many chemicals. In this article, employing the population balance framework, we develop a model for a column crystallizer where particle agglomeration is a significant growth mechanism. The main part of the model can be reduced to a system of integrodifferential equations (IDEs) of the Volterra type. To solve this system simultaneously, we examine two numerical schemes that yield a direct method of solution and an implicit Runge–Kutta type method. Our numerical experiments show that the extension of a Hermite predictor–corrector method originally advanced in Khanh (1994) for a single IDE is effective in solving our model. The numerical method is presented for a generalization of the model which can be used to study and simulate a number of possible operating profiles of the column.