Related papers: Linear Stationary Iterative Methods for the Force-…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
The phenomenon of linear motion of conductor in a magnetic field is commonly found in electric machineries such as, electromagnetic brakes, linear induction motor, electromagnetic flowmeter etc. The design and analysis of the same requires…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…
In this paper, pseudo-transient continuation method has been modified and implemented in power system long-term stability analysis. This method is a middle ground between integration and steady state calculation, thus is a good compromise…
Stability issues with reinforcement learning methods persist. To better understand some of these stability and convergence issues involving deep reinforcement learning methods, we examine a simple linear quadratic example. We interpret the…
To address the computational challenges of ab initio molecular dynamics and the accuracy limitations of empirical force fields, the introduction of machine learning force fields has proven effective in various systems including metals and…
In this paper, we propose a multiphysics finite element method for a quasi-static thermo-poroelasticity model with a nonlinear convective transport term. To design some stable numerical methods and reveal the multi-physical processes of…
Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the…
In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories,…
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
The following paper compares a consistent Newton-Raphson and fixed-point iteration based solution strategy for a variational multiscale finite element formulation for incompressible Navier-Stokes. The main contributions of this work include…
Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…
This paper introduces Force Matching (ForM), a novel framework for generative modeling that represents an initial exploration into leveraging special relativistic mechanics to enhance the stability of the sampling process. By incorporating…
A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant…
This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element…