Evidences that Software Based on Non-overlapping Discretization Is Most Efficient for Applying Highly Parallelized Supercomputers to Solving Partial Differential Equations

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• 关键词：Discretization ; methods ; Highly ; parallelized super ; computers ; 100 % ; parallel algorithms ; Parallel ; solution of pdes ; Parallel software for elasticity ; High performance computing ; DDM
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9576
• 期：1
• 页码：1-16
• 全文大小：1,158 KB
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  11.Herrera, I., de la Cruz, L.M., Rosas-Medina, A.: Non-Overlapping Discretization Methods for Partial, Differential Equations. Numer. Meth. Part D E 30, 1427–1454 (2014). doi:10.​1002/​num21852 . (Open source)CrossRef MATH
  12.Herrera, I., Rosas-Medina, A.: The derived-vector space framework and four general purposes massively parallel DDM algorithms. EABE (Engineering Analysis with Boundary Elements) 37, 646–657 (2013)MathSciNet CrossRef MATH
  13.Herrera, I., Contreras, I.: An innovative tool for effectively applying highly parallelized hardware to problems of elasticity. Geofísica Int. 55(1), 363–386 (2016)
  14.Herrera, I.: Theory of differential equations in discontinuous piecewise-defined-functions. Numer. Meth. Part D E 23(3), 597–639 (2007). DOI10.1002NO.20182MathSciNet CrossRef MATH
  15.Herrera, I., Yates, R.A.: The multipliers-free domain decomposition methods. Numer. Meth. Part D. E. 26, 874–905 (2010). doi:10.​1002/​num.​20462 MathSciNet MATH
  16.Herrera, I., Yates, R.A.: The multipliers-free dual primal domain decomposition methods for nonsymmetrical matrices numer. Meth. Part D. E. 27(5), 1262–1289 (2011). doi:10.​1002/​Num.​20581 MathSciNet CrossRef MATH
  17.Contreras, I.: Parallel Processing of PDEs. Ph.D. thesis, Advisor Herrera I. UNAM (2016)
  
• 作者单位：Ismael Herrera-Revilla (18)
  Iván Contreras (18)
  
  18. Instituto de Geofísica Universidad Nacional Autónoma de México, UNAM, Ciudad de México, Mexico
  
• 丛书名：High Performance Computing and Applications
• ISBN：978-3-319-32557-6
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9576

文摘

One of the main problems for applying the highly parallelized supercomputers available today to computational physico-mathematical modeling of science and engineering is to develop software capable of effectively solving in parallel partial differential equations or systems of such equations. For this purpose much work on domain decomposition methods has been done. Recently, I. Herrera introduced a new ‘non-overlapping discretization method’ that for the application of domain decomposition methods has many advantages over standard methods of discretization. Based on theoretical grounds, some of these advantages have been indicated in previous publications. This paper, however, is devoted to present numerical evidences of such advantages and some of the outstanding parallelization-efficiencies that are feasible when domain decomposition methods are applied to the discrete system derived using non-overlapping discretization methods.