The current state of the art in programming for scientific computing is still rather low-level. The mathematical model behind a computing application usually is written using pen and paper, whereas the corresponding numerical software often is developed manually in Fortran or C. This is especially true in application areas such as mechanical analysis, where complex non-linear problems are the norm, and high performance is required. Ideally, a high-level programming environment would provide computer support for these development steps. This motivated the development of the ObjectMath system. Using ObjectMath, complex mathematical models may be structured in an object oriented way, symbolically simplified, and transformed to efficient numerical code in C++ or Fortran.
However, many scientific computing problems are quite computationally demanding, which makes it desirable to use parallel computers. Unfortunately, generating parallel code from arbitrary mathematical models is an intractable problem. Therefore, we have focused most of our efforts on a specific problem domain where the main computation is to solve ordinary differential equation systems where most of the computing time is spent in application specific code, rather than in the serial solver kernel. We have investigated automatic parallelisation of the computation of ordinary differential equation systems at three different levels of granularity: the equation system level, the equation level, and the clustered task level. At the clustered task level we employ domain specific knowledge and existing scheduling and clustering algorithms to partition and distribute the computation.
Kluwer Academic Publishers, 1997.