Strategies for producing fast finite element solutions of the incompressible Navier-Stokes equations on massively parallel architectures

Abstract

To take advantage of the inherent flexibility of the finite element method in solving for flows within complex geometries, it is necessary to produce efficient implementations of the method. Segregation of the solution scheme and the use of parallel computers are two ways of doing this. Here, the optimisation of a sequential segregated finite element algorithm is discussed, together with the various strategies by which this is done. Furthermore, the implications of parallelising the code onto a massively parallel computer, the MasPar, are explored. This machine is of Single Instruction Multiple Data type and so modifications to the computer code have been necessary. A general methodology for the implementation of finite element programs is presented based on projecting the levels of data within the algorithm into a form which is ideal for parallelisation. Application of this methodology, in a high level language, has resulted in a code which runs at just under 30MFlops (in double precision). The computations are performed with minimal inter-processor communication and this represents an efficiency of 20% of the theoretical peak speed. Even though only high level language constructs have been used, this efficiency is comparable with other work using low level constructs on machines of this architecture. In particular, the use of data parallel arrays and the utilisation of the non-unique machine specific features of the computer architecture have produced an efficient, fast program