MULTIFRONTAL VS FRONTAL TECHNIQUES FOR ‘i. - CHEMICAL PROCESS SIMULATION ON ,. SUPERCOMPUTERS

A critical computational step in large-scale process simulation using rigorous equation-based models is the solution of a sparse linear equation system. Traditional sparse solvers based on indirect addressing are not effective on supercomputers because they do not vectorize well. By relying on vectorized dense matrix kernels, the multifrontal and frontal methods provide much better performance, as demonstrated using several examples. These examples are also used to compare the performance of frontal and multifrontal solvers. On problems with good initial matrix orderings the frontal method is most effective, while without a good initial ordering the multifrontal method is attractive. INTRODUCTION . . Steady-state or dynamic simulation tools are widely used in the design, optimization, and operation of chemical processes. Increasingly these tools are being used industrially in very large-scale, plantwide studies based on rigorous physical and chemical models. These trends have been made possible by impressive gains in computer performance and advances in numerical methods. Leading the way, modem supercomputers offer vector and parallel processing architectures for solving problems that, until now, could not be solved with other computational tools. Today, this leading-edge technology is increasingly seen at price levels that make it more widely available to process systems engineers. Thus, the use of supercomputer technolpgy in process simulation is more practicable than ever before, and provides opportunities to solve larger-scale and more realistic plant models than ever before. However, since most current methods for solving process simulation problems were developed for use on conventional serial machines, they usually do not effectively take advantage of the vector and parallel processing architecture of supercomputers. Thus, to exploit supercomputing (as opposed to just using a supercomputer) requires the rethinking of the solution strategies used in process simulation. In this t To whom all correspondence should be addressed. (Fax: 217-244-8068; Internet: [email protected]). Presented at Fifth International Symposium on Process Systems Engineering (PSE ‘94), Kyongju, Korea, 30 May-3 June, 1994. paper, we consider the sparse linear equation solving strategies used in this context.