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Multivariate Numerical Integration

This project focuses on adaptive multivariate numerical integration, targeting functions with potential singularities within the interior domain. Utilizing the Gauss-Kronrod 21-point weighted sum scheme, the aim is to compute an integral If from an approximate value Qf while ensuring the error Ef is below a specified tolerance. The project involves implementing an adaptive univariate integration routine, applying this routine in various dimensions, and parallelizing outer Gauss-Kronrod iterations. Further updates include support for Epsilon and Deltas in distributed memory systems, enhancing data and task parallelism.

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Multivariate Numerical Integration

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  1. Multivariate Numerical Integration Rida Assaf Western Michigan University rida.assaf@wmich.edu

  2. Adaptive Multivariate integration • For a given function of the form : If = Given the approximate Qf, calculate If where : Ef = |Qf– If | < tolerance - f might have a lot of singularities in the interior domain.

  3. Adaptive Multivariate integration • Calculate If using Gauss-Konrod 21 points weighted sum scheme :

  4. Adaptive Multivariate integration • Dealing with n-dimensional functions for n 3 for n = 3 our function looks like : If =

  5. Code • Tasks: • Implement adaptive univariate integration routine ✔ • Use the adaptive routine in all directions ✔ • Parallelize the outer Gauss-Konrod iterations✔

  6. Updates • Updates: • Functions support Epsilon and Deltas ✔ • Distributed Memory Systems support(MPI) • Data Parallelism • Task Parallelism

  7. Questions? Thank you!

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