What question did this study set out to answer?

To quantify and eliminate the artificial time delay caused by stabilization techniques in exponential time differencing Runge–Kutta schemes for the Allen–Cahn gradient flow equation.

December 8, 2023ESAIM Mathematical Modelling and Numerical AnalysisOpen Access

Quantifying and eliminating the time delay in stabilization exponential time differencing Runge–Kutta schemes for the Allen–Cahn equation

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Authors

HZHong ZhangNational University of Defense Technology LLLele LiuZunyi Medical University QXQian XuZhejiang University of Technology

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Implication

Numerical investigation demonstrates delay-free convergence using relaxation exponential time differencing Runge-Kutta schemes in Allen-Cahn systems, highlighting preserved energy stability.

Key Points

To quantify and eliminate the artificial time delay caused by stabilization techniques in exponential time differencing Runge–Kutta schemes for the Allen–Cahn gradient flow equation.
Applied Fourier pseudo-spectral spatial discretization to the Allen–Cahn equation with polynomial and logarithmic potentials to formulate a semi-discrete maximum principle.
Reformulated first- and second-order exponential time differencing Runge–Kutta (ETDRK) integrators as parametric Runge–Kutta schemes to evaluate stabilization-induced lag.
Integrated a relaxation technique to eliminate temporal delay and derived temporal error estimates in the maximum norm topology under a fixed spatial mesh.
Quantified the lagging effect inherently introduced by stabilization parameters in standard ETDRK schemes.
Demonstrated that the proposed relaxation ETDRK schemes completely eliminate time-delay convergence errors while unconditionally preserving the mesh-dependent maximum principle and energy stability.

Cite This Study

Zhang et al. (2023) studied this question.

synapsesocial.com/papers/6a796b67fbd9051d3b0dc13d https://doi.org/10.1051/m2an/2023101

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Implication

Numerical investigation demonstrates delay-free convergence using relaxation exponential time differencing Runge-Kutta schemes in Allen-Cahn systems, highlighting preserved energy stability.

Quantifying and eliminating the time delay in stabilization exponential time differencing Runge–Kutta schemes for the Allen–Cahn equation

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Implication

Key Points

Cite This Study

Quantifying and eliminating the time delay in stabilization exponential time differencing Runge–Kutta schemes for the Allen–Cahn equation

Discussion

Member takes

Implication

Key Points

Cite This Study

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