École Nationale Supérieure de
Techniques Avancées

Résumé

This report presents the details of my internship at KTH Department of Mathematics. I worked in the Numerical Division with my supervisor, Professor Jennifer Ryan, on the Smoothness- Increasing AccuracyConserving (SIAC) filter. The purpose of this internship was to optimize the SIAC filter to make it more computationally efficient. This filter is a post-processing method to improve the smoothness and accuracy of numerical solutions to partial differential equations. For this purpose, we have developed various codes in Python, first to obtain these numerical solutions with the discontinuous Galerkin method and then to make the computation of the SIAC filter faster. To this end, we have implemented a version of the low-rank Anderson acceleration that solves a fixed-point problem with low-rank matrices, and we have applied it to the SIAC filter to study its performance. For each code implemented, a theoretical background is first detailed. Then, the structure of our code and our choices of implementation are explained, as well as the improvements we have made to them. Finally, their results are presented with comments and analyses.