Overview / Usage

Scope of the project:

The scope of this project is Numerical methods, Data Parallelism and High Performance Computing. Finding the approximate value of an integral is a problem under numerical integration.

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The composite trapezium rule:

Suppose we have a function f(x) that is integrable on points a and b. The composite trapezium rule is derived when we divide points a and b into N number of subintervals having equal lengths and then we apply the trapezium rule to evaluate each integral.

Let the interval [a, b] be subdivided into N equal parts of length h. That is, h = (b – a)/N. The trapezium rule would then be applied to evaluate each N integrals.

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Case Study Integral

In this project, the case study integral is 4/(1+(x*x)) for approximating the value of PI.

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Methodology / Approach

Methodology:

1. Expressing the composite trapezium rule as a dot product so as to exploit the features of OpenMP/oneMKL composability.
2. Expressing the composite trapezium rule with partition technique to exploit the features of OpenMP/DPC++ composability
3. Comparing OpenMP gpu offloading with DPC++ for data, memory and device management.

Technologies Used

Development Environment: Intel devcloud; for developing, testing and running the project

Intel Hardware: Intel® Xeon® E-2176G;

**oneAPI Toolkit: **oneAPI base and HPC toolkit;

Programming Support: Direct-based programming with OpenMP and API-based programming with oneMKL.