4.7 Article

Exponential Runge-Kutta Parareal for non-diffusive equations

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Computer Science, Interdisciplinary Applications

High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid

Stephane Gaudreault et al.

Summary: A novel numerical approach for solving shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. The method uses a space-time tensor formalism and direct flux reconstruction for spatial discretization. Exponential integration is employed for larger time step sizes and improved efficiency in time integration. New multistep-type exponential propagation iterative methods allow high-order accuracy in time integration without significant increases in computational time.

JOURNAL OF COMPUTATIONAL PHYSICS (2022)

Article Mathematics, Applied

On the stability of exponential integrators for non-diffusive equations

Tommaso Buvoli et al.

Summary: This paper investigates the stability and efficiency of exponential integrators on non-diffusive equations and proposes a simple repartitioning approach to improve their stability. The effectiveness of the approach is validated through numerical experiments, and it is found that the repartitioning method does not require the use of high-order spatial derivatives unlike the approach of adding hyperviscosity.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2022)

Article Computer Science, Interdisciplinary Applications

An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs

Marco Caliari et al.

Summary: Rational Exponential Integrators (REXI) are numerical methods suitable for time integration of linear partial differential equations with imaginary eigenvalues. A novel REXI scheme proposed in this paper drastically improves accuracy and efficiency, along with the ability to easily determine the required number of terms for accurate results. Comparative numerical simulations for a shallow water equation show the efficiency of the approach, indicating that REXI schemes can be efficiently implemented on graphic processing units.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

Article Mathematics, Applied

EXPONENTIAL POLYNOMIAL BLOCK METHODS

Tommaso Buvoli

Summary: In this paper, exponential integration is introduced to initial value problems, resulting in a new class of parallel exponential polynomial block methods (EPBMs) with improved stability. High-order EPBMs are significantly more efficient than other methods in obtaining highly accurate solutions.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2021)

Article Mathematics, Applied

A CLASS OF EXPONENTIAL INTEGRATORS BASED ON SPECTRAL DEFERRED CORRECTION

Tommaso Buvoli

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2020)

Article Computer Science, Interdisciplinary Applications

Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere

Francois P. Hamon et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Computer Science, Interdisciplinary Applications

Exponential methods for solving hyperbolic problems with application to collisionless kinetic equations

Nicolas Crouseilles et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Article Mathematics, Applied

A parallel time integrator for solving the linearized shallow water equations on the rotating sphere

Martin Schreiber et al.

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS (2019)

Article Mathematics, Applied

SEMI-LAGRANGIAN EXPONENTIAL INTEGRATION WITH APPLICATION TO THE ROTATING SHALLOW WATER EQUATIONS

Pedro S. Peixoto et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2019)

Article Mathematics, Applied

NECESSARY CONDITIONS AND TIGHT TWO-LEVEL CONVERGENCE BOUNDS FOR PARAREAL AND MULTIGRID REDUCTION IN TIME

Ben S. Southworth

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS (2019)

Article Mathematics, Applied

PARAREAL CONVERGENCE FOR OSCILLATORY PDEs WITH FINITE TIME-SCALE SEPARATION

Adam G. Peddle et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2019)

Article Computer Science, Interdisciplinary Applications

KIOPS: A fast adaptive Krylov subspace solver for exponential integrators

Stephane Gaudreault et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

Article Mathematics, Interdisciplinary Applications

Wave propagation characteristics of Parareal

Daniel Ruprecht

COMPUTING AND VISUALIZATION IN SCIENCE (2018)

Article Mathematics, Applied

A block Krylov subspace implementation of the time-parallel Paraexp method and its extension for nonlinear partial differential equations

G. L. Kooij et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2017)

Article Computer Science, Interdisciplinary Applications

Acceleration of unsteady hydrodynamic simulations using the parareal algorithm

Araz Eghbal et al.

JOURNAL OF COMPUTATIONAL SCIENCE (2017)

Article Mathematics, Applied

Highly stable implicit-explicit Runge-Kutta methods

Giuseppe Izzo et al.

APPLIED NUMERICAL MATHEMATICS (2017)

Article Mathematics, Applied

Parallel exponential Rosenbrock methods

Vu Thai Luan et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2016)

Article Mathematics, Interdisciplinary Applications

Numerical simulation of skin transport using Parareal

Andreas Kreienbuehl et al.

COMPUTING AND VISUALIZATION IN SCIENCE (2015)

Article Computer Science, Software Engineering

Comparison of software for computing the action of the matrix exponential

Marco Caliari et al.

BIT NUMERICAL MATHEMATICS (2014)

Article Mathematics, Applied

Explicit exponential Runge-Kutta methods of high order for parabolic problems

Vu Thai Luan et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2014)

Article Mathematics, Applied

AN ASYMPTOTIC PARALLEL-IN-TIME METHOD FOR HIGHLY OSCILLATORY PDES

Terry Haut et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2014)

Article Mathematics, Applied

Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs

J. Loffeld et al.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2013)

Article Mathematics, Applied

STABLE PARAREAL IN TIME METHOD FOR FIRST- AND SECOND-ORDER HYPERBOLIC SYSTEMS

Xiaoying Dai et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2013)

Article Mathematics, Applied

PARAEXP: A PARALLEL INTEGRATOR FOR LINEAR INITIAL-VALUE PROBLEMS

Martin J. Gander et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2013)

Article Computer Science, Software Engineering

Algorithm 919: A Krylov Subspace Algorithm for Evaluating the φ-Functions Appearing in Exponential Integrators

Jitse Niesen et al.

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE (2012)

Article Computer Science, Interdisciplinary Applications

Event-based parareal: A data-flow based implementation of parareal

L. A. Berry et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2012)

Article Mathematics, Applied

TOWARD AN EFFICIENT PARALLEL IN TIME METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

Matthew Emmett et al.

COMMUNICATIONS IN APPLIED MATHEMATICS AND COMPUTATIONAL SCIENCE (2012)

Article Computer Science, Interdisciplinary Applications

Linearly implicit methods for nonlinear PDEs with linear dispersion and dissipation

Ian Grooms et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2011)

Article Computer Science, Theory & Methods

Scheduling of tasks in the parareal algorithm

Eric Aubanel

PARALLEL COMPUTING (2011)

Article Mathematics, Applied

COMPUTING THE ACTION OF THE MATRIX EXPONENTIAL, WITH AN APPLICATION TO EXPONENTIAL INTEGRATORS

Awad H. Al-Mohy et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2011)

Article Mathematics

Exponential integrators

Marlis Hochbruck et al.

ACTA NUMERICA (2010)

Article Mathematics, Applied

Comparison of methods for evaluating functions of a matrix exponential

H. A. Ashi et al.

APPLIED NUMERICAL MATHEMATICS (2009)

Article Mathematics, Applied

A NEW SCALING AND SQUARING ALGORITHM FOR THE MATRIX EXPONENTIAL

Awad H. Al-Mohy et al.

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS (2009)

Article Mathematics, Applied

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

Christian Klein et al.

JOURNAL OF NONLINEAR SCIENCE (2007)

Article Mathematics, Applied

An error analysis of the modified scaling and squaring method

S. Koikari

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2007)

Article Computer Science, Software Engineering

A class of explicit exponential general linear methods

A. Ostermann et al.

BIT NUMERICAL MATHEMATICS (2006)

Article Mathematics, Applied

Exponential Runge-Kutta methods for parabolic problems

M Hochbruck et al.

APPLIED NUMERICAL MATHEMATICS (2005)

Article Computer Science, Interdisciplinary Applications

Generalized integrating factor methods for stiff PDEs

S Krogstad

JOURNAL OF COMPUTATIONAL PHYSICS (2005)

Article Mathematics, Applied

Fourth-order time-stepping for stiff PDEs

AK Kassam et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2005)

Article Computer Science, Interdisciplinary Applications

Parallel-in-time simulation of the unsteady Navier-Stokes equations for incompressible flow

JMF Trindade et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS (2004)

Article Engineering, Multidisciplinary

Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid-structure applications

C Farhat et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2003)

Article Computer Science, Interdisciplinary Applications

Exponential time differencing for stiff systems

SM Cox et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2002)