Related papers: A Structure-Preserving Stagewise Rescaling Algorit…
We present error estimates for four unconditionally energy stable numerical schemes developed for solving Allen-Cahn equations with nonlocal constraints. The schemes are linear and second order in time and space, designed based on the…
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the…
The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears.…
Peridynamics is a nonlocal continuum-mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences…
In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…
To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown…
We report on the existence of stable, completely delocalized response regimes in a nonlinear defective periodic structure. In this state of complete delocalization, despite the presence of the defect, the system exhibits in-phase…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
The M1 moment model for electronic transport is commonly used to describe non-local thermal transport effects in laser-plasma simulations. In this article, we propose a new asymptotic-preserving scheme based on the Unified Gas Kinetic…
In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we…
We present a new asymptotic strategy for general micro-macro models which analyze complex viscoelastic fluids governed by coupled multiscale dynamics. In such models, the elastic stress appearing in the macroscopic continuum equation is…
This work focuses on the formulation of a four-equation model for simulating unsteady two-phase mixtures with phase transition and strong discontinuities. The main assumption consists in a homogeneous temperature, pressure and velocity…
In recent years, metasurfaces have shown extremely powerful abilities for manipulation of electromagnetic waves. However, the local electromagnetic response of conventional metasurfaces yields to an intrinsic performance limitation in terms…
Metasurfaces are extremely useful for controlling and manipulating electromagnetic waves. Full-wave numerical simulation is highly desired for their design and optimization, but it is notoriously difficult, even for two-dimensional…
Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme…
We present an adaptive space-time mesh refinement approach based a domain decomposition approach (Singh and Wheeler, 2018) that allows different time-step sizes and mesh refinements in different subdomains. Our numerical experiments…
A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to simultaneously upscale the stochastic solutions in the physical…
Programmable metasurfaces have recently attracted considerable interest for their versatile applications in areas such as beam steering, holography, and wireless communications, utilizing either phase or amplitude modulation. Despite this,…