#### DMCA

## Difference Approximations for the Second Order Wave Equation (2001)

Venue: | Center for Applied Scientific Computing, Lawrence Livermore National Lab |

Citations: | 21 - 2 self |

### Citations

178 | A Cartesian Grid Embedded Boundary Method for Poissons Equation on Irregular Domains”,
- Johansen
- 1998
(Show Context)
Citation Context ...as used by Ditkowski, Dridi, and Hesthaven [3] for solving Maxwell’s equations on a Cartesian grid. The methods described in these papers all solve first order systems (in time). Johansen and Colella =-=[6]-=- derived a finite-volume scheme for solving Poisson’s equation with Dirichlet boundary conditions using an embedded boundary technique. Away from the boundary, the truncation error for the Laplace ope... |

79 | An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions”,
- Pember, Bell, et al.
- 1995
(Show Context)
Citation Context ...thods for both the Neumann and Dirichlet problems. More recently, several embedded boundary methods have been presented for various types of partial differential equations. For example, Pember et al. =-=[8]-=- used a Cartesian grid method for solving the time-dependent equations of gas dynamics. Zhang and LeVeque [11] solved the acoustic wave equation with discontinuous coefficients written as a first orde... |

32 |
The immersed interface method for acoustic wave equations with discontinuous coefficients. Wave Motion,
- Zhang, LeVeque
- 1997
(Show Context)
Citation Context ... presented for various types of partial differential equations. For example, Pember et al. [8] used a Cartesian grid method for solving the time-dependent equations of gas dynamics. Zhang and LeVeque =-=[11]-=- solved the acoustic wave equation with discontinuous coefficients written as a first order system. They derived special difference stencils that satisfy the jump conditions at the interior interfaces... |

28 | Convergent cartesian grid methods for Maxwells equations in complex geometries,
- Ditkowski, Dridi, et al.
- 2001
(Show Context)
Citation Context ... special difference stencils that satisfy the jump conditions at the interior interfaces, where the coefficients are discontinuous. A staggered grid method was used by Ditkowski, Dridi, and Hesthaven =-=[3]-=- for solving Maxwell’s equations on a Cartesian grid. The methods described in these papers all solve first order systems (in time). Johansen and Colella [6] derived a finite-volume scheme for solving... |

22 |
The Numerical Treatment of Differential Equations, 3rd edition
- Collatz
- 1960
(Show Context)
Citation Context ...itions date back to Weller and Shortley [10], who used a finite-volume method (perhaps before that term was coined) to set up first order accurate difference approximations near the boundary. Collatz =-=[2]-=- derived higher order difference methods for both the Neumann and Dirichlet problems. More recently, several embedded boundary methods have been presented for various types of partial differential equ... |

17 | Block pseudospectral methods for Maxwell’s equations. II. Twodimensional, discontinuous-coefficient case
- DRISCOLL, FORNBERG
- 1999
(Show Context)
Citation Context ...irst order systems are by now well developed, and many useful techniques have been established, such as higher order accurate boundary conditions [9], accurate treatment of discontinuous coefficients =-=[4]-=-, and nonreflecting boundary conditions for external domains. The method presented here currently lacks these refinements, so a direct comparison on a realistic problem is hard to make. Instead, this ... |

9 |
Mesh refinement
- Browning, Kreiss, et al.
- 1973
(Show Context)
Citation Context ...oduce instabilities; see [5]. 4. If the solution is not properly resolved, i.e., if one does not use enough points/wavelength, then one creates spurious waves which travel in the wrong direction; see =-=[1]-=-. 1942 H.-O. KREISS, N. A. PETERSSON, AND J. YSTRÖM To avoid the three latter difficulties, one may introduce a so-called staggered grid. However, this amounts to nothing else but solving (1.4) in di... |

4 |
Calculation of stresses within the boundary of photoelastic models
- Weller, Shortley
- 1939
(Show Context)
Citation Context ...ue that directly approaches second order hyperbolic systems. Embedded boundary techniques for discretizing Laplace’s equation subject to Dirichlet boundary conditions date back to Weller and Shortley =-=[10]-=-, who used a finite-volume method (perhaps before that term was coined) to set up first order accurate difference approximations near the boundary. Collatz [2] derived higher order difference methods ... |

3 | Simulations of acoustic wave phenomena using high-order finite difference approximations
- Strand
- 1999
(Show Context)
Citation Context ...ration method for this system. Numerical methods for first order systems are by now well developed, and many useful techniques have been established, such as higher order accurate boundary conditions =-=[9]-=-, accurate treatment of discontinuous coefficients [4], and nonreflecting boundary conditions for external domains. The method presented here currently lacks these refinements, so a direct comparison ... |