Automatic Grid Control in Adaptive BVP Solvers
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/634028
- author
- Pulverer, Gernot ; Söderlind, Gustaf LU and Weinmüller, Ewa
- organization
- publishing date
- 2008
- type
- 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
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- 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
- 2016-04-04 11:15:45
- date last changed
- 2018-11-21 21:03:42
@article{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 = {{Institute for Analysis and Scientific Computing Vienna University of Technology, Vienna}},
series = {{ASC Report No. 11/2008}},
title = {{Automatic Grid Control in Adaptive BVP Solvers}},
url = {{http://www.asc.tuwien.ac.at/preprint/2008/asc11x2008.pdf}},
volume = {{2008}},
year = {{2008}},
}