Introduction to the Workshop: Some Bottlenecks and Deficiencies of Existing Vector Computers and Their Consequences for the Development of General PDE Software

In the first part of this introductory paper a review of the different types of vector computer programs and algorithms is presented. Then the hardware of the presently most relevant vector computers together with their bottlenecks will be discussed as well as the trends in development. The weakest point of the existing vector computers is the compiler, this problem is closely related to the lacking vector statements of Fortran 77. Therefore some proposals of Fortran 8X will be presented. In the second part of this paper the authors report about some experiences which have been obtained in the development of “black-box software” for PDE’s. There will be given a pragmatic definition of a “data flow algorithm”, and the separation of data selection and processing will be demonstrated for the evaluation of difference formulae. Then the i/o bottleneck is discussed for the iterative solution of large linear systems in diagonal storing. There will be presented our view of portability of software for different vector computers. The numerical example for ILU-preconditioning demonstrates how vecto-risation might invert experiences gained on general purpose computers. Finally some examples demonstrate the application of the Fidisol program package on different vector computers.