High-performance implementation of discontinuous Galerkin methods with application in fluid flow. (English) Zbl 1478.76053
Kronbichler, Martin (ed.) et al., Efficient high-order discretizations for computational fluid dynamics. Selected papers based on the presentations at the summer school, Udine, Italy, July 16–20, 2018. Cham: Springer. CISM Courses Lect. 602, 57-115 (2021).
Summary: In this book chapter, the high-performance implementation of discontinuous Galerkin methods is reviewed, with the main focus on sum factorization algorithms. The main computational properties of the algorithms are compared to capabilities of modern computer hardware, highlighting the opportunities and limitations of discontinuous Galerkin discretizations. The chapter closes with a presentation of how to apply these algorithms to the compressible Euler equations, the acoustic wave equation, and the incompressible Navier-Stokes equations.
For the entire collection see [Zbl 1468.76003].
For the entire collection see [Zbl 1468.76003].
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
sum factorization algorithm; explicit Runge-Kutta time integration; parallel computation; compressible Euler equations; acoustic wave; incompressible Navier-Stokes equationsSoftware:
Nektar++; ExWave; ExaDG; Peano; deal.ii; pTatin3D; NGSolve; likwid; PARDISO; UMFPACK; p4est; FEniCS; SPECFEM3D; DUNE; Firedrake; Nek5000; FLEXIReferences:
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