Numerical methods for nonlocal and fractional models
Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …
across all scientific and engineering disciplines. However, across an equally wide swath …
Maximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemes
The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …
ranging from physics and biology to materials and social sciences. In this paper, we …
[HTML][HTML] Accelerating phase-field-based microstructure evolution predictions via surrogate models trained by machine learning methods
D Montes de Oca Zapiain, JA Stewart… - npj Computational …, 2021 - nature.com
The phase-field method is a powerful and versatile computational approach for modeling the
evolution of microstructures and associated properties for a wide variety of physical …
evolution of microstructures and associated properties for a wide variety of physical …
[HTML][HTML] Accelerating phase-field predictions via recurrent neural networks learning the microstructure evolution in latent space
The phase-field method is a popular modeling technique used to describe the dynamics of
microstructures and their physical properties at the mesoscale. However, because in these …
microstructures and their physical properties at the mesoscale. However, because in these …
A new Lagrange multiplier approach for gradient flows
We propose a new Lagrange multiplier approach to design unconditional energy stable
schemes for gradient flows. The new approach leads to unconditionally energy stable …
schemes for gradient flows. The new approach leads to unconditionally energy stable …
A generalized SAV approach with relaxation for dissipative systems
Y Zhang, J Shen - Journal of Computational Physics, 2022 - Elsevier
The scalar auxiliary variable (SAV) approach [31] and its generalized version GSAV
proposed in [20] are very popular methods to construct efficient and accurate energy stable …
proposed in [20] are very popular methods to construct efficient and accurate energy stable …
The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems
The invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches
are two recently proposed methods to develop linear and unconditionally energy stable …
are two recently proposed methods to develop linear and unconditionally energy stable …
Time-fractional Allen–Cahn equations: analysis and numerical methods
In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …
Modelling and computation of liquid crystals
Liquid crystals are a type of soft matter that is intermediate between crystalline solids and
isotropic fluids. The study of liquid crystals has made tremendous progress over the past four …
isotropic fluids. The study of liquid crystals has made tremendous progress over the past four …