Marc Massot (École Polytechnique)
Towards a New Approach of Mesh Adaptation Methods and its Impact on Accuracy for the Simulation of Stiff PDEs abstract
Abstract:
In this presentation, we address the objective of accurately simulating multi-scale PDEs in time and space at a reasonable cost. This leads to the use of dynamic mesh adaptation and dedicated numerical schemes. Our main focus for this seminar is on examining the impact of mesh adaptation on the accuracy of the solution. We draw attention to the potential coupling of mesh adaptation and numerical scheme for the classical approaches and explain why we intend to use fully adaptive multi-resolution in the sense of Harten based on wavelets. We present a theory based on modified equations for the convective part of the PDEs and include the fully adaptive multi-resolution in the error estimate. It provides a theoretical basis for understanding the impact of mesh adaptation / mesh compression on the quality of results. We will also briefly present the open-source code framework we use "samurai", as well as a new data-structure based on interval representation and algebra of sets. This data-structure allows to both reach a very small memory trace of the compressed mesh as well as handle all the potential versions of the AMR and adaptive multiresolution with a single tool. The use of another library "ponio" allows to connect the mesh adaptation library to various time integration strategies.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-07