Speakers
Description
The efficient and accurate resolution of multiphysics problems posed on intricate geometries typically requires time-consuming meshing, and the accurate representation of the geometry and solutions features with standard meshes may require excessive computational power.
Polytopic meshes can be used for complexity reduction for multi-physics problems posed on intricate geometries. For instance, the possibility of using general shape elements permits the exact representation of very general domains and interfaces, or the accurate representation of such domains without the need of overly refined meshes. Another example is the possibility to use hierarchies of nested agglomerated meshes, which can be used to design efficient multigrid solvers.
The Polydeal library extends deal.II with robust support for polygonal and polyhedral discretizations, integrating smoothly with its existing framework. We will demonstrate how these new features can be used in practice, offering greater flexibility for complex geometries while preserving the familiar deal.II workflow.
As proof of concept, we will demonstrate the use within Polydeal of a novel multilevel agglomeration and preconditioning strategy designed to solve the monodomain equation in cardiac electro-physiology using high-order discontinuous Galerkin (DG) methods.
