# SC²S Colloquium - October 05, 2016

Date: |
October 05, 2016 |

Room: |
02.07.023 |

Time: |
3:00 pm, s.t. |

## Ludwig Gärtner: A GPU-based Solver for the Shallow Water Equations in SWE-X10

Computing simulations on graphical processing units is one possibility to gain an increase in performance by calculating multiple parts of the simulation simultaneously. Therefor the implementation has to be adjusted to support the execution in parallel. SWE-X10 is a program that models tsunamis by simulating the Shallow Water Equations. This work deals with the adaptation of SWE-X10 to include a GPU-based solver. This includes describing the original implementation, and the changes that were made to support execution on a GPU. The performance tests reveal that even the basic implementation, without much performance tweaking, yields decent results. Furthermore this work presents the mathematical and technical background which is needed to retrace considerations and the actual implementation.

## Kevin Galim: Preconditioners for Tikhonov Regularization in Image Deblurring

In this thesis, new approaches for image deblurring are developed by combining Tikhonov regularization with preconditioning. The image blurring process can be expressed as ill posed linear equation with additive noise. To solve this type of equation and to reconstruct the original image, Tikhonov regularization is applied using a specific regularization matrix as input parameter. Typically, the identity matrix is chosen which, however, produces moderate results. A new attempt is to use preconditioners as regularization matrix, which are also used to solve ill posed problems. Matrices derived from the Incomplete LU factorization (ILU) preconditioner, the Sparse Approximate Inverse (SPAI) preconditioner and variations of these are tested in a simple image deblurring test where especially the inverse of the ILU preconditioner and a variation of the SPAI preconditioner yield superior results.