The University of Southampton
University of Southampton Institutional Repository

Computation of high-order maps to multiple machine precision

Computation of high-order maps to multiple machine precision
Computation of high-order maps to multiple machine precision

The Beam Dynamics simulation package in COSY INFINITY is built upon a differential algebra data type. With it, it is possible to compute transfer maps or arbitrary systems to arbitrary order. However, this data type is limited by the precision of the underlying floating point number model provided by the computer processor. We will present a method to extend the effective precision of the calculations based purely on standard floating point operations. Those algorithms are then integrated into the differential algebra data type to efficiently extend the available precision, without unnecessarily affecting overall efficiency. To that effect, the precision of each coefficient is adjusted automatically during the calculation. We will then proceed to show the effectiveness of our implementation by calculating high precision maps of combinations of homogeneous dipole segments, for which the exact results are known, and comparing the high precision coefficients with the results produced by the traditional COSY beam physics package.

COSY INFINITY, Differential algebra, High precision, High precision aberrations
0217-751X
1019-1039
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Berz, Martin
f8159a81-aa52-4ba3-8b8f-a672aec96b47
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Berz, Martin
f8159a81-aa52-4ba3-8b8f-a672aec96b47

Wittig, Alexander and Berz, Martin (2009) Computation of high-order maps to multiple machine precision. International Journal of Modern Physics A, 24 (5), 1019-1039. (doi:10.1142/S0217751X09044474).

Record type: Article

Abstract

The Beam Dynamics simulation package in COSY INFINITY is built upon a differential algebra data type. With it, it is possible to compute transfer maps or arbitrary systems to arbitrary order. However, this data type is limited by the precision of the underlying floating point number model provided by the computer processor. We will present a method to extend the effective precision of the calculations based purely on standard floating point operations. Those algorithms are then integrated into the differential algebra data type to efficiently extend the available precision, without unnecessarily affecting overall efficiency. To that effect, the precision of each coefficient is adjusted automatically during the calculation. We will then proceed to show the effectiveness of our implementation by calculating high precision maps of combinations of homogeneous dipole segments, for which the exact results are known, and comparing the high precision coefficients with the results produced by the traditional COSY beam physics package.

Full text not available from this repository.

More information

Published date: 20 February 2009
Keywords: COSY INFINITY, Differential algebra, High precision, High precision aberrations

Identifiers

Local EPrints ID: 419780
URI: http://eprints.soton.ac.uk/id/eprint/419780
ISSN: 0217-751X
PURE UUID: 5cbff76b-574e-4ad1-8fe5-db0403db681e
ORCID for Alexander Wittig: ORCID iD orcid.org/0000-0002-4594-0368

Catalogue record

Date deposited: 20 Apr 2018 16:30
Last modified: 07 Oct 2020 02:16

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×