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The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…
A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…
Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…
This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work…
Multiple-shooting is a parameter estimation approach for ordinary differential equations. In this approach, the trajectory is broken into small intervals, each of which can be integrated independently. Equality constraints are then applied…
In this paper, we study the existence of nontrivial solutions of the Dirichlet boundary value problem for the following elliptic system: \begin{equation} \left\{ \begin{aligned} -\Delta u & = au + bv + f(x,u,v); &\quad\mbox{ for…
We consider a projection method for time-dependent incompressible Navier-Stokes equations with a total pressure boundary condition. The projection method is one of the numerical calculation methods for incompressible viscous fluids often…
The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…
This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a…
Curvilinear, multiblock summation-by-parts finite difference operators with the simultaneous approximation term method provide a stable and accurate framework for solving the wave equation in second order form. That said, the standard…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear elliptic partial differential equations. In particular, our…
This research presents a dynamic modeling framework and parameter identification methods for describing the highly nonlinear behaviors of flexibly connected dual-AUV systems. The modeling framework is established based on the lumped mass…
In this work we discuss a Hamiltonian system of ordinary differential equations under Dirichlet boundary conditions. The system of equations in consideration features a mixed (concave-convex) power nonlinearity depending on a positive…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…
This work presents a new approach to efficiently model the cathode in the moving boundary value problem of electrochemical machining. Until recently, the process simulation with finite elements had the drawback of remeshing required by the…
Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the…
The problem of identifying an obstruction into a fluid duct has several applications, one of them, for example in medicine the presence of Stenosis in coronary vessels is a life threatening disease. In this paper, we formulate a continuous…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…