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Experimental methods in chemical engineering: process simulation

Jacopo De Tommaso, Francesco Rossi, Nooshin Moradi, Carlo Pirola, Gregory S. Patience, Federico Galli
2020 Canadian Journal of Chemical Engineering  
ACKNOWLEDGEMENTS The authors aknowledge professor Rahmat Sotudeh Gharebagh for his precious comments and suggestions, and the fruitful discussions.  ...  ACKNOWLEDGEMENTS The authors aknowledge professor Rahmat Sotudeh Gharebagh for his precious comments and suggestions, and the fruitful discussions.  ...  Another feature of Newton-type methods is their capability of solving nonlinear systems of arbitrarily large scale, provided that adequate computing power is available.  ... 
doi:10.1002/cjce.23857 fatcat:3v5uhmrfrnccbms6b4zfk7i5xa

Hybrid analog-digital solution of nonlinear partial differential equations

Yipeng Huang, Ning Guo, Mingoo Seok, Yannis Tsividis, Kyle Mandli, Simha Sethumadhavan
2017 Proceedings of the 50th Annual IEEE/ACM International Symposium on Microarchitecture - MICRO-50 '17  
With a physically prototyped analog accelerator, we use this hybrid analog-digital method to solve the two-dimensional viscous Burgers' equation -an important and representative PDE.  ...  We use a hybrid analog-digital computer architecture to solve nonlinear PDEs that draws on the strengths of each model of computation and avoids their weaknesses.  ...  We discuss the pitfalls of the Newton method for solving nonlinear equations; we show how a continuous model of computation avoids them.  ... 
doi:10.1145/3123939.3124550 dblp:conf/micro/HuangGSTMS17 fatcat:rfhoa72tbvfoxjzza2y3w65vfe

Localized Nonlinear Solution Strategies for Efficient Simulation of Unconventional Reservoirs [article]

Jiamin Jiang
2020 arXiv   pre-print
To perform localized computations, an a-priori strategy is essential to first determine the active subset of simulation cells for the subsequent iteration.  ...  The results show that large degrees of solution locality present across timesteps and iterations. Comparing to a standard Newton solver, the new solvers enable superior computational performance.  ...  The author also thanks Chevron for permission to publish this paper.  ... 
arXiv:2008.01539v1 fatcat:mvn4sl7rxffyfdefjwjfbx3rrq

Newton-conjugate-gradient methods for solitary wave computations

Jianke Yang
2009 Journal of Computational Physics  
The combination of Newton-type methods (for solving nonlinear equations) and Krylov subspace methods (for solving the resulting linear Newton-correction equations) is a well known technique.  ...  In this paper, the Newton-conjugate-gradient methods are developed for solitary wave computations.  ...  Lakoba for helpful discussions. He also thanks three anonymous referees for useful suggestions which significantly improved the clarify of this manuscript.  ... 
doi:10.1016/j.jcp.2009.06.012 fatcat:xerruhastfhmlmon2wloa4amfu

Jacobian-free Newton–Krylov methods: a survey of approaches and applications

D.A. Knoll, D.E. Keyes
2004 Journal of Computational Physics  
Jacobian-free Newton-Krylov (JFNK) methods are synergistic combinations of Newton-type methods for superlinearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton  ...  JFNK has potential for application throughout problems governed by nonlinear partial differential equations and integro-differential equations.  ...  Acknowledgements The authors thank all of their co-authors and co-explorers in Newton-Krylov methodology over the past dozen years, especially S. Balay  ... 
doi:10.1016/j.jcp.2003.08.010 fatcat:w26jxxlalngzbogwvaa5efazgm

Solving differential Riccati equations: A nonlinear space-time method using tensor trains [article]

Tobias Breiten, Sergey Dolgov, Martin Stoll
2019 arXiv   pre-print
They are time-depent, matrix-valued, and in particular nonlinear equations that require special methods for their solution.  ...  We propose the use of an all-at-once space-time solution leading to a large nonlinear space-time problem for which we propose the use of a Newton-Kleinman iteration.  ...  This means that we propose the use of an outer nonlinear solver of Newton-type that at its core needs to solve a linearized problem.  ... 
arXiv:1912.06944v1 fatcat:pyjzkj2vvre53nlldqykt7uuqy

Solving differential Riccati equations: A nonlinear space-time method using tensor trains

Tobias Breiten, ,Institute of Mathematics, Technical University of Berlin, 10623 Berlin, Germany, Sergey Dolgov, Martin Stoll, ,University of Bath, Department of Mathematical Sciences, BA2 7AY Bath, United Kingdom, ,Technische Universität Chemnitz, Department of Mathematics, Scientific Computing Group, 09107 Chemnitz, Germany
2019 Numerical Algebra, Control and Optimization  
They are time-dependent, matrix-valued, and in particular nonlinear equations that require special methods for their solution.  ...  Low-rank methods have been used heavily for computing a low-rank solution at every step of a time-discretization.  ...  We would like to thank Gerhard Kirsten (University of Bologna) as well as Björn Baran and Jens Saak (both Max Planck Institute Magdeburg) for providing us with the matlab codes as well as for fruitful  ... 
doi:10.3934/naco.2020034 fatcat:t7qjnxwiojebvf5anxi5hqdcje

Numerical Solution of Large Sets of Algebraic Nonlinear Equations

Ph. L. Toint
1986 Mathematics of Computation  
This paper describes the application of the partitioned updating quasi-Newton methods for the solution of high-dimensional systems of algebraic nonlinear equations.  ...  This concept was introduced and successfully tested in nonlinear optimization of partially separable functions (see [6] ). Here its application to the case of nonlinear equations is explored.  ...  Hence, we can conclude that analyzing this type of structure, and using it when available, can be of importance when solving sets of nonlinear equations. 3.3.2. Comparing the methods tested.  ... 
doi:10.2307/2008222 fatcat:2agqmok43vdondtgiutxv3fy7e

Numerical solution of large sets of algebraic nonlinear equations

Ph. L. Toint
1986 Mathematics of Computation  
This paper describes the application of the partitioned updating quasi-Newton methods for the solution of high-dimensional systems of algebraic nonlinear equations.  ...  This concept was introduced and successfully tested in nonlinear optimization of partially separable functions (see [6] ). Here its application to the case of nonlinear equations is explored.  ...  Hence, we can conclude that analyzing this type of structure, and using it when available, can be of importance when solving sets of nonlinear equations. 3.3.2. Comparing the methods tested.  ... 
doi:10.1090/s0025-5718-1986-0815839-9 fatcat:qrgaermcjrfqvefkbnlnhuu4qa

The Role of Multi-method Linear Solvers in PDE-based Simulations [chapter]

S. Bhowmick, L. McInnes, B. Norris, P. Raghavan
2003 Lecture Notes in Computer Science  
We present a framework for using multi-method solvers in such simulations to potentially improve the execution time and reliability of linear system solution.  ...  We demonstrate how such m ulti-method composite and adaptive solvers can be developed using advanced software architectures such a s PETSc, and we report on their performance in a computational uid dynamics  ...  Acknowledgments We gratefully acknowledge Barry Smith, who enhanced PETSc functionality to facilitate our work and participated in several discussions on the role and development o f m ulti-method solvers  ... 
doi:10.1007/3-540-44839-x_87 fatcat:ojrixugzdze4rnfg6xa2x3fscm

Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Adjoint Derivative Computations

Gaetan K. W. Kenway, Graeme J. Kennedy, Joaquim R. R. A. Martins
2014 AIAA Journal  
Fully coupled Newton-Krylov methods are presented for the solution of aerostructural systems and for the corresponding adjoint systems.  ...  The parallel scalability of the methods is demonstrated for a full aircraft configuration using an Euler computational fluid dynamics model with more than 8 × 10 6 state variables and a detailed structural  ...  SciNet is funded by the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; Ontario Research Fund, Research Excellence; and the University of Toronto.  ... 
doi:10.2514/1.j052255 fatcat:wj7e6iwcmne2ragdmbm4zayroq

Parameter identification for chemical models in combustion problems

R. Becker, M. Braack, B. Vexler
2005 Applied Numerical Mathematics  
We present an algorithm for parameter identification in combustion problems modeled by partial differential equations.  ...  The method includes local mesh refinement controlled by a posteriori error estimation with respect to the error in the parameters. The algorithm is applied to two types of combustion problems.  ...  We discuss shortly an alternative algorithm which combines the comparative "low" cost of the Gauß-Newton method and the better convergence properties of the full Newton.  ... 
doi:10.1016/j.apnum.2004.09.017 fatcat:p4gi2b4f5rgqvjgteqbb4tapwa

Inexact Newton methods for model simulation

Stefania Bellavia, Silvia Magheri, Claudia Miani
2011 International Journal of Computer Mathematics  
Traditionally, when solved in presence of forward-looking variables, these models are nonlinear, large-scale and sparse and give rise to large and highly structured nonlinear systems.  ...  Robust and efficient solution techniques for solving macroeconometric models are increasingly becoming a key factor in developing models employed by policy-making institutions for policy simulations and  ...  Newton-Krylov methods are combination of Newton-type procedures for nonlinear systems and Krylov methods for solving the arising Newton linear systems.  ... 
doi:10.1080/00207160.2011.563844 fatcat:x2dxsonfdzfalj6bbvnsa57wzi

Where do computational mathematics and computational statistics converge?

Austen C. Duffy
2014 Wiley Interdisciplinary Reviews: Computational Statistics  
The foundational aspects shared by both computational mathematics and computational statistics are explored with elementary discussions suitable to non-experts and aspiring students of the computational  ...  This overview presents a discussion on several topics of importance shared by the fields of computational mathematics and computational statistics.  ...  The derivative based methods for solving nonlinear equations discussed previously such as Newton methods or conjugate gradient methods can be naturally extended to the optimization realm.  ... 
doi:10.1002/wics.1313 fatcat:vyjonjuit5fiporzs3aai4d7ae

Efficient reordered nonlinear Gauss–Seidel solvers with higher order for black-oil models

Øystein S. Klemetsdal, Atgeirr F. Rasmussen, Olav Møyner, Knut-Andreas Lie
2019 Computational Geosciences  
Altogether, this gives optimal localization and control of the nonlinear solution process.  ...  The method requires repeated linearization of large nonlinear systems and produces ill-conditioned linear systems.  ...  Møyner is funded by VISTA, a basic research program funded by Equinor and conducted in close collaboration with the Norwegian Academy of Science and Letters.  ... 
doi:10.1007/s10596-019-09844-5 fatcat:wuppppvsb5eddfy5a43ajhrwg4
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