Alice RAELI - Post-doctoral fellow at Institut Montpelliérain Alexander Grothendieck - NUMERICAL MODELLING OF ELLIPTIC PROBLEMS ON OCTREE-BASED MESHES
In the framework of Energy Store Technologies and Phase Changing Materials, the geometry of the system or the way in which some of its properties are described may induce internal discontinuities. As a consequence, there arises the need for solving linear elliptic equations with varying coeffcients across internal interfaces, which implies that the gradient of the solution can undergo significant variations through the internal boundaries. In this seminar, Dr. Raeli will present a compact finite-difference scheme on a tree-based adaptive grid that can be effciently solved using a natively parallel data structure. Numerical illustrations are offered in both two and three-dimensional configurations. Future perspectives to improve the solution of elliptic problems in the presence of discontinuities will include the usage of Hybrid High-Order methods to increase the approximation order.
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