A direct method for accurate solution and gradient computations for elliptic interface problems

2018 ◽  
Vol 80 (3) ◽  
pp. 709-740 ◽  
Author(s):  
Xiaohong Chen ◽  
Xiufang Feng ◽  
Zhilin Li
Keyword(s):  
Direct Method ◽  
Accurate Solution ◽  
Interface Problems ◽  
Elliptic Interface Problems ◽  
A Direct Method

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

2022 ◽  
Vol 12 (2) ◽  
pp. 627
Author(s):  
Salvatore Ventre ◽  
Francesca Cau ◽  
Andrea Chiariello ◽  
Gaspare Giovinco ◽  
Antonio Maffucci ◽  
...  
Keyword(s):  
Fusion Reactor ◽  
Direct Method ◽  
Computational Cost ◽  
Weak Form ◽  
Accurate Solution ◽  
Plasma Fusion ◽  
Hybrid Parallelization ◽  
Large Linear System ◽  
A Direct Method ◽  
Process Level

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 DIRECT METHOD OF OPERATIONAL CALCULUS (I)

1982 ◽  
Vol 2 (4) ◽  
pp. 389-402 ◽  
Author(s):  
Lianrong Qiu
Keyword(s):  
Direct Method ◽  
Operational Calculus ◽  
Calculus I ◽  
A Direct Method

A Direct Method of Preparation of Diazirine

1962 ◽  
Vol 84 (6) ◽  
pp. 1063-1064 ◽  
Author(s):  
W. H. Graham
Keyword(s):  
Direct Method ◽  
A Direct Method

scholarly journals Plastic waste to fuels by hydrocracking at mild conditions

2021 ◽  
Vol 7 (17) ◽  
pp. eabf8283
Author(s):  
Sibao Liu ◽  
Pavel A. Kots ◽  
Brandon C. Vance ◽  
Andrew Danielson ◽  
Dionisios G. Vlachos
Keyword(s):  
Direct Method ◽  
Acid Sites ◽  
Liquid Fuels ◽  
High Yield ◽  
Tandem Catalysis ◽  
Hy Zeolite ◽  
Environmental Threat ◽  
Single Use ◽  
Initial Activation ◽  
A Direct Method

Single-use plastics impose an enormous environmental threat, but their recycling, especially of polyolefins, has been proven challenging. We report a direct method to selectively convert polyolefins to branched, liquid fuels including diesel, jet, and gasoline-range hydrocarbons, with high yield up to 85% over Pt/WO3/ZrO2 and HY zeolite in hydrogen at temperatures as low as 225°C. The process proceeds via tandem catalysis with initial activation of the polymer primarily over Pt, with subsequent cracking over the acid sites of WO3/ZrO2 and HY zeolite, isomerization over WO3/ZrO2 sites, and hydrogenation of olefin intermediates over Pt. The process can be tuned to convert different common plastic wastes, including low- and high-density polyethylene, polypropylene, polystyrene, everyday polyethylene bottles and bags, and composite plastics to desirable fuels and light lubricants.

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