Concurrent dynamic simulation: multicomputer algorithms research applied to ordinary differential-algebraic process systems in chemical engineering

We consider systematic parallel solution of ordinary differential-algebraic equations (DAE's) of low index (including stiff ODE's). We target multicomputers, message-passing concurrent computers, such as Intel's iPSC/2 hypercube and the Symult s2010 2D mesh. The programming model is reactive and/or loosely synchronized communicating sequential processes. We present new approaches to efficient application-level message passing through the Zipcode communication layer (built upon the Caltech Reactive Kernel), which is shown to be both portable and effective for complex multicomputer codes. Zipcode promotes the elegant expression of message passing in large applications, an important sub-goal. We present closed-form O(1)-memory, O(1)-time data distributions providing parametric control over degree of coefficient blocking and scattering. These new distributions permit effective formulations of the DAE's and higher sparse linear algebra performance. We present results for concurrent sparse, unsymmetric linear algebra. A two-phase approach is used, like Harwell's MA28. New results include: reduced communication pivoting and improvement of triangular-solve performance via the parametric distributions: LU factorization load balance is traded against solve performance. Overall performance is thereby increased. Good factorization speedups are attained for examples, but exploitation of multiple concurrent pivots remains a needed extension. Triangular solves prove disappointing on an absolute scale, despite significant effort. Two approaches to concurrent simulation are developed: the Waveform Relaxation (Picard-Lindelof) methodology extends to binary distillation simulation and further; it is inherently very concurrent. We address the achievable concurrent performance of sequential approaches via Concurrent DASSL, which extends Petzold's DASSL algorithm to multicomputers. A simulation driver for arbitrary networks of distillation columns is described. For a 9009-integration-state system with seven distillation columns, we demonstrate a speedup of approximately five. The low speedup is attributable to the simplicity of the thermodynamic model used, and the nearly narrow-banded Jacobian structure. Other chemical-engineering systems could perform substantially better. We suggest Waveform Relaxation as the key focus of future research for the particular distillation problem class cited. We indicate future areas for application of Concurrent DASSL, and suggest ways to improve its concurrent performance, coupled with improvements in sparse linear algebra