We design and compute first-order implicit-in-time variational schemes with high-order
spatial discretization for initial value gradient flows in generalized optimal transport metric …

This paper aims to establish a novel and efficient topology optimization method for the
thermal-fluid. To adaptively design the fluid–solid coupling structure and make the objective …

The article considers a three-dimensional mathematical model of population dynamics
based on a system of non-stationary parabolic advection-diffusion-reaction equations with …

In this paper, we propose an arbitrary Lagrangian Eulerian (ALE) meshfree method that
utilizes the radial basis function-finite difference (RBF-FD) method for solving diffusion …

A second-order accurate in time, positivity-preserving, and unconditionally energy stable
operator splitting scheme is proposed and analyzed for reaction-diffusion systems with the …

We present an error analysis for a fully discrete finite difference scheme for the three-
component Macromolecular Microsphere Composite (MMC) hydrogels system, a ternary …

Shape transformation on evolving curved surfaces is essential for its diverse applications
across various scientific disciplines and facilitates the deeper understanding of natural …

We present a new energy dissipation and maximum bound principle preserving scheme for
solving a nonlocal ternary Allen-Cahn (NtAC) model, where the standard Laplace operator …

This paper presents a method by combining the semi-implicit spectral deferred correction
(SDC) method with the operator splitting scheme to simulate the fractional Gray-Scott (GS) …

Abstract The convective Allen–Cahn (CAC) equation has been widely used for simulating
multiphase flows of incompressible fluids, which contains an extra convective term but still …