Discontinuous Galerkin methods

UP

Martin Kronbichler, Niklas Fehn, Benjamin Krank, Andrea La Spina, Svenja Schoeder

Our research on discontinuous Galerkin methods comprises both the construction of new schemes, such as hybridizable discontinuous Galerkin methods, as well as the efficient implementation on modern computers.

Our implementations include the following features:

• Efficient evaluation of integrals for high order shape functions with sum factorization
• Tuning for large-scale parallel computations
• Node-level performance modeling such as characterization into compute-bound and memory-bound parts
• SIMD vectorization of compute kernels (AVX2, AVX512, ...)
• Support for many-core architectures, including Intel Xeon Phi Knights Landing and NVIDIA GPUs

The generic algorithm kernels are available for both continuous and discontinuous finite elements in the open-source finite element library deal.II, see also the github page of deal.II.

Our development of discontinuous Galerkin methods focuses on the following application fields:

• Incompressible Navier-Stokes equations
• Acoustic wave propagation in the context of photoacoustic imaging
• Weakly compressible Navier-Stokes equations