Numerical treatment of interfaces for second-order wave equations

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On the Existence of Energy Estimates for Difference Approximations for Hyperbolic Systems

H.-O. Kreiss and G. Scherer · 1977

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Summation by Parts for Finite Difference Approximations for d / d ​ x d/dx

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A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy

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Summation by parts operators for finite difference approximations of second derivatives

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3D simulations of Einstein’s equations: Symmetric hyperbolicity, live gauges, and dynamic control of the constraints

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Towards standard testbeds for numerical relativity

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Implicit-Explicit Runge-Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

Lorenzo Pareschi and Giovanni Russo · 2005

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Modeling the black hole excision problem

B. Szilágyi, H.-O. Kreiss, and J. Winicour · 2005

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Harmonic initial-boundary evolution in general relativity

Original

M. C. Babiuc, B. Szilágyi, and J. Winicour · 2006

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Optimized high-order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions

P. Diener, E. N. Dorband, E. Schnetter, and M. Tiglio · 2007

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Stable and Accurate wave–propagation in discontinuous media

Ken Mattsson, Frank Ham, and Gianluca Iaccarino · 2008

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Stable and Accurate Second-Order Formulation of the Shifted Wave Equation

Ken Mattsson and Florencia Parisi · 2010

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