Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients

@article{Owhadi2017GambletsFO,
  title={Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients},
  author={H. Owhadi and L. Zhang},
  journal={J. Comput. Phys.},
  year={2017},
  volume={347},
  pages={99-128}
}
  • H. Owhadi, L. Zhang
  • Published 2017
  • Mathematics, Computer Science
  • J. Comput. Phys.
  • Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems at each time step constitutes a complexity bottleneck in their application to PDEs with rough coefficients. We present a generalization of gamblets introduced in [62] enabling the resolution of these implicit systems in near-linear complexity and provide rigorous a-priori error bounds on the resulting numerical… CONTINUE READING
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