Global adaptive quadrature for the approximate computation of multidimensional integrals on a distributed-memory multiprocessor

In this paper we discuss the problem of computing a multidimensional integral on a MIMD distributed-memory multiprocessor. Adaptive quadrature is known as a good approach to the problem of achieving accuracy and reliability while attempting to minimize the number of function evaluations. The implementation makes use of dynamical data structures able to manage subinterval partition. On a distributed-memory multiprocessor, each processor is able to execute code and to manipulate data structures in its own local memory only, and data are sent from one processor to another one by explicit message-passing. Efficient implementation of an adaptive algorithm for the multidimensional quadrature on a parallel computer is quite difficult, because of the need for continuous information exchange between processors. Our algorithm is based on a global adaptive strategy which dynamically balances the workload and reduces the data communication between processors in order to use the message-passing environment efficiently. The results and timings for several tests are given.