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Difference Approximations for the Second Order Wave Equation
 Center for Applied Scientific Computing, Lawrence Livermore National Lab
, 2001
"... Abstract. Difference approximations are derived for the second order wave equation in one and two space dimensions, without first writing it as a first order system. Both the Dirichlet and the Neumann problems are treated for the onedimensional case. Relations between the boundary error and the int ..."
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Cited by 21 (2 self)
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Abstract. Difference approximations are derived for the second order wave equation in one and two space dimensions, without first writing it as a first order system. Both the Dirichlet and the Neumann problems are treated for the onedimensional case. Relations between the boundary error
A STUDY INTO DISCONTINUOUS GALERKIN METHODS FOR THE SECOND ORDER WAVE EQUATION
, 2015
"... A study into discontinuous Galerkin methods for the second order wave equation Davis, Benjamin J. ..."
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A study into discontinuous Galerkin methods for the second order wave equation Davis, Benjamin J.
Time and Space Adaptivity for the SecondOrder Wave Equation
, 2004
"... The aim of this paper is to show that, for a linear secondorder hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise linear finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a ..."
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Cited by 6 (2 self)
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The aim of this paper is to show that, for a linear secondorder hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise linear finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive
Perfectly Matched Layers for Second Order Wave Equations
, 2010
"... Numerical simulation of propagating waves in unbounded spatial domains is a challenge common to many branches of engineering and applied mathematics. Perfectly matched layers (PML) are a novel technique for simulating the absorption of waves in open domains. The equations modeling the dynamics of ph ..."
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Cited by 1 (1 self)
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of phenomena of interest are usually posed as differential equations (or integral equations) which must be solved at every time instant. In many application areas like general relativity, seismology and acoustics, the underlying equations are systems of second order hyperbolic partial differential equations
Time and Space Adaptivity for the SecondOrder Wave Equation
"... The aim of this paper is to show that, for a linear secondorder hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise a#ne finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a p ..."
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The aim of this paper is to show that, for a linear secondorder hyperbolic equation discretized by the backward Euler scheme in time and continuous piecewise a#ne finite elements in space, the adaptation of the time steps can be combined with spatial mesh adaptivity in an optimal way. We derive a
Difference approximations of the Neumann problem for the second order wave equation
 SIAM J. Numer. Anal
, 2004
"... Abstract. Stability theory and numerical experiments are presented for a finite difference method that directly discretizes the Neumann problem for the second order wave equation. Complex geometries are discretized using a Cartesian embedded boundary technique. Both second and third order accurate a ..."
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Cited by 9 (1 self)
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Abstract. Stability theory and numerical experiments are presented for a finite difference method that directly discretizes the Neumann problem for the second order wave equation. Complex geometries are discretized using a Cartesian embedded boundary technique. Both second and third order accurate
Energy conserving explicit local timestepping for secondorder wave equations
 SIAM J. Sci. Comput
"... Abstract. Locally refined meshes impose severe stability constraints on explicit timestepping methods for the numerical simulation of time dependent wave phenomena. To overcome that stability restriction, local timestepping methods are developed, which allow arbitrarily small time steps precisely ..."
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Cited by 20 (3 self)
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the standard secondorder “leapfrog ” scheme, timestepping methods of arbitrary order of accuracy are derived. Numerical experiments illustrate the efficiency and usefulness of these methods and validate the theory. Key words. secondorder hyperbolic problems, explicit methods, time reversible methods
SecondOrder Wave Equation for Spin Fields: 8Spinors and Canonical Formulation
, 1987
"... The algebraic structure of the 8spinor formalism is ' discussed, and the general jorm of the 8component wave equation, equivalent to the secondorder 4component one, is presented. This allows a canonical formulation that will be the first stage of the future Clebsch parametrization, i,e., a ..."
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The algebraic structure of the 8spinor formalism is ' discussed, and the general jorm of the 8component wave equation, equivalent to the secondorder 4component one, is presented. This allows a canonical formulation that will be the first stage of the future Clebsch parametrization, i
The Influence of the Mass Matrix on the Dispersive Nature of the SemiDiscrete, SecondOrder Wave Equation
, 1998
"... The application of discrete solution methods to the secondorder wave equation can yield a dispersive representation of the nondispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of pr ..."
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Cited by 7 (2 self)
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The application of discrete solution methods to the secondorder wave equation can yield a dispersive representation of the nondispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction
Results 1  10
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16,124