Chaoyu Quan

Stability and Convergence of Multi-Product Expansion Splitting Methods with Negative Weights for Semilinear Parabolic Equations

Xianglong Duan, Chaoyu Quan, Yang Jiang

Abstract. The operator splitting method has been widely used to solve differential equations by splitting the equation into more manageable parts. In this work, we resolve a long-standing problem—how to establish the stability of multi-product expansion (MPE) splitting methods with negative weights. …

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Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using General Multipliers

Chaoyu Quan, Huaijin Wang, Xuping Wang, Chuanju Xu

A unified framework is proposed to establish the energy dissipation of implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, based on general multipliers that are linear combinations of first-order differences of numerical solutions. A generalized Dahlquist's theory is developed to establish the …

Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using General Multipliers

Chaoyu Quan, Hao Wang, Xuping Wang, Chuanju Xu

A unified framework is proposed to establish the energy dissipation of implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, based on general multipliers that are linear combinations of first-order differences of numerical solutions. A generalized Dahlquist's theory is developed to establish the …

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Maximum bound preservation of exponential integrators for Allen–Cahn equations

Chaoyu Quan, Zhi Zhou

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Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using a Simple Multiplier

Chaoyu Quan, Huaijin Wang, Xuping Wang, Chuanju Xu

This paper proposes a theoretical framework for establishing the energy dissipation of general implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, by constructing a dissipative modified energy consisting of the original energy and a non-negative quadratic modification. We first test IMEX-LMMs with …

Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using a Simple Multiplier

Chaoyu Quan, Huaijin Wang, Xuping Wang, Chuanju Xu

This paper proposes a theoretical framework for establishing the energy dissipation of general implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, by constructing a dissipative modified energy consisting of the original energy and a non-negative quadratic modification. We first test IMEX-LMMs with …

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A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations

Hong-lin Liao, Chaoyu Quan, Tao Tang, Tao Zhou

The rigorous stability analysis of high-order implicit-explicit linear multistep (IELM) methods for nonlinear parabolic equations by using discrete energy arguments is a long standing open issue due to their non-A-stability property. A novel semi-generating function approach combined with a global discrete energy …

A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations

Hong-lin Liao, Chaoyu Quan, Tao Tang, Tao Zhou

The rigorous stability analysis of high-order implicit-explicit linear multistep (IELM) methods for nonlinear parabolic equations by using discrete energy arguments is a long standing open issue due to their non-A-stability property. A novel semi-generating function approach combined with a global discrete energy …

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A generalized matrix-valued Allen--Cahn model and its numerical solution

Yaru Liu, Chaoyu Quan, Dong Wang

This paper introduces a generalized matrix-valued Allen--Cahn model, where the unknown matrix-valued field belongs to $\mathbb{R}^{m_1\times m_2}$ with dimension $m_1\geq m_2$. By taking different values of $m_1$ and $m_2$, this model covers the classical scalar-valued, vector-valued, and square-matrix-valued Allen--Cahn equations. At the …

A generalized matrix-valued Allen--Cahn model and its numerical solution

Yaru Liu, Chaoyu Quan, Dong Wang

This paper introduces a generalized matrix-valued Allen--Cahn model, where the unknown matrix-valued field belongs to $\mathbb{R}^{m_1\times m_2}$ with dimension $m_1\geq m_2$. By taking different values of $m_1$ and $m_2$, this model covers the classical scalar-valued, vector-valued, and square-matrix-valued Allen--Cahn equations. At the …

A Class of High Order Unconditional Maximum Principle Preserving Extended IFRK Schemes for Allen-Cahn Equation

Zhuhan Jiang, Chaoyu Quan, Xuan Zhao

Abstract. This paper proposes a novel framework for constructing up to sixth-order, explicit, and unconditional maximum principle preserving extended integrating factor Runge–Kutta (eIFRK) schemes for the Allen-Cahn equation. The proposed framework significantly relaxes the constraints on the exponential coefficients and offers a …

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A relaxed Lagrange multiplier approach for phase field models

Jinpeng Zhang, Chaoyu Quan, Xiaoping Wang

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