Related papers: Ghost Force Influence of a Quasicontinuum Method i…
Numerical error induced by the "ghost forces" in the quasicontinuum method is studied in the context of dynamic problems. The error in the ({W}^{1,\infty}) norm is analyzed for the time scale (\mc{O}(\eps)) and the time scale (\mc{O}(1))…
We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation is derived as the modification of an energy-based…
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around…
In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is…
The "Auxiliary Extra Dimension" model was proposed in order to provide a geometrical interpretation to modifications of general relativity, in particular to non-linear massive gravity. In this context, the theory was shown to be ghost free…
In this paper we develop a new Peridynamic approach that naturally includes varying horizon sizes and completely solves the "ghost force" issue. Therefore, the concept of dual-horizon is introduced to consider the unbalanced interactions…
Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating…
Exhaustive ghost solutions to Einstein-Weyl equations for two dimensional spacetimes are obtained, where the ghost neutrinos propagate in the background spacetime, but do not influence the background spacetime due to the vanishing…
We consider an open, bounded, simply connected (Lipschitz) domain in $\mathbb{R}^d$, which contains a closed polyhedral surface or polygonal contour, referred to as the interface. From this interface, forces are exerted in the normal…
We study a rarefied gas, described by the Boltzmann equation, between two coaxial rotating cylinders in the small Knudsen number regime. When the radius of the inner cylinder is suitably sent to infinity, the limiting evolution is expected…
The ghost fluid method allows a propagating interface to remain sharp during a numerical simulation. The solution of the Riemann problem at the interface provides proper information to determine interfacial fluxes as well as the velocity of…
In this paper, we present and analyze an unfitted finite element method for the elliptic interface problem. We consider the case that the interface is $C^2$-smooth or polygonal, and the exact solution $u \in H^{1+s}(\Omega_0 \cup \Omega_1)$…
We present multigrid methods for solving elliptic partial differential equations on arbitrary domains using the nodal ghost finite element method, an unfitted boundary approach where the domain is implicitly defined by a level-set function.…
The Hessian's determinant for a version of massive gravity given by an infinite expansion of a square root function of the induced metric, vanishes. We show that it allows us to eliminate one of four scalar fields used to generate the…
The unstable nature of the material point method is widely documented and is a barrier to the method being used for routine engineering analyses of large deformation problems. The vast majority of papers concerning this issue are focused on…
Possible nonlinear completion of massive gravity is presented. An additional scalar ghost contained in linear theory condensates to give rise to positive-energy excitations.
We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor that impedes the propagations of electromagnetic waves. Our method is a modification of the existing approach…
We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical…
Galileons are higher-derivative theories of a real scalar which nevertheless admit second order equations of motion. They have interesting applications as dark energy models and in early universe cosmology, and have been conjectured to…
This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges arising from irregular domains. Both finite element method…