×

Tools for scientific computation. (English) Zbl 0798.65095

Scientific Computation (short: SC) denotes the use of computers for the modelling and simulation of complex scientific and technological processes. Its goal is to perform specified computer simulation related tasks more reliably, quickly and cheaply, and more conveniently for the user. Thus the concept of tools is at the center of SC; the paper attempts a survey of the (1992) status of such tools. It begins with classifications from various points of views; then a number of typical tools are discussed in more detail. (Hardware oriented tools are omitted here.)
As an example of an integrated problem solving environment, //ELLPACK (“Parallel” ELLPACK) is presented and some of its principal aspects are discussed. The remainder of the paper is devoted to a closer look at a few important and novel tools for SC which are not as perfectly integrated as //ELLPACK. It begins with a description of the main features of LAPACK, the (then) new linear algebra library for high-performance computers. As an example of an algebraic tool, the use of Gröbner bases for the computation of zeros of multivariate polynomial systems is described. Tools for “Automatic differentiation” permit the use of analytic procedures in SC. More and more important are automatic restructuring tools which adapt programs to particular concurrent computer architectures. The selection of appropriate codes from program libraries requires yet another type of SC tools.
Some considerations about future developments and a list of relevant journals conclude the article.
Reviewer: H.J.Stetter

MSC:

65Nxx Numerical methods for partial differential equations, boundary value problems
65Fxx Numerical linear algebra
68W30 Symbolic computation and algebraic computation
65Y05 Parallel numerical computation
68-02 Research exposition (monographs, survey articles) pertaining to computer science
65H10 Numerical computation of solutions to systems of equations
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] ; : Scientific computing and differential equations – An introduction to numerical methods. Academic Press 1992. · Zbl 0749.65041
[2] ; : Solving elliptic problems using ELLPACK. Springer Series in Computational Math. 2, Springer-Verlag, Berlin etc. 1985. · Zbl 0562.65064
[3] Houstis, Math. Comp. Simul. 31 pp 497– (1989)
[4] The Parallel ELLPACK Group: /ELLPACK Programming environment: User’s guide. Dept. Comp. Sci. Report, Purdue University, Dec. 1991, 62 p.
[5] NCSA Group: NCSA X Dataslice for the XWindow system. Tech. Report, Univ. Illinois Urbana-Champaign, Sept. 1989.
[6] ; ; ; : LINPACK User’s guide. SIAM Press 1979.
[7] ; ; ; : Matrix eigensystem routines – EISPACK guide extension. Lecture Notes in Computer Science 51, Springer Verlag, Berlin etc. 1977. · Zbl 0368.65020
[8] Lawson, TOMS 5 pp 308– (1979)
[9] Dongarra, TOMS 14 pp 1– (1988)
[10] Dongarra, TOMS 16 pp 1– (1990)
[11] Fortran 90 ISO/IEC Standard 1539. ISO Publication Dept., Geneva 1991.
[12] ; : Fortran 90 explained. Oxford University Press 1990. · Zbl 0703.68030
[13] Schwarz, SIAM Rev. 30 pp 450– (1988)
[14] : Groebner bases: an algorithmic method in polynomial ideal theory. In: (ed.): Progress, directions and open problems in multidimensional systems theory. Reidel Publ. Co. 1985, pp. 184–232.
[15] ; : An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations. In: ; ; (eds.): Numerical mathematics. Singapore 1988. ISNM 86, Birkhäuser Verlag, Basel etc. 1989.
[16] ; (eds.): Automatic differentiation of algorithms: Theory, implementation, and applications. SIAM Press 1991.
[17] : A taxonomy of automatic differentiation tools. In: [16], pp. 315–329. · Zbl 0782.65029
[18] ; ; ; ; : ADIFOR–generating derivative codes from Fortran programs. Argonne Preprint MCS-P263-0991, Febr. 1992.
[19] Zima, Parallel Computing 6 pp 1– (1988)
[20] ; : Programming distributed memory architectures using Kali. In: ; ; ; (eds.): Advances in languages and compilers for parallel processing. Pitman/MIT Press 1991, pp. 364–384.
[21] MIMDizer User’s Guide, Version 7.02. Pacific Sierra Research Corp., Placerville CA 1991.
[22] Boisvert, Math. Comp. Simul. 31 pp 453– (1989)
[23] ; (Eds.): Programming environments for high-level scientific problem solving. Proc. Working Conference, Elsevier Science Publ. 1992.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.