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Title: On the Differential Algebra Underlying the COSY INFINITY Computer Code Due to M. Berz

Abstract

The mathematical foundations of the differential algebraic approach to beam optics due to M. Berz are described. They are simplified by identifying the underlying algebraic structure with the well known algebra of truncated polynomials. Concrete examples of derivations in this algebra, consistent with the truncation operation, are given.

Authors:
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1118957
Report Number(s):
BNL-101537-2013-IR
DOE Contract Number:
AC02-98CH10886
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; 97 MATHEMATICS AND COMPUTING

Citation Formats

Garczynski, V. On the Differential Algebra Underlying the COSY INFINITY Computer Code Due to M. Berz. United States: N. p., 1992. Web. doi:10.2172/1118957.
Garczynski, V. On the Differential Algebra Underlying the COSY INFINITY Computer Code Due to M. Berz. United States. doi:10.2172/1118957.
Garczynski, V. Wed . "On the Differential Algebra Underlying the COSY INFINITY Computer Code Due to M. Berz". United States. doi:10.2172/1118957. https://www.osti.gov/servlets/purl/1118957.
@article{osti_1118957,
title = {On the Differential Algebra Underlying the COSY INFINITY Computer Code Due to M. Berz},
author = {Garczynski, V.},
abstractNote = {The mathematical foundations of the differential algebraic approach to beam optics due to M. Berz are described. They are simplified by identifying the underlying algebraic structure with the well known algebra of truncated polynomials. Concrete examples of derivations in this algebra, consistent with the truncation operation, are given.},
doi = {10.2172/1118957},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Jul 01 00:00:00 EDT 1992},
month = {Wed Jul 01 00:00:00 EDT 1992}
}

Technical Report:

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  • This is a reference manual for the arbitrary order particle optics and beam dynamics code COSY INFINITY. It is current as of June 28, 1990. COSY INFINITY is a code to study and design particle optical systems, including beamlines, spectrometers, and particle accelerators. At its core it is using differential algebraic (DA) methods, which allow a very systematic and simple calculation of high order effects. At the same time, it allows the computation of dependences on system parameters, which is often interesting in its own right and can also be used for fitting. COSY INFINITY has a full structured objectmore » oriented language environment. This provides a simple interface for the casual user. At the same time, it offers the demanding user a very flexible and powerful tool for the study and design of systems, and more generally, the utilization of DA methods. The power and generality of the environment is perhaps best demonstrated by the fact that the physics routines of COSY INFINITY are written in its own input language and are very compact. The approach also considerably facilitates the implementation of new features because they are incorporated with the same commands that are used for design and study. 26 refs.« less
  • We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK's symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less
  • We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK`s symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less
  • The Differential Systems Simulator, Version 2(DSS/2), is a software package that can be used to solve sets of differential equations. This report discusses the work performed in implementing the package on the IBM 360/195 at K-25. It records the names of the data sets produced and the JCL procedures used. It is not intended as a detailed programer's guide for the installation of a system such as DSS/2. 7 figures, 2 tables.