The three-layer Saffman-Taylor problem introduces two coupled moving interfaces
separating the three fluids. A very recent weakly nonlinear analysis of this problem in a …

In this paper, we present an efficient rescaling scheme for computing the long-time dynamics
of expanding interfaces. The idea is to design an adaptive time-space mapping such that in …

Performing magnetostatic analysis accurately and efficiently is very important for multi-
objective optimization of electromagnetic device designs. In this research, a kernel-free …

In this work, we propose a second-order version and a fourth-order version of a Cartesian
grid-based boundary integral method for an interface problem of the Laplace equation on …

We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw cell subject to
an in-plane applied electric field. We develop a spectrally accurate boundary integral …

The evolution of precipitates in stressed solids is modeled by coupling a quasi-steady
diffusion equation and a linear elasticity equation with dynamic boundary conditions. The …

We investigate the disturbance flow generated by the oscillatory motion of a solid particle in
linear viscoelastic (LVE) fluids. We begin with one-mode Maxwell fluids and then add …

Abstract The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific
community of diffuse-interface methods. To accurately capture the long-time evolution of the …

In this paper, we investigate numerically the long-time dynamics of a two-dimensional
dendritic precipitate. We focus our study on the self-similar scaling behavior of the primary …

Performing magnetostatic analysis accurately and efficiently is crucial for the multi-objective
optimization of electromagnetic device designs. Therefore, an accurate and computationally …