Exponential integrators

By Marlis Hochbruck, Alexander Ostermann. 2010

1,170 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

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Citations in the corpus

DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps (2022, methodology): “The proposed solvers and analysis are highly motivated by the methods of exponential integrators [25, 31] in the ODE literature.”
The phase field method for geometric moving interfaces and their numerical approximations (2019, positive): “Example 3: Exponential integrator Another way of utilizing the linear splitting of the J ′(u) = Au+N(u) is to develop exponential integrators [121, 259, 282], The central idea is to use an equivalent formulation of the phase field equation”
Numerical methods for kinetic equations* (2014, methodology): “We mention here that exponential methods for parabolic partial differential equations and highly oscillatory problems have a long tradition and have been extensively studied by several authors; see the recent review by Hochbruck and Ostermann (2010).”
From linear to nonlinear MPC: bridging the gap via the real-time iteration (2020, background): “However, this can be considered a special case of the more general family of exponential integrators [31].”
DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models (2022, positive): “It is shown in recent works (Lu et al., 2022; Zhang & Chen, 2022) that ODE solvers based on exponential integrators (Hochbruck & Ostermann, 2010) converge much faster than the traditional Preprint solvers for solving the unconditional diffusion ODE (3).”
The Matrix Exponential (2015, neutral): “The key idea here is to use different approximations to the error k by approximating the error equation (1.5) in a suitable way.”
Fast Sampling of Diffusion Models with Exponential Integrator (2022, methodology): “The semilinear structure presented in probability ﬂow ODE has been widely investigated in physics and numerical simulation (Hochbruck & Ostermann, 2010; Whalen et al., 2015), from which we get inspirations.”
Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators (2011, background): “See Hochbruck and Ostermann [15] for a survey of the state of the art in exponential integrators.”
UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models (2023, background): “Recent works [40, 25, 26] show that ODE solvers built on exponential integrators [17] appear to have faster convergence than directly solving the diffusion ODE (1).”