Fourth-order two-stage explicit exponential integrators for time-dependent PDEs

Luân, Vũ Thái

doi:10.1016/j.apnum.2016.10.008

Cited by 24 publications

(10 citation statements)

References 26 publications

(62 reference statements)

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“…These include a fourth-order twostage scheme, a fourth-order parallel stages scheme, and a fifth-order threestage scheme. Our main references in this section are [26,27,28,29,30].…”

Section: Exponential Rosenbrock Methodsmentioning

confidence: 99%

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Further development of efficient and accurate time integration schemes for meteorological models

Luân

Pudykiewicz

Reynolds

2019

Journal of Computational Physics

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“…These include a fourth-order twostage scheme, a fourth-order parallel stages scheme, and a fifth-order threestage scheme. Our main references in this section are [26,27,28,29,30].…”

Section: Exponential Rosenbrock Methodsmentioning

confidence: 99%

“…First, we consider a fourth-order scheme satisfying the stiff order conditions, named exprb42 in [30]:…”

Section: Selected Exponential Schemes For Numerical Experimentsmentioning

confidence: 99%

Further development of efficient and accurate time integration schemes for meteorological models

Luân

Pudykiewicz

Reynolds

2019

Journal of Computational Physics

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“…In this section, based on [24,26,29,32,34] we present a compact summary of the introduction of exponential Rosenbrock methods and their derivations for methods of order up to 5. We then display some efficient schemes for our numerical experiments for some applications in visual computing.…”

Section: Explicit Exponential Rosenbrock Methodsmentioning

confidence: 99%

Explicit Exponential Rosenbrock Methods and their Application in Visual Computing

Luan,

Michels

2018

Preprint

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We introduce a class of explicit exponential Rosenbrock methods for the time integration of large systems of stiff differential equations. Their application with respect to simulation tasks in the field of visual computing is discussed where these time integrators have shown to be very competitive compared to standard techniques. In particular, we address the simulation of elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects like stability and energy conservation, large stiffnesses, high fidelity and visual accuracy.

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“…Exponential Runge-Kutta methods are a popular class of exponential integrators [9], which have shown a great promise as an alternative to standard time integration solvers for stiff systems and applications in recent years, see e.g. [8,10,11,12,13,14,15,16,17,18,19,20,22]. The main idea behind these methods is to solve the linear portion of (1.1) exactly and integrate the remaining nonlinear portion explicitly based on a representation of the exact solution using the variation-of-constants formula.…”

Section: Introductionmentioning

confidence: 99%

Efficient exponential Runge--Kutta methods of high order: construction and implementation

Luân¹

2020

Preprint

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Exponential Runge-Kutta methods have shown to be competitive for the time integration of stiff semilinear parabolic PDEs. The current construction of stiffly accurate exponential Runge-Kutta methods, however, relies on a convergence result that requires weakening many of the order conditions, resulting in schemes whose stages must be implemented in a sequential way. In this work, after showing a stronger convergence result, we are able to derive two new families of fourth-and fifth-order exponential Runge-Kutta methods, which, in contrast to the existing methods, have multiple stages that are independent of one another and share the same format, thereby allowing them to be implemented in parallel or simultaneously, and making the methods to behave like using with much less stages. Moreover, all of their stages involve only one linear combination of the product of ϕ-functions (using the same argument) with vectors. Overall, these features make these new methods to be much more efficient to implement when compared to the existing methods of the same orders. Numerical experiments on a one-dimensional semilinear parabolic problem, a nonlinear Schrdinger equation, and a two-dimensional Gray-Scott model are given to confirm the accuracy and efficiency of the two newly constructed methods.

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Fourth-order two-stage explicit exponential integrators for time-dependent PDEs

Cited by 24 publications

References 26 publications

Further development of efficient and accurate time integration schemes for meteorological models

Further development of efficient and accurate time integration schemes for meteorological models

Explicit Exponential Rosenbrock Methods and their Application in Visual Computing

Efficient exponential Runge--Kutta methods of high order: construction and implementation

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