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Volume 7, Issue 1
Stable and Accurate Second-Order Formulation of the Shifted Wave Equation

Ken Mattsson & Florencia Parisi

Commun. Comput. Phys., 7 (2010), pp. 103-137.

Published online: 2010-07

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  • Abstract

High order finite difference approximations are derived for a one-dimensional model of the shifted wave equation written in second-order form. The domain is discretized using fully compatible summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration. This discretization yields a strictly stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension. The present study is the first step towards a strictly stable simulation of the second-order formulation of Einstein's equations in three spatial dimensions.

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@Article{CiCP-7-103, author = {}, title = {Stable and Accurate Second-Order Formulation of the Shifted Wave Equation}, journal = {Communications in Computational Physics}, year = {2010}, volume = {7}, number = {1}, pages = {103--137}, abstract = {

High order finite difference approximations are derived for a one-dimensional model of the shifted wave equation written in second-order form. The domain is discretized using fully compatible summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration. This discretization yields a strictly stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension. The present study is the first step towards a strictly stable simulation of the second-order formulation of Einstein's equations in three spatial dimensions.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.08.135}, url = {http://global-sci.org/intro/article_detail/cicp/7621.html} }
TY - JOUR T1 - Stable and Accurate Second-Order Formulation of the Shifted Wave Equation JO - Communications in Computational Physics VL - 1 SP - 103 EP - 137 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/10.4208/cicp.2009.08.135 UR - https://global-sci.org/intro/article_detail/cicp/7621.html KW - AB -

High order finite difference approximations are derived for a one-dimensional model of the shifted wave equation written in second-order form. The domain is discretized using fully compatible summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration. This discretization yields a strictly stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension. The present study is the first step towards a strictly stable simulation of the second-order formulation of Einstein's equations in three spatial dimensions.

Ken Mattsson & Florencia Parisi. (2020). Stable and Accurate Second-Order Formulation of the Shifted Wave Equation. Communications in Computational Physics. 7 (1). 103-137. doi:10.4208/cicp.2009.08.135
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