Date of Award
Doctor of Philosophy
Dr. Elise de Doncker
Dr. Dennis Pence
Dr. Joseph McKean
Dr. J. Donald Nelson
For a procedure as numerical integration, of high computational expense which is used extensively in large-scale computations, it is natural to aim at the design of algorithms which can be used on parallel computes. This work deeds with the design of efficient and portable parallel algorithms on MIMD (Multiple Instruction Multiple Data) architectures with shared memory, and on distributed memory systems.
A parallel global adaptive algorithm is presented for multivariate integration over simplex type regions. Process synchronization is achieved through the use of monitors. Macros were developed, for managing the task pool with a heap data structure. Layered over the Argonne monitor macro package, the algorithm is portable to a variety of machines.
Convergence properties and speedup are analyzed for a class of global adaptive multivariate integration algorithms on shared memory MIMD machines. The analysis considers functions with a given number of continuous derivatives in the (cube or simplex) integration region, with possible exception of a type of vertex singularity.
In many problems, integration is required over a triangularized (twodimensional) region. A parallel global adaptive algorithm is presented for integration over a set of triangles on distributed memory systems. On such systems, the task pool which evolves adaptively in the course of the computations is distributed over the local memories of the processors. The Reactive Kernel/Cosmic Environment is used as the processor communication system, thereby also assuring the algorithm’s portability to various systems. Two new dynamic load balancing systems governing the flow of work between processors, were constructed and tested.
Vakalis, Ignatios E., "Multivariate Quadrature on MIMD Machines with Shared or Distributed Memory" (1992). Dissertations. 1990.