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In this letter, we revisit the IEQ method and provide a new perspective onits ability to preserve the original energy dissipation laws. The invariantenergy quadratization (IEQ) method has been widely used to design energy stablenumerical schemes for phase-field or gradient flow models. Although there aremany merits of the IEQ method, one major disadvantage is that the IEQ methodusually respects a modified energy law, where the modified energy is expressedin the auxiliary variables. Still, the dissipation laws in terms of theoriginal energy are not guaranteed. Using the widely-used Cahn-Hilliardequation as an example, we demonstrate that the Runge-Kutta IEQ method indeedcan preserve the original energy dissipation laws for certain situations up toarbitrary high-order accuracy. Interested readers are highly encouraged toapply our idea to other phase-field equations or gradient flow models.

A Remark on the Invariant Energy Quadratization (IEQ) Method for Preserving the Original Energy Dissipation Laws