Overcoming order reduction in diffusion-reaction splitting. Part 1: Dirichlet boundary conditions

L Einkemmer, A Ostermann - SIAM Journal on Scientific Computing, 2015 - SIAM
For diffusion-reaction equations employing a splitting procedure is attractive as it reduces
the computational demand and facilitates a parallel implementation. Moreover, it opens up …

[HTML][HTML] An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere

S Gaudreault, JA Pudykiewicz - Journal of Computational Physics, 2016 - Elsevier
The exponential propagation methods were applied in the past for accurate integration of
the shallow water equations on the sphere. Despite obvious advantages related to the exact …

Dynamic models for Large Eddy Simulation of compressible flows with a high order DG method

A Abba, L Bonaventura, M Nini, M Restelli - Computers & Fluids, 2015 - Elsevier
The impact of dynamic models for applications to LES of compressible flows is assessed in
the framework of a numerical model based on high order discontinuous finite elements. The …

Semi-Lagrangian exponential integration with application to the rotating shallow water equations

PS Peixoto, M Schreiber - SIAM Journal on Scientific Computing, 2019 - SIAM
In this paper we propose a novel way to integrate time-evolving partial differential equations
that contain nonlinear advection and stiff linear operators, combining exponential integration …

Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems

M Schreiber, PS Peixoto, T Haut… - … International Journal of …, 2018 - journals.sagepub.com
This paper presents, discusses and analyses a massively parallel-in-time solver for linear
oscillatory partial differential equations, which is a key numerical component for evolving …

Energy conserving discontinuous Galerkin spectral element method for the Vlasov–Poisson system

É Madaule, M Restelli, E Sonnendrücker - Journal of Computational …, 2014 - Elsevier
We propose a new, energy conserving, spectral element, discontinuous Galerkin method for
the approximation of the Vlasov–Poisson system in arbitrary dimension, using Cartesian …

Second order fully semi-Lagrangian discretizations of advection-diffusion-reaction systems

L Bonaventura, E Calzola, E Carlini… - Journal of Scientific …, 2021 - Springer
We propose a second order, fully semi-Lagrangian method for the numerical solution of
systems of advection-diffusion-reaction equations, which is based on a semi-Lagrangian …

Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators

H Montanelli, N Bootland - Mathematics and Computers in Simulation, 2020 - Elsevier
Dozens of exponential integration formulas have been proposed for the high-accuracy
solution of stiff PDEs such as the Allen–Cahn, Korteweg–de Vries and Ginzburg–Landau …

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

M Caliari, L Einkemmer, A Moriggl… - Journal of Computational …, 2021 - Elsevier
Rational exponential integrators (REXI) are a class of numerical methods that are well suited
for the time integration of linear partial differential equations with imaginary eigenvalues …

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

M Schreiber, R Loft - Numerical Linear Algebra with …, 2019 - Wiley Online Library
With the stagnation of processor core performance, further reductions in the time to solution
for geophysical fluid problems are becoming increasingly difficult with standard time …