Predictor-Corrector Domain Decomposition Algorithm for Parabolic Problems on Graphs

Tumanova, Natalija

doi:10.3846/13926292.2012.645891

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…Thus 2D and 3D generalizations of the given mathematical model should be investigated. Construction of robust and efficient parallel algorithms can be done by using domain decomposition and splitting in space methods [29].…”

Section: Discussionmentioning

confidence: 99%

Numerical approximation of one model of bacterial self-organization

Čiegis

Bugajev

2012

NAMC

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This paper presents finite difference approximations of one dimensional in space mathematical model of a bacterial self-organization. The dynamics of such nonlinear systems can lead to formation of complicated solution patterns. In this paper we show that this chemotaxisdriven instability can be connected to the ill-posed problem defined by the backward in time diffusion process. The method of lines is used to construct robust numerical approximations. At the first step we approximate spatial derivatives in the PDE by applying approximations targeted for special physical processes described by differential equations. The obtained system of ODE is split into a system describing separately fast and slow physical processes and different implicit and explicit numerical solvers are constructed for each subproblem. Results of numerical experiments are presented and convergence of finite difference schemes is investigated.

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Section: Discussionmentioning

confidence: 99%

Numerical approximation of one model of bacterial self-organization

Čiegis

Bugajev

2012

NAMC

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Section: Summary Of the Third Chaptermentioning

confidence: 99%

The Investigation of Efficiency of Physical Phenomena Modelling Using Differential Equations on Distributed Systems

Bugajev¹

2015

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Vadovas prof. habil. dr. Raimondas ČIEGIS (Vilniaus Gedimino technikos universitetas, informatikos inžinerija-07T). Vilniaus Gedimino technikos universiteto Informatikos inžinerijos mokslo krypties disertacijos gynimo taryba: Pirmininkas prof. habil. dr. Antanas ČENYS (Vilniaus Gedimino technikos universitetas, informatikos inžinerija-07T). Nariai: prof. habil. dr. Rimantas BARAUSKAS (Kauno technologijos universitetas, informatika-09P), prof. habil. dr. Gintautas DZEMYDA (Vilniaus universitetas, informatikos inžinerija-07T), prof. dr. Arvet PEDAS (Tartu universitetas, matematika-01P), prof. dr. Olegas VASILECAS (Vilnius Gedimino technikos universitetas, informatikos inžinerija-07T). Disertacija bus ginama viešame Informatikos inžinerijos mokslo krypties disertacijos gynimo tarybos posėdyje 2015 m. lapkričio 27 d. 9 val. Vilniaus Gedimino technikos universiteto senato posėdžių salėje.

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“…As well as the use of an appropriate IBC, application of an accurate and efficient numerical scheme to solve the PDEs is also an important issue. Conventional numerical schemes mainly solve a PDE separately in reaches and around junctions (Szymkiewicz, 2010;Zhang et al, 2010;Sanders et al, 2011;Tumanova and ýLHJLV, 2012;Yang et al, 2012), which may result in the loss of computational efficiency. The authors developed a finite volume (FV) and finite element (FE) schemes for the parabolic PDEs in connected graphs (Yoshioka and Unami, 2012b;Yoshioka et al, 2013a-b).…”

Section: Introductionmentioning

confidence: 99%

Internal Boundary Conditions for Solute Transport Equations in Locally One-dimensional Open Channel Networks

Yoshioka

Unami

Fujihara

2013

Journal of Rainwater Catchment Systems

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Transport phenomena of solute in open channel networks are described in the framework of longitudinal dispersion. Modeling of the longitudinal dispersion in an open channel network in general requires the use of a solute transport equation coupled with an internal boundary condition to appropriately determine the dynamics of solute concentration around junctions. However, only a few researches have focused on dependence of the longitudinal dispersion on the internal boundary conditions. This paper carries out theoretical and numerical analysis on two internal boundary conditions that have different physical and mathematical basis with each other. A conforming Petrov-Galerkin finite element scheme is used to solve the solute transport equation. Computational results of a series of numerical simulations reveal that the dynamics of the solute concentration in open channel networks critically depends on the internal boundary conditions in particular for the diffusion-dominant cases that arise in typical situations, indicating their importance in practical analysis.

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Predictor-Corrector Domain Decomposition Algorithm for Parabolic Problems on Graphs

Cited by 6 publications

References 15 publications

Numerical approximation of one model of bacterial self-organization

Numerical approximation of one model of bacterial self-organization

The Investigation of Efficiency of Physical Phenomena Modelling Using Differential Equations on Distributed Systems

Internal Boundary Conditions for Solute Transport Equations in Locally One-dimensional Open Channel Networks

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