Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint

Abstract

A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by combining invariant energy quadratization and scalar auxiliary variable approaches with the recent L1${}^{+}$ formula. The new developed methods are proved to be volume-preserving and unconditionally energy stable on arbitrary nonuniform time meshes. The accelerated algorithm and adaptive time strategy are employed in numerical implement. Numerical results show that the proposed algorithms are computationally efficient in multi-scale simulations, and appropriate for accurately resolving the intrinsically initial singularity of solution and for efficiently capturing the fast dynamics away initial time.

arXiv comment21 pages, 75 figures, 3 tables

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Cited by in corpus (5)

• Highly efficient schemes for time fractional Allen-Cahn equation using extended SAV approach
• A Non-uniform Time-stepping Convex Splitting Scheme for the Time-fractional Cahn-Hilliard Equation
• Time-fractional Cahn-Hilliard equation: Well-posedness, degeneracy, and numerical solutions
• Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
• Highly efficient and energy dissipative schemes for the time fractional Allen-Cahn equation