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

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

3. Adaptive Multivariate integration  Calculate I f 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 : I f =

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!