相关论文: Excision and avoiding the use of boundary conditio…

We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…

Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…

We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples,…

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite…

We have considered a stationary outflowing envelope from the star accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with…

The Sommerfeld boundary conditions, imposed on hyperbolic differential equations to obtain solutions in the form of outgoing waves, are formulated here so as to make explicit the role of an appropriate null vector field. When applied to the…

We study the hydrodynamic behaviour of the asymmetric simple exclusion process on the lattice of size $n$. In the bulk, the exclusion dynamics performs rightward flux. At the boundaries, the dynamics is attached to reservoirs. We…

Using an approach that treats the Ricci scalar itself as a degree of freedom, we analyze the cosmological evolution within an f(R) model that has been proposed recently (exponential gravity) and that can be viable for explaining the…

We derive geometric formulas for the mass of asymptotically hyperbolic manifolds using coordinate horospheres. As an application, we obtain a new rigidity result of hyperbolic space: if a complete asymptotically hyperbolic manifold has…

In an attempt to simulate black hole echoes (generated by potential quantum-gravitational structure) in numerical relativity, we recently described how to implement a reflecting boundary outside of the horizon of a black hole in spherical…

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…

The complex Langevin method is a general method to treat systems with complex action, such as QCD at nonzero density. The formal justification relies on the absence of certain boundary terms, both at infinity and at the unavoidable poles of…

We propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables…

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation…

With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…

We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time,…

Many applications require efficient methods for solving continuous shortest path problems. Such paths can be viewed as characteristics of static Hamilton-Jacobi equations. Several fast numerical algorithms have been developed to solve such…

We study the dynamics of a non-minimally coupled scalar field cosmology with a potential function. We use the framework of dynamical systems theory to investigate all evolutional paths admissible for all initial conditions. Additionally, we…

In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a…

We prove an existence result for a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation…