SUMMARYA wide variety of methods have been proposed for solving implicit second-order systems of differential equations such as arise in structural and mechanical vibration analyses. Here we discuss a class of methods, based on second derivative formulae, some of which have previously been used by Enright.' We show them to have desirable analytic and implementation properties. We relate these methods to others recently proposed by Brusa and Nigro and by Serbin, showing that we obtain algorithms which have all the desirable properties of their methods and which can also be extended to classes of practical problems which were not considered by these other authors. Since implicit first-order systems are also important in practice, for example in finite element analyses of heat conduction problems, we demonstrate the efficient implementation of the second derivative formulae in this case too.

No abstract

No abstract

SUMMARYIn computational mechanics analyses such as those in computational uid dynamics and computational structure mechanics, some 60 -90% of total modelling time is taken by specifying and creating the model of the geometry and mesh. The rest of the time is spent in actual analyses and interpreting the results. This is especially true for industries such as aerospace and electronics, where 3D geometrically complex models with multiple physical processes are common. Advances in computational hardware and software have tended to increase the proportion of time spent in model creation, partly because such advances have made it feasible to solve hard and complex geometry problems in a timely fashion. This paper shows one way to exploit the advances in computation to reduce the model creation time and potentially the overall modelling time, namely the use of domain decomposition to deÿne consistent and coherent global models based on existing component geometry and mesh models. In keeping with existing modelling processes the re-engineering cost for the process is minimal.

SUMMARYThis is the first of a series of papers on the Genesis distributed-memory benchmarks, which were developed under the European ESPRIT research program. The benchmarks provide a standard reference Fortran77 uniprocessor version, a distributed memory MIMD version, and in some cascs a Fortran90 vcrsion suitable for SIMD computers. The problems selected all have a scientific origin (mostly from physics or theoretical chemistry), and range from synthetic code fragments dcsigncd to mcasurc the basic hardware properties of the computer (especially communication and synchronisation overheads), through commonly used library submutines, to full application codes. This first paper defines the methodology to be used to analyse the benchmark results, and gives an example of a fully analysed application benchmark from General Relativity (CR1). First, suitable absolute performance metrics are carefully defined, then thc pcrformance analysis treats the execution time and absolute pcrformance as functions of at least two variables, namely the problem size and the number of proecssors. The theoretical predictions are compared with, or fitted to, the measured results, and then used to predict (with due caution) how the performance might scale for larger problems and more processors than were actually available during the benchmarking. Benchmark measurements are given primarily for the Geman SUPRENUM computer, but also for the IBM 30835, Convcx C210 and a Parsys Supernode with 32 T800-20 transputers.

No abstract

No abstract

SUMMARYWe extend the well-known Houbolt method for dynamic vibration problems to a class of methods suitable for a variable-order variable-step computer program implementation. We discuss the numerical stability properties of these methodsand derive a family of extensions with improved stability properties. Finally we present some numerical results which compare a variety of Houbolt methods with other well-known Backward Differentiation methods, demonstrating in passing the practical value of the stability concepts.