相关论文: Absorbing boundary conditions for Einstein's field…
We present a method of deriving two boundary conditions at a thin membrane for diffusion from experimental data. This method can be really useful in complex membrane systems in which we do not know mechanisms of processes occurring within…
Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Methods currently detailed…
The Sommerfeld boundary conditions, applied to an asymptotically weak gravitational field, are shown to imply that the 1/r part of the curvature tensor of a space-time, satisfying the Einstein equations, is of type null in the Petrov…
We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant $\lambda$ are…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
In the computation of compressible fluid flows, numerical boundary conditions are always necessary for all physical variables at computational boundaries while just partial physical variables are often prescribed as physical boundary…
We consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…
We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
We study the situation in which the distribution of temperature a body is due to its interaction with radiation. We consider the boundary value problem for the stationary radiative transfer equation under the assumption of the local…
We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically…
Global uniform boundedness of solutions to 3D viscous Primitive equations in a bounded cylindrical domain with physical boundary condition is proved in space $H^m$ for any $m\geqslant2$. A bounded absorbing set for the solutions in $H^m$ is…
The choice of boundary condition makes an essential difference in the solution structure of diffusion equations. The Dirichlet and Neumann boundary conditions and their combination have been the most used, but their legitimacy has been…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
We study the existence and uniqueness of solutions to the static vacuum Einstein equations in bounded domains, satisfying the Bartnik boundary conditions of prescribed metric and mean curvature on the boundary.
We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are…
This paper is concerned with the Boltzmann equation with specular reflection boundary condition. We construct a unique global solution and obtain its large time asymptotic behavior in the case that the initial data is close enough to a…
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a…