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Boundary Conditions

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Shaoqiang Tang – One of the best experts on this subject based on the ideXlab platform.

  • Matching Boundary Conditions for lattice dynamics
    International Journal for Numerical Methods in Engineering, 2012
    Co-Authors: Xianming Wang, Shaoqiang Tang
    Abstract:

    SUMMARY We design a class of accurate and efficient absorbing Boundary Conditions for molecular dynamics simulations of crystalline solids. In one space dimension, the proposed matching Boundary Conditions take the form of a linear constraint of displacement and velocity at atoms near the Boundary, where the coefficients are determined by matching the dispersion relation with a minimal number of atoms involved. Bearing the nice features of compactness, locality, and high efficiency, the matching Boundary Conditions are then extended to treat the out-of-plane wave problems in the square lattice. We construct multidirectional absorbing Boundary Conditions via operator multiplications. Reflection coefficient analysis and numerical studies verify their effectiveness for spurious reflection suppression in all directions. Compact and local in both space and time, they are directly applicable to nonlinear lattices and multiscale simulations. Copyright © 2012 John Wiley & Sons, Ltd.

  • Matching Boundary Conditions for diatomic chains
    Computational Mechanics, 2010
    Co-Authors: Xianming Wang, Shaoqiang Tang
    Abstract:

    We propose a class of efficient matching Boundary Conditions to suppress spurious reflection for multiscale computations of one dimensional diatomic chains. This provides the first local effective treatment of both acoustic and optical phonons. Adopting the extended zone scheme of the dispersion relation, we design a class of force Boundary Conditions by enforcing perfect absorption at certain selected wave numbers. Reflection suppression is improved by involving more neighboring atoms in the condition. The effectiveness of the proposed matching Boundary Conditions is demonstrated by reflection coefficient analysis, numerical tests, and comparisons with the time history treatment.

Peter Van Nieuwenhuizen – One of the best experts on this subject based on the ideXlab platform.

  • Consistent Boundary Conditions for open strings
    Nuclear Physics B, 2003
    Co-Authors: Ulf Lindström, Martin Rocek, Peter Van Nieuwenhuizen
    Abstract:

    Abstract We study Boundary Conditions for the bosonic, spinning (NSR) and Green–Schwarz open string, as well as for (1+1)-dimensional supergravity. We consider Boundary Conditions that arise from (1) extremizing the action, (2) BRST, rigid or local supersymmetry, or κ(Siegel)-symmetry of the action, (3) closure of the set of Boundary Conditions under the symmetry transformations, and (4) the Boundary limits of bulk Euler–Lagrange equations that are “conjugate” to other Boundary Conditions. We find corrections to Neumann Boundary Conditions in the presence of a bulk tachyon field. We discuss a Boundary superspace formalism. We also find that path integral quantization of the open string requires an infinite tower of Boundary Conditions that can be interpreted as a smoothness condition on the doubled interval; we interpret this to mean that for a path-integral formulation of open strings with only Neuman Boundary Conditions, the description in terms of orientifolds is not just natural, but is actually fundamental.

Xianming Wang – One of the best experts on this subject based on the ideXlab platform.

  • Matching Boundary Conditions for lattice dynamics
    International Journal for Numerical Methods in Engineering, 2012
    Co-Authors: Xianming Wang, Shaoqiang Tang
    Abstract:

    SUMMARY We design a class of accurate and efficient absorbing Boundary Conditions for molecular dynamics simulations of crystalline solids. In one space dimension, the proposed matching Boundary Conditions take the form of a linear constraint of displacement and velocity at atoms near the Boundary, where the coefficients are determined by matching the dispersion relation with a minimal number of atoms involved. Bearing the nice features of compactness, locality, and high efficiency, the matching Boundary Conditions are then extended to treat the out-of-plane wave problems in the square lattice. We construct multidirectional absorbing Boundary Conditions via operator multiplications. Reflection coefficient analysis and numerical studies verify their effectiveness for spurious reflection suppression in all directions. Compact and local in both space and time, they are directly applicable to nonlinear lattices and multiscale simulations. Copyright © 2012 John Wiley & Sons, Ltd.

  • Matching Boundary Conditions for diatomic chains
    Computational Mechanics, 2010
    Co-Authors: Xianming Wang, Shaoqiang Tang
    Abstract:

    We propose a class of efficient matching Boundary Conditions to suppress spurious reflection for multiscale computations of one dimensional diatomic chains. This provides the first local effective treatment of both acoustic and optical phonons. Adopting the extended zone scheme of the dispersion relation, we design a class of force Boundary Conditions by enforcing perfect absorption at certain selected wave numbers. Reflection suppression is improved by involving more neighboring atoms in the condition. The effectiveness of the proposed matching Boundary Conditions is demonstrated by reflection coefficient analysis, numerical tests, and comparisons with the time history treatment.

Ercília Sousa – One of the best experts on this subject based on the ideXlab platform.

  • High-order methods and numerical Boundary Conditions
    Computer Methods in Applied Mechanics and Engineering, 2007
    Co-Authors: Ercília Sousa
    Abstract:

    Abstract In this paper we present high-order difference schemes for convection diffusion problems. When we apply high-order numerical methods to problems where physical Boundary Conditions are not periodic there is a need to choose adequate numerical Boundary Conditions in order to preserve the high-order accuracy. Next to the Boundary we do not usually have enough discrete points to apply the high-order scheme and therefore at these nodes we must consider different approximations, named the numerical Boundary Conditions. The choice of numerical Boundary Conditions can influence the overall accuracy of the scheme and most of the times do influence the stability. Here, we discuss which orders of accuracy are reasonable to be considered at the numerical Boundary Conditions, such that we do not pay a high price in accuracy and stability.

  • On the influence of numerical Boundary Conditions
    Applied Numerical Mathematics, 2002
    Co-Authors: Ercília Sousa, Ian Sobey
    Abstract:

    Our understanding about the behaviour of numerical solutions for evolutionary convectiondiffusion equations is mainly based on analysis of infinite domains situations with stability given by yon Neumann analysis. Almost all practical problems involve physical domains with boundaries. For evolution problems with Dirichlet Boundary Conditions, some algorithms can be used without alteration near a Boundary. However, the application of higher order methods such as Quickest or second order upwinding introduces difficulty near an inflow Boundary, since for interior points adjacent to the Boundary there are insufficient upstream points for the high order scheme to be applied without alteration. For that reason such methods require a careful treatment on the inflow Boundary, where additional numerical Boundary Conditions have to be introduced. The choice of numerical Boundary Conditions turns out to be crucial for stability. A test problem is described, showing the practical advantages of some numerical Boundary Conditions versus the others by comparison with an exact solution.

Ulf Lindström – One of the best experts on this subject based on the ideXlab platform.

  • Consistent Boundary Conditions for open strings
    Nuclear Physics B, 2003
    Co-Authors: Ulf Lindström, Martin Rocek, Peter Van Nieuwenhuizen
    Abstract:

    Abstract We study Boundary Conditions for the bosonic, spinning (NSR) and Green–Schwarz open string, as well as for (1+1)-dimensional supergravity. We consider Boundary Conditions that arise from (1) extremizing the action, (2) BRST, rigid or local supersymmetry, or κ(Siegel)-symmetry of the action, (3) closure of the set of Boundary Conditions under the symmetry transformations, and (4) the Boundary limits of bulk Euler–Lagrange equations that are “conjugate” to other Boundary Conditions. We find corrections to Neumann Boundary Conditions in the presence of a bulk tachyon field. We discuss a Boundary superspace formalism. We also find that path integral quantization of the open string requires an infinite tower of Boundary Conditions that can be interpreted as a smoothness condition on the doubled interval; we interpret this to mean that for a path-integral formulation of open strings with only Neuman Boundary Conditions, the description in terms of orientifolds is not just natural, but is actually fundamental.