scholarly journals Homogenization of elliptic problems involving interfaces and singular data

2019 ◽  
Vol 189 ◽  
pp. 111562 ◽  
Author(s):  
Micol Amar ◽  
Ida De Bonis ◽  
Giuseppe Riey
Keyword(s):  
Elliptic Problems ◽  
Singular Data

NVESTIGATION OF THE EFFICIENCY OF DISTRIBUTED INFORMATION SYSTEMS BASED ON THE PROCESSING OF LARGE AMOUNTS OF DATA

2019 ◽  
Author(s):  
Mykhajlo Klymash ◽  
Olena Hordiichuk — Bublivska ◽  
Ihor Tchaikovskyi ◽  
Oksana Urikova
Keyword(s):  
Distributed Systems ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Data Decomposition ◽  
Distributed Information ◽  
Software Model ◽  
Computing Performance ◽  
Mapreduce Model ◽  
Singular Data

In this article investigated the features of processing large arrays of information for distributed systems. A method of singular data decomposition is used to reduce the amount of data processed, eliminating redundancy. Dependencies of com­putational efficiency on distributed systems were obtained using the MPI messa­ging protocol and MapReduce node interaction software model. Were analyzed the effici­ency of the application of each technology for the processing of different sizes of data: Non — distributed systems are inefficient for large volumes of information due to low computing performance. It is proposed to use distributed systems that use the method of singular data decomposition, which will reduce the amount of information processed. The study of systems using the MPI protocol and MapReduce model obtained the dependence of the duration calculations time on the number of processes, which testify to the expediency of using distributed computing when processing large data sets. It is also found that distributed systems using MapReduce model work much more efficiently than MPI, especially with large amounts of data. MPI makes it possible to perform calculations more efficiently for small amounts of information. When increased the data sets, advisable to use the Map Reduce model.

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

scholarly journals Robust Iterative Solvers for Gao Type Nonlinear Beam Models in Elasticity

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
B. Borsos ◽  
János Karátson
Keyword(s):  
Finite Element ◽  
Newton Method ◽  
Newton's Method ◽  
Numerical Experiments ◽  
Elliptic Problems ◽  
Iterative Solvers ◽  
Finite Element Solution ◽  
Element Solution ◽  
Nonlinear Beam ◽  
Quasi Newton

Abstract The goal of this paper is to present various types of iterative solvers: gradient iteration, Newton’s method and a quasi-Newton method, for the finite element solution of elliptic problems arising in Gao type beam models (a geometrical type of nonlinearity, with respect to the Euler–Bernoulli hypothesis). Robust behaviour, i.e., convergence independently of the mesh parameters, is proved for these methods, and they are also tested with numerical experiments.

Multiple solutions for nonlocal elliptic problems with concave–convex nonlinearities and weights

2021 ◽  
pp. 207-218
Author(s):  
Safia Benmansour ◽  
Atika Matallah ◽  
Mustapha Meghnafi
Keyword(s):  
Multiple Solutions ◽  
Elliptic Problems
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