3,979 research outputs found
A Continuous Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions
We present an anisotropic mesh adaptation strategy using a continuous
mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with
optimal test functions, extending our previous work on adaptation. The
proposed strategy utilizes the inbuilt residual-based error estimator of the
DPG discretization to compute both the polynomial distribution and the
anisotropy of the mesh elements. In order to predict the optimal order of
approximation, we solve local problems on element patches, thus making these
computations highly parallelizable. The continuous mesh model is formulated
either with respect to the error in the solution, measured in a suitable norm,
or with respect to certain admissible target functionals. We demonstrate the
performance of the proposed strategy using several numerical examples on
triangular grids.
Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models,
adaptations, Anisotrop
Generation of Curved High-order Meshes with Optimal Quality and Geometric Accuracy
We present a novel methodology to generate curved high-order meshes featuring optimal mesh quality and geometric accuracy. The proposed technique combines a distortion measure and a geometric Full-size image (<1 K)-disparity measure into a single objective function. While the element distortion term takes into account the mesh quality, the Full-size image (<1 K)-disparity term takes into account the geometric error introduced by the mesh approximation to the target geometry. The proposed technique has several advantages. First, we are not restricted to interpolative meshes and therefore, the resulting mesh approximates the target domain in a non-interpolative way, further increasing the geometric accuracy. Second, we are able to generate a series of meshes that converge to the actual geometry with expected rate while obtaining high-quality elements. Third, we show that the proposed technique is robust enough to handle real-case geometries that contain gaps between adjacent entities.This research was partially supported by the Spanish Ministerio de EconomÃa y Competitividad under grand contract
CTM2014-55014-C3-3-R, and by the Government of Catalonia under grand contract 2014-SGR-1471. The work of the last author was supported by the European Commission through the Marie Sklodowska-Curie Actions
(HiPerMeGaFlows project).Peer ReviewedPostprint (published version
Generation of curved high-order meshes with optimal quality and geometric accuracy
We present a novel methodology to generate curved high-order meshes featuring optimal mesh quality and geometric accuracy. The proposed technique combines a distortion measure and a geometric L2-disparity measure into a single objective function. While the element distortion term takes into account the mesh quality, the L2-disparity term takes into account the geometric error introduced by the mesh approximation to the target geometry. The proposed technique has several advantages. First, we are not restricted to interpolative meshes and therefore, the resulting mesh approximates the target domain in a non-interpolative way, further increasing the geometric accuracy. Second, we are able to generate a series of meshes that converge to the actual geometry with expected rate while obtaining high-quality elements. Third, we show that the proposed technique is robust enough to handle real-case geometries that contain gaps between adjacent entities.Peer ReviewedPostprint (published version
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90641/1/AIAA-53965-537.pd
A Comparison of Hybridized and Standard DG Methods for Target-Based hp-Adaptive Simulation of Compressible Flow
We present a comparison between hybridized and non-hybridized discontinuous
Galerkin methods in the context of target-based hp-adaptation for compressible
flow problems. The aim is to provide a critical assessment of the computational
efficiency of hybridized DG methods. Hybridization of finite element
discretizations has the main advantage, that the resulting set of algebraic
equations has globally coupled degrees of freedom only on the skeleton of the
computational mesh. Consequently, solving for these degrees of freedom involves
the solution of a potentially much smaller system. This not only reduces
storage requirements, but also allows for a faster solution with iterative
solvers. Using a discrete-adjoint approach, sensitivities with respect to
output functionals are computed to drive the adaptation. From the error
distribution given by the adjoint-based error estimator, h- or p-refinement is
chosen based on the smoothness of the solution which can be quantified by
properly-chosen smoothness indicators. Numerical results are shown for
subsonic, transonic, and supersonic flow around the NACA0012 airfoil.
hp-adaptation proves to be superior to pure h-adaptation if discontinuous or
singular flow features are involved. In all cases, a higher polynomial degree
turns out to be beneficial. We show that for polynomial degree of approximation
p=2 and higher, and for a broad range of test cases, HDG performs better than
DG in terms of runtime and memory requirements
Self-Adaptive Methods for PDE
[no abstract available
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