Generation of Block Structured Grids on Complex Domains for High Performance Simulation

p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

“…On a range of numerical examples, our new indicator demonstrated comparable or better solution quality than that of a limited uniformly This work is an integral part of our ongoing effort to produce a p-adaptive DG solver for the SWE capable of efficient utilization of massively parallel and heterogeneous computing architectures (Faghih-Naini et al 2023). It bundles a number of other numerical and computational techniques such as a novel block-structured grid generator for ocean domains (Zint et al 2019(Zint et al , 2022Faghih-Naini et al 2022) and the code generation framework (Lengauer et al 2014;Schmitt et al 2014a;Kuckuk and Köstler 2016). Our future research goals include adding the FPGA support-already available for the unstructured-mesh version of the model (Kenter et al 2021;Faj et al 2023)-and implementing semi-implicit time stepping schemes based on the hierarchical scale separation (HSS) approach (Aizinger et al 2015;Schütz and Aizinger 2017) related to the p-multigrid method.…”

“…Fig. 5, shows our (topologically) block-structured grid (Zint et al 2019) with 3 584 elements along with the steady-state solution for different approximations. Whereas a piecewise constant DG approximation is very diffusive, the limited linear and quadratic solutions look much better.…”

“…The gravity acceleration g is set to 1. The employed block-structured grid (Zint et al 2019) consists of 48 000 triangles, and r in Fig. 8 (left) indicates the line along which the free surface elevation is plotted in Fig.…”