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A p-Multigrid Strategy with Anisotropic p-Adaptation Based on Truncation Errors for High-Order Discontinuous Galerkin Methods
[article]
2018
pre-print
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In this paper, we combine both methods and present a novel anisotropic p-adaptation multigrid algorithm for steady-state problems that uses the multigrid scheme both as a solver and as an anisotropic error ...
On the one hand, local mesh adaptation strategies based on error estimation have been proposed to reduce the number of degrees of freedom while keeping a similar accuracy. ...
Acknowledgments The authors would like to thank David Kopriva for his friendly advise and cooperation. ...
doi:10.1016/j.jcp.2018.11.009
arXiv:1806.11456v1
fatcat:z3lnvh3nszhixa2hyogy6xwruy
An Anisotropic p-Adaptation Multigrid Scheme for Discontinuous Galerkin Methods
[chapter]
2020
Lecture Notes in Computational Science and Engineering
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Acknowledgements This project has received funding from the European Union's Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie grant agreement No 675008 for the SSeMID project ...
Every time the error is estimated, an anisotropic p-multigrid strategy is used to generate a truncation error map for each element, like the one in Fig. 1a . ...
Introduction In recent decades, high-order discontinuous Galerkin (DG) methods have been gaining increasing popularity for high-accuracy solutions of systems of conservation laws, such as the compressible ...
doi:10.1007/978-3-030-39647-3_44
fatcat:wll2gknan5ahhkqzr3rs4gl3bi
Numerical Stabilization of the Melt Front for Laser Beam Cutting
[chapter]
2010
Numerical Mathematics and Advanced Applications 2009
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We develop a hybrid scheme consisting of a combination of a second order MUSCL scheme and a high order finite difference scheme. ...
The model is based on Navier-Stokes equations for viscous incompressible flow and convection-diffusion equation describing pollution transport. ...
problem, based on (P k 2 , P k-1 ) discontinuous elements for k = 1, 2 or 3. ...
doi:10.1007/978-3-642-11795-4_6
fatcat:nx4nvuxaxfbcdjknopny53ck5e
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations
2005
Journal of Computational Physics
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We present a p-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier-Stokes equations. ...
Fourier analysis of the two-level p-multigrid algorithm for convection-diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number ...
A portion of this work was supported by NASA contract NAG-1-02037. ...
doi:10.1016/j.jcp.2005.01.005
fatcat:tsjnuxsa5bgd7e2fmilsctffd4
Smoothed Aggregation Multigrid for the Discontinuous Galerkin Method
2009
SIAM Journal on Scientific Computing
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The discontinuous Galerkin method (dGFEM) has become popular for the discretization of elliptic and hyperbolic partial differential equations for about a decade. ...
The method is scalable, if also the computational work for a problem containing n unknowns grows like O(n log n). Multigrid methods are known to be scalable for elliptic problems on regular grids. ...
The multigrid algorithm needs to be combined with a p-multilevel method or some related domain decomposition approach to yield a hierarchical solver for high order numerical systems. ...
doi:10.1137/080728457
fatcat:akcpit7x4vcbtos4ucgixfee2y
UNSTRUCTURED GRID TECHNIQUES
1997
Annual Review of Fluid Mechanics
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The topics of mesh generation and adaptation, spatial discretization, and solution techniques for steady flows are covered. ...
Remaining difficulties in these areas are highlighted, and directions for future work are outlined. ...
strategies with multigrid methods. ...
doi:10.1146/annurev.fluid.29.1.473
fatcat:n4c2wf6prbeyvnscis762jugtm
A review of algebraic multigrid
2001
Journal of Computational and Applied Mathematics
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This paper gives a review of the ÿrst hierarchical and purely matrix-based approach, algebraic multigrid (AMG). ...
For practically relevant problem sizes, classical one-level methods had already reached their limits and new hierarchical algorithms had to be developed in order to allow an e cient solution of even larger ...
In practice, we want to achieve rapid convergence with as small sets of interpolatory variables P i as possible (in order to allow for a rapid coarsening and to obtain reasonably sparse Galerkin operators ...
doi:10.1016/s0377-0427(00)00516-1
fatcat:q2kwtxvbmbakpgnbxihbplrece
Delayed approximate matrix assembly in multigrid with dynamic precisions
[article]
2020
arXiv
pre-print
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matrix entries carry little information or are not yet available with high accuracy. ...
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. ...
We use our second test setup with only one type of a discontinuous material jump over three orders of magnitude. Initial results are given for ∈ {1, 10 −3 } (Fig. 10 ). ...
arXiv:2005.03606v1
fatcat:iyad6selxfeeflgp7xdq7tawum
Scalable angular adaptivity for Boltzmann transport
[article]
2019
arXiv
pre-print
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This adaptivity uses Haar wavelets, which perform structured h-adaptivity built on top of a hierarchical P_0 FEM discretisation of a 2D angular domain, allowing different anisotropic angular resolution ...
Fixed angular refinement, along with regular and goal-based error metrics are shown in three example problems taken from neutronics/radiative transfer applications. ...
This highly anisotropic problem shows the need for low-order adaptive methods, as we can see in Fig. 20a that the convergence of a spectral P n method has degraded to roughly that of the uniform P 0 ...
arXiv:1901.04929v1
fatcat:rkpzwy4dtvbmddjbls6p5k2sgi
Error Estimation and Adaptive Mesh Refinement for Aerodynamic Flows
[chapter]
2010
Notes on Numerical Fluid Mechanics and Multidisciplinary Design
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One extremely promising class of high-order schemes based on the finite element frame-
work are Discontinuous Galerkin (DG, for short) methods. ...
A. Oliver, J. Lu, and D. L. Darmofal. p-multigrid solution of high-order
discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. J. Comp. ...
doi:10.1007/978-3-642-03707-8_24
fatcat:2m2ao7uwivaeropjt55kdht43u
Filtering algebraic multigrid and adaptive strategies
2007
Computing and Visualization in Science
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This paper proposes a variant of Wagner's method with substantially improved robustness properties. ...
Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. ...
Based on [8] we propose an adaptive strategy using the latest correction as test vector when the convergence rate stalls. ...
doi:10.1007/s00791-007-0066-9
fatcat:s7gftzdxgvbldlqead3a6kugam
A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions
[chapter]
2011
ERCOFTAC Series
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A priori estimates are applied to the anisotropic mesh adaptation for 2D viscous flows and 3D ones including Large Eddy Simulation. ...
The BE poses a formidable challenge for numerical approximation methods, on account of its high dimensional phase-space setting: for a problem in N spatial dimensions, the single molecule phase-space is ...
made possible the publication of this book of Abstracts, the (online or CD) publication of the Extended Abstracts and Full Contributions, and the organization of ADMOS 2013, VI International Conference on ...
doi:10.1007/978-94-007-0231-8_5
fatcat:f6ll6iawcbeo7pbj4rb7t4o2tq
Finite Element Methods for the Incompressible Navier-Stokes Equations
[chapter]
2000
Fundamental Directions in Mathematical Fluid Mechanics
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These notes are based on lectures given in a Short Course on Theoretical and Numerical ...
Design such a method for high-order schemes. ...
(I) The traditional method for a posteriori time-step selection is based on the concept of controlling the local "truncation error" but neglecting the global error accumulation. ...
doi:10.1007/978-3-0348-8424-2_6
fatcat:vf5hwpwjyfe6hjwf5hs6772wf4
A Matrix Dependent/Algebraic Multigrid Approach for Extruded Meshes with Applications to Ice Sheet Modeling
2016
SIAM Journal on Scientific Computing
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based on the first-order Stokes equations [46] . ...
A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. ...
We thank Ali Pinar for suggesting the idea of combining coloring and connected component algorithms to detect hinged peninsulas within graphs. ...
doi:10.1137/15m1040839
fatcat:pvpdnaoh2rcoldrob5g4pbdr4m
Quasi-matrix-free Hybrid Multigrid on Dynamically Adaptive Cartesian Grids
2018
ACM Transactions on Mathematical Software
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They align with matrix-free geometric multigrid solvers as they never assemble the system matrices which is cumbersome for dynamically adaptive grids and full multigrid. ...
We present a family of spacetree-based multigrid realizations using the tree's multiscale nature to derive coarse grids. ...
Marion wants to thank him for hosting her research stay at Technion which laid the foundations for the present work. ...
doi:10.1145/3165280
fatcat:wmygp64iy5f3bbnwiu5l4g6bfq
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