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

DOI10.1016/j.jcp.2021.110289OpenAlexW3080937007WikidataQ114163465 ScholiaQ114163465MaRDI QIDQ2124321

Alexander Moriggl, Lukas Einkemmer, Marco Caliari, Alexander Ostermann

Publication date: 8 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.11607

zbMATH Keywords

hyperbolic problemshighly oscillatory problemsGPU computingparallel in timerational exponential integrators

Mathematics Subject Classification ID

Numerical linear algebra (65Fxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Computer aspects of numerical algorithms (65Yxx)

Related Items (8)

Higher Order Phase Averaging for Highly Oscillatory Systems ⋮ High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid ⋮ Full discretization error analysis of exponential integrators for semilinear wave equations ⋮ An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware ⋮ Exponential Runge-Kutta parareal for non-diffusive equations ⋮ Euler polynomials for the matrix exponential approximation ⋮ BAMPHI: matrix-free and transpose-free action of linear combinations of \(\varphi\)-functions from exponential integrators ⋮ On the stability of exponential integrators for non-diffusive equations

Uses Software

• FFTW
• MKL
• cuFFT
• ParaDiag

Cites Work

• Exponential versus IMEX high-order time integrators for thermal convection in rotating spherical shells
• Newton interpolation at Leja points
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Matrix-free GPU implementation of a preconditioned conjugate gradient solver for anisotropic elliptic PDEs
• Parallel exponential Rosenbrock methods
• Exponential methods for solving hyperbolic problems with application to collisionless kinetic equations
• Near optimal rational approximations of large data sets
• A splitting approach for the magnetic Schrödinger equation
• Linearly implicit time stepping methods for numerical weather prediction
• 50 Years of Time Parallel Time Integration
• GPU Accelerated Algorithms for Computing Matrix Function Vector Products with Applications to Exponential Integrators and Fractional Diffusion
• The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential
• A Direct Solver for Time Parallelization
• Exponential integrators
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• Preconditioning and Iterative Solution of All-at-Once Systems for Evolutionary Partial Differential Equations
• A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator
• On approximate approximations using Gaussian kernels
• Parallel methods for integrating ordinary differential equations
• Stability and Convergence of the Crank–Nicolson/Adams–Bashforth scheme for the Time‐Dependent Navier–Stokes Equations
• An exponential integrator for the drift-kinetic model

This page was built for publication: An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs