Related papers: Nonlinearity continuation method for steady-state …
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…
In this article, we study the standing-wave solutions to a class of systems of nonlinear Schr\"odinger equations. Our target is all the standard forms of the NLS systems, with two unknowns, that have a common linear part and cubic…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
This paper focuses on power flow analysis through the lens of the Newton flow, a continuous-time formulation of Newton's method. Within this framework, we explore how quantized-state concepts, originally developed as an alternative to time…
This paper presents a more stable implementation and a highly accurate numerical tool for predicting flooding in urban areas. We started with the (linearised) well-posedness analysis by [1], where far-field boundary conditions were proposed…
State estimation from limited sensor measurements is ubiquitously found as a common challenge in a broad range of fields including mechanics, astronomy, and geophysics. Fluid mechanics is no exception -- state estimation of fluid flows is…
We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…
We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…
In this paper, we consider unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in unsaturated porous media, modeled by a non-linear extension of Biot's quasi-static consolidation model. The coupled, elliptic-parabolic…
The object of this paper is twofold. Firstly, we study a class of generalized Newtonian fluid related to "power law ". For the corresponding non-Newtonian Navier-Stokes problems, the existence of a weak and periodic solutions is proved in…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
In this paper we prove the existence and uniqueness of a solution to the nonstationary two dimensional system of equations describing miscible liquids with nonsmooth, multivalued and nonmonotone boundary conditions of subdifferential type.…
In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…
The aim of this paper is a short survey of models and methods that developed by the authors. These models and methods are used to optimize general networks with nonlinear non-convex restrictions and objectives possessing mixed…
We prove input-to-state stability (ISS) of perturbed Newton-type methods for generalized equations arising from Nash equilibrium (NE) and generalized NE (GNE) problems. This ISS property allows the use of inexact computations in…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
In this paper a problem of stationary flow of generalized Newtonian fluid in a thin channel is considered. An efficient algorithm of solution is proposed that includes a flexible procedure for a continuous approximation of the apparent…
A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…
In a Hilbert space setting, we study the stability properties of the regularized continuous Newton method with two potentials, which aims at solving inclusions governed by structured monotone operators. The Levenberg-Marquardt…
In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational…