Additive and iterative operator splitting methods and their numerical investigation

Faragó, István; Gnandt, Boglárka; Havasi, Ágnes

doi:10.1016/j.camwa.2007.11.017

Cited by 14 publications

(18 citation statements)

References 10 publications

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“…We employ a novel numerical scheme that involves a combination with the additive splitting method (ASM; Faragó et al 2008;Hamilton et al 1990). The method involves the splitting of an equation into a subset of (simpler) equations.…”

Section: Numerical Approach Results and Discussionmentioning

confidence: 99%

Solar Wind Strahl Broadening by Self-Generated Plasma Waves

Pavan

Viñas

Yoon³

et al. 2013

ApJ

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This Letter reports on the results of numerical simulations which may provide a possible explanation for the strahl broadening during quiet solar conditions. The relevant processes involved in the broadening are due to kinetic quasi-linear wave-particle interaction. Making use of static analytical electron distribution in an inhomogeneous field, it is found that self-generated electrostatic waves at the plasma frequency, i.e., Langmuir waves, are capable of scattering the strahl component, resulting in energy and pitch-angle diffusion that broadens its velocity distribution significantly. The present theoretical results provide an alternative or complementary explanation to the usual whistler diffusion scenario, suggesting that self-induced electrostatic waves at the plasma frequency might play a key role in broadening the solar wind strahl during quiet solar conditions.

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Section: Numerical Approach Results and Discussionmentioning

confidence: 99%

Solar Wind Strahl Broadening by Self-Generated Plasma Waves

Pavan

Viñas

Yoon³

et al. 2013

ApJ

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“…However, decoupling the equations introduce an additional source of error [8]. The convergence and precision of OS methods have been extensively studied for linear or quasi-linear operators [8,19].…”

Section: Operator Splitting Methodsmentioning

confidence: 99%

“…Unlike SNIA, each sub-step of an iterative scheme solves an approximation to the fully coupled PDE system. The simplest of these methods is the iterative split operator (ISO) [19]:…”

Section: Sequential Iterative Approachmentioning

confidence: 99%

Modelling in-situ upgrading of heavy oil using operator splitting method

et al. 2015

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The in-situ upgrading (ISU) of bitumen and oil shale is a very challenging process to model numerically because of the large number of components that need to be modelled using a system of equations that are both highly non-linear and strongly coupled. Operator splitting methods are one way of potentially improving computational performance. Each numerical operator in a process is modelled separately, allowing the best solution method to be used for the given numerical operator. A significant drawback to the approach is that decoupling the governing equations introduces an additional source of numerical error, known as the splitting error. The best splitting method for modelling a given process minimises the splitting error whilst improving computational performance compared to a fully implicit approach. Although operator splitting has been widely used for the modelling of reactive-transport problems, it has not yet been applied to the modelling of ISU. One reason is that it is not clear which operator splitting technique to use. Numerous such techniques are described in the literature and each leads to a different splitting error. While this error has been extensively analysed for linear operators for a wide Julien Maes range of methods, the results cannot be extended to general non-linear systems. It is therefore not clear which of these techniques is most appropriate for the modelling of ISU. In this paper, we investigate the application of various operator splitting techniques to the modelling of the ISU of bitumen and oil shale. The techniques were tested on a simplified model of the physical system in which a solid or heavy liquid component is decomposed by pyrolysis into lighter liquid and gas components. The operator splitting techniques examined include the sequential split operator (SSO), the Strang-Marchuk split operator (SMSO) and the iterative split operator (ISO). They were evaluated on various test cases by considering the evolution of the discretization error as a function of the time-step size compared with the results obtained from a fully implicit simulation. We observed that the error was least for a splitting scheme where the thermal conduction was performed first, followed by the chemical reaction step and finally the heat and mass convection operator (SSO-CKA). This method was then applied to a more realistic model of the ISU of bitumen with multiple components, and we were able to obtain a speed-up of between 3 and 5.

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“…It means that we do not consider only complete iteration steps, but we solve the subproblems one after the other and stop after an arbitrary number of calculations, as formulated in [3] for = 2. Thus not only , ∈ N, but any required order can be achieved.…”

Section: Remark 34mentioning

confidence: 99%

“…The attention paid to iterative splitting has been increasing in the last decade, numerous papers discuss the accuracy of the method [2,3] and present a possible area of applications [8]. All these studies consider operator decomposition into two suboperators, thus define a system with two subproblems.…”

Section: Introductionmentioning

confidence: 99%

Generalizations and error analysis of the iterative operator splitting method

Ladics

Faragó²

2013

Open Mathematics

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The properties of iterative splitting with two bounded linear operators have been analyzed by Faragó et al. For more than two operators, iterative splitting can be defined in many different ways. A large class of the possible extensions to this case is presented in this paper and the order of accuracy of these methods are examined. A separate section is devoted to the discussion of two of these methods to illustrate how this class of possible methods can be classified with respect to the order of accuracy. MSC:34A30, 35K57, 65L05, 65M06

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Additive and iterative operator splitting methods and their numerical investigation

Cited by 14 publications

References 10 publications

Solar Wind Strahl Broadening by Self-Generated Plasma Waves

Solar Wind Strahl Broadening by Self-Generated Plasma Waves

Modelling in-situ upgrading of heavy oil using operator splitting method

Generalizations and error analysis of the iterative operator splitting method

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