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A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact…
This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…
Concerning the Laplace operator with homogeneous Dirichlet boundary conditions, the classical notion of isospectrality assumes that two domains are related when they give rise to the same spectrum. In two dimensions, non isometric,…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
The justification of hydrodynamic limits in non-convex domains has long been an open problem due to the singularity at the grazing set. In this paper, we investigate the unsteady neutron transport equation in a general bounded domain with…
We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary…
We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme to tackle a linear one-dimensional advection equation. By mapping lattice Boltzmann schemes to Finite Difference schemes, we…
We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an…
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…
We consider generic families $X_\param$ of smooth dynamical systems depending on parameters $\param\in P$ where $P$ is a 2-dimensional simply connected domain and assume that each $X_\param$ only has a finite number of restpoints and…
We present a numerical method to compute the Landauer conductance of noninteracting two-dimensional massless Dirac fermions in disordered systems. The method allows for the introduction of boundary conditions at the ribbon edges and…
We present a condition that guarantees spatially uniformity in the solution trajectories of a diffusively-coupled compartmental ODE model, where each compartment represents a spatial domain of components interconnected through diffusion…
In the context of integrable partial difference equations on quad-graphs, we introduce the notion of open boundary reductions as a new means to construct discrete integrable mappings and their invariants. This represents an alternative to…
In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…
This paper aims at determining under which conditions the semi-discrete optimal transport is twice differentiable with respect to the parameters of the discrete measure and exhibits numerical applications. The discussion focuses on minimal…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence…
Boundary problem for linear partial differential algebraic equations system with multiple characteristic curves is considered. It is supposed that matrix-functions pencil of the system under consideration is smoothly equivalent to special…
The covariant light-front equations have been solved exactly for a two fermion system with different boson exchange ladder kernels. We present a method to study the cutoff dependence of these equations and to determine whether they need to…
A numerical scheme utilizing a grid which is staggered in both space and time is proposed for the numerical solution of the (2+1)D Dirac equation in presence of an external electromagnetic potential. It preserves the linear dispersion…