SC²S Colloquium - April 9, 2014

Pablo Gómez: Reduced Models for Sparse Grid Discretizations of the Multi Asset Black Scholes Equation

Option pricing for multi-asset options is a computationally expensive task that often has to be performed quickly and repeatedly. As Monte Carlo methods only offer a slow convergence rate and discretization approaches suffer from the curse of dimensionality they struggle to meet these requirements. Therefore we apply model order reduction techniques in combination with a sparse grids approach to achieve the necessary computational efficiency as well as accuracy for the computation of basket options with a small number of underlying assets. Using the proper orthogonal decomposition we were able to price options with up to 4 underlying assets. The resulting error is comparable to the one of a high-fidelty sparse grid model and the computation 80 up to 160 times faster than for the high-fidelty sparse grids model. Finally we show the applicability of a multi-level principal component analysis approach to reduce the necessary number of snapshots.

Paul Nieleck: Extending Zoltan by additional SFC orders to improve locality on unstructured grids

The tool kit Zoltan provides an ordering function that is based on inverse Hilbert space-filling curves for orderings of elements in 2D or 3D. Zoltan is used by the simulation software SeisSol to order the elements of a three-dimensional unstructured grid, with the goal to preserve locality of the elements and thus increase the computation performance of the simulation. Currently only one particular (inverse) Hilbert space-filling curve is implemented in Zoltan. With this work Zoltan is extended by additional space-filling curve orders. We also evaluate if the different orderings applied to three-dimensional unstructured grids can further increase the computation performance of SeisSol.