Summary form only given. The key architectural implications of realistically scaling a representative member of this important class of applications is examined. Using scaling methods that reflect the concerns of an application scientist leads to different conclusions than does naive scaling in terms of data set size. In particular, it is shown that under the most realistic scaling model, both the communication to computation ratio and the amount of cache memory per processor required for effective performance increase with scaling. The effect of a shared address space versus message passing as the communication abstraction is also examined. It is shown that the lack of a shared address space substantially increases the programming complexity and performance overheads of a message-passing implementation.