Stencils and problem partitionings: their influence on the performance of multiple processor systems
IEEE Transactions on Computers
A Partitioning Strategy for Nonuniform Problems on Multiprocessors
IEEE Transactions on Computers
Communication effect basic linear algebra computations on hypercube architectures
Journal of Parallel and Distributed Computing
On mapping parallel algorithms into parallel architectures
Journal of Parallel and Distributed Computing
Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
Parallel solution of triangular systems on distributed-memory multiprocessors
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Limits on parallelism in the numerical solution of linear partial differential equations
SIAM Journal on Scientific and Statistical Computing
Some Complexity Results for Matrix Computations on Parallel Processors
Journal of the ACM (JACM)
Structure of Computers and Computations
Structure of Computers and Computations
Your Favorite Parallel Algorithms Might Not Be as Fast as You Think
IEEE Transactions on Computers
Information requirements and the implications for parallel computation
Information requirements and the implications for parallel computation
On the Impact of Communication Complexity on the Design of Parallel Numerical Algorithms
IEEE Transactions on Computers
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In earlier work, it was established that, for a large class of linear partial differential equations (PDEs), increasing the problem size necessarily increases the amount of data that is needed to approximate the solution of some scalar value in the solution field. In consequence, increasing the problem size of these PDEs increases the execution time, independent of the algorithm, the number of processors, and the interprocessor communication network used to solve the problem. In this paper, the analysis is extended to take into account the effect of the radius of the interprocessor communication network on the growth in the execution time. It is shown that the increasing amount of data also contributes to an increase in the time spent in interprocessor communication in optimal parallel algorithms for the problem. In particular, for any physically-realizable multiprocessor, the time spent on interprocessor communication will be the dominant constraint on the performance of optimal algorithms when the problem and multiprocessor sizes are large.