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Automatic Grid Control in Adaptive BVP Solvers

Pulverer, Gernot; Söderlind, Gustaf LU and Weinmüller, Ewa (2008) In ASC Report No. 11/2008 2008(11).
Abstract
Modern adaptive techniques in two-point boundary value problems generate the mesh by constructing a function that maps a uniform grid to the desired nonuniform grid. This paper describes a new control algorithm for constructing a grid density function $phi(x)$, such that the local mesh width $Delta x_{j+1/2}=x_{j+1}-x_j$ is computed as $Delta x_{j+1/2} = varepsilon_N / varphi_{j+1/2}$. Here $varepsilon_N$ is the accuracy control parameter corresponding to $N$ interior points, while ${varphi_{j+1/2}}_0^N$ is a discrete approximation to $phi(x)$ accounting for mesh width variation. Feedback control theory is applied to generate a new density from the previous one. Further, digital filters may be employed to process the error estimate as well... (More)
Modern adaptive techniques in two-point boundary value problems generate the mesh by constructing a function that maps a uniform grid to the desired nonuniform grid. This paper describes a new control algorithm for constructing a grid density function $phi(x)$, such that the local mesh width $Delta x_{j+1/2}=x_{j+1}-x_j$ is computed as $Delta x_{j+1/2} = varepsilon_N / varphi_{j+1/2}$. Here $varepsilon_N$ is the accuracy control parameter corresponding to $N$ interior points, while ${varphi_{j+1/2}}_0^N$ is a discrete approximation to $phi(x)$ accounting for mesh width variation. Feedback control theory is applied to generate a new density from the previous one. Further, digital filters may be employed to process the error estimate as well as the step density, and causal digital filters can be used in the mesh refining step. (Less)
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author
organization
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Contribution to journal
publication status
published
subject
in
ASC Report No. 11/2008
volume
2008
issue
11
publisher
Institute for Analysis and Scientific Computing Vienna University of Technology, Vienna
language
English
LU publication?
yes
id
156da733-230e-4b79-ada3-1bd38bcea67b (old id 634028)
alternative location
http://www.asc.tuwien.ac.at/preprint/2008/asc11x2008.pdf
date added to LUP
2009-05-28 15:00:33
date last changed
2016-06-03 11:16:46
@misc{156da733-230e-4b79-ada3-1bd38bcea67b,
  abstract     = {Modern adaptive techniques in two-point boundary value problems generate the mesh by constructing a function that maps a uniform grid to the desired nonuniform grid. This paper describes a new control algorithm for constructing a grid density function $phi(x)$, such that the local mesh width $Delta x_{j+1/2}=x_{j+1}-x_j$ is computed as $Delta x_{j+1/2} = varepsilon_N / varphi_{j+1/2}$. Here $varepsilon_N$ is the accuracy control parameter corresponding to $N$ interior points, while ${varphi_{j+1/2}}_0^N$ is a discrete approximation to $phi(x)$ accounting for mesh width variation. Feedback control theory is applied to generate a new density from the previous one. Further, digital filters may be employed to process the error estimate as well as the step density, and causal digital filters can be used in the mesh refining step.},
  author       = {Pulverer, Gernot and Söderlind, Gustaf and Weinmüller, Ewa},
  language     = {eng},
  number       = {11},
  publisher    = {ARRAY(0x96afa70)},
  series       = {ASC Report No. 11/2008},
  title        = {Automatic Grid Control in Adaptive BVP Solvers},
  volume       = {2008},
  year         = {2008},
}