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Efficient time integration of complex Ginzburg-Landau equations

Published on:

5 March 2024

Primary Category:

Numerical Analysis

Paper Authors:

Marco Caliari,

Fabio Cassini

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Key Details

Proposes high-order exponential schemes for efficient time integration

Avoids timestep restrictions of explicit & split-step methods

Efficiently computes matrix exponential actions

Demonstrates superior performance over standard techniques

Applicable to wide variety of complex Ginzburg-Landau equations

AI generated summary

Efficient time integration of complex Ginzburg-Landau equations

This paper proposes using high-order exponential time integration schemes to efficiently compute numerical solutions of complex Ginzburg-Landau equations. These schemes have favorable stability properties and avoid timestep restrictions from model stiffness. Matrix exponential actions are computed efficiently via Fourier analysis with periodic boundary conditions, or with a tensor-oriented approach using finite differences. Simulations of 2D and 3D complex Ginzburg-Landau equations demonstrate the schemes outperform standard split-step and explicit Runge-Kutta methods.

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