Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs. Gallardo, J., Ortega-Acosta, S., de la Asunción, M., & Mantas-Ruiz, J. Journal of Scientific Computing, 48(1):141-163, 2011.
Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs [link]Paper  abstract   bibtex   
We present a new kind of high-order reconstruction operator of polynomial type, which is used in combination with the scheme presented in Castro et al. (J. Sci. Comput. 39:67–114, 2009 ) for solving nonconservative hyperbolic systems. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus achieving a substantial improvement of the speedup with respect to normal CPUs. As an application, the two-dimensional shallow water equations with geometrical source term due to the bottom slope is considered.
@Article{gallardo2011compact,
  author   = {Gallardo, Jos{\'e}-M. and Ortega-Acosta, Sergio and de la Asunci{\'o}n, Marc and Mantas-Ruiz, Jos{\'e}-Miguel},
  title    = {{T}wo-{D}imensional {C}ompact {T}hird-{O}rder {P}olynomial {R}econstructions. {S}olving {N}onconservative {H}yperbolic {S}ystems {U}sing {GPU}s},
  journal  = {Journal of Scientific Computing},
  year     = {2011},
  volume   = {48},
  number   = {1},
  pages    = {141-163},
  abstract = {We present a new kind of high-order reconstruction operator of polynomial type, which is used in combination with the scheme presented in Castro et al. (J. Sci. Comput. 39:67–114, 2009 ) for solving nonconservative hyperbolic systems. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus achieving a substantial improvement of the speedup with respect to normal CPUs. As an application, the two-dimensional shallow water equations with geometrical source term due to the bottom slope is considered.
},
  url      = {http://dx.doi.org/10.1007/s10915-011-9470-x},
}

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