PERFORMANCE, ACCURACY, AND PREDICTIVE CHUNK OPTIMIZATION OF PARALLEL SIMPSON AND TRAPEZOIDAL INTEGRATION METHODS
Abstract
Parallel numerical integration is a fundamental component of many scientific and engineering applications, yet its performance depends strongly on workload partitioning strategies. In shared-memory environments, the choice of chunk size directly affects load balancing, scheduling overhead, and cache utilization, particularly when adaptive numerical methods are employed. This paper presents an analysis of the performance, accuracy, and scalability of four numerical integration techniques: Simpson’s rule, Adaptive Simpson’s rule, the Trapezoidal rule, and the Adaptive Trapezoidal rule, implemented in a multi-threaded execution model. Execution-time distributions are analyzed across a wide range of chunk sizes and thread counts, revealing substantial performance variability and method-dependent optimal chunk configurations. In addition to performance evaluation, numerical accuracy is assessed to highlight trade-offs between computational efficiency and error reduction. Based on empirical observations, optimal chunk ranges are identified and used to construct a predictive model that estimates near-optimal chunk configurations as a function of the number of threads. The proposed approach enables efficient parameter selection without exhaustive tuning and demonstrates the feasibility of predictive chunk optimization for parallel numerical integration.
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