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Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine (2018)
Journal Article
Dumbser, M., Fambri, F., Tavelli, M., Bader, M., & Weinzierl, T. (2018). Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine. Axioms, 7(3), Article 63. https://doi.org/10.3390/axioms7030063

In this paper we discuss a new and very efficient implementation of high order accurate arbitrary high order schemes using derivatives discontinuous Galerkin (ADER-DG) finite element schemes on modern massively parallel supercomputers. The numerical... Read More about Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine.

A Multi-Core Ready Discrete Element Method With Triangles Using Dynamically Adaptive Multiscale Grids (2018)
Journal Article
Krestenitis, K., & Weinzierl, T. (2019). A Multi-Core Ready Discrete Element Method With Triangles Using Dynamically Adaptive Multiscale Grids. Concurrency and Computation: Practice and Experience, 31(19), Article e4935. https://doi.org/10.1002/cpe.4935

The simulation of vast numbers of rigid bodies of non‐analytical shapes and of tremendously different sizes that collide with each other is computationally challenging. A bottleneck is the identification of all particle contact points per time step.... Read More about A Multi-Core Ready Discrete Element Method With Triangles Using Dynamically Adaptive Multiscale Grids.

Quasi-matrix-free hybrid multigrid on dynamically adaptive Cartesian grids (2018)
Journal Article
Weinzierl, M., & Weinzierl, T. (2018). Quasi-matrix-free hybrid multigrid on dynamically adaptive Cartesian grids. ACM Transactions on Mathematical Software, 44(3), Article 32. https://doi.org/10.1145/3165280

We present a family of spacetree-based multigrid realizations using the tree’s multiscale nature to derive coarse grids. They align with matrix-free geometric multigrid solvers as they never assemble the system matrices, which is cumbersome for dynam... Read More about Quasi-matrix-free hybrid multigrid on dynamically adaptive Cartesian grids.