Hr-adaptivity for Nonconforming High-order Meshes with the Target Matrix Optimization Paradigm

@article{Dobrev2020HradaptivityFN,
  title={Hr-adaptivity for Nonconforming High-order Meshes with the Target Matrix Optimization Paradigm},
  author={Veselin A. Dobrev and Patrick M. Knupp and Tzanio V. Kolev and Ketan Mittal and Vladimir Z. Tomov},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.02166}
}
We present an $hr$-adaptivity framework for optimization of high-order meshes. This work extends the $r$-adaptivity method for mesh optimization by Dobrev et al., where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element's current and target geometric parameters: element aspect-ratio, size, skew, and orientation. Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper we… Expand
Adaptive Surface Fitting and Tangential Relaxation for High-Order Mesh Optimization
TLDR
A new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes is proposed, which utilizes discrete finite element functions to define implicit surfaces, which are used to adapt the positions of certainMesh nodes. Expand

References

SHOWING 1-10 OF 38 REFERENCES
Towards Simulation-Driven Optimization of High-Order Meshes by the Target-Matrix Optimization Paradigm
TLDR
This work presents a method for simulation-driven optimization of high-order curved meshes, where all targets were based strictly on geometric information, and the construction of target-matrices is enhanced by using discrete fields of interest, e.g., proximity to a particular region. Expand
Optimization of a regularized distortion measure to generate curved high-order unstructured tetrahedral meshes
We present a robust method for generating high-order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high-order nodes, second,Expand
Introducing the target-matrix paradigm for mesh optimization via node-movement
  • P. Knupp
  • Computer Science
  • Engineering with Computers
  • 2011
TLDR
A general-purpose algorithm for mesh optimization via node-movement, known as the Target-Matrix Paradigm, is introduced, which can be considered to be a direct optimization method in which weights are automatically constructed to enable definitions of application-specific mesh quality. Expand
Mesh Smoothing for the Spectral Element Method
TLDR
Mesh quality improvements are shown to reduce the condition number of the preconditioned linear systems governing the numerical solution of the discretized partial differential equations, with corresponding reductions in iteration counts. Expand
Anisotropic Mesh Adaptivity and Control Volume Finite Element Methods for Numerical Simulation of Multiphase Flow in Porous Media
Numerical simulation of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. The governing equations are the continuity equation andExpand
Curvilinear mesh generation using a variational framework
TLDR
By adopting a variational approach to the generation process, many of the current popular high-order generation methods can be encompassed under a single unifying framework, which allows to compare the effectiveness of these methods and to assess the quality of the meshes they produce in a systematic fashion. Expand
Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation
TLDR
Dynamic cases with moving interfaces show the new mesh smoothing method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods. Expand
A new computational framework for multi-scale ocean modelling based on adapting unstructured meshes†
TLDR
The model presented here is novel in its use of unstructured meshes and anisotropic adaptivity in 3D, its ability to represent a range of coupled multi-scale solution structures and to simulate non-hydrostatic dynamics. Expand
h, r, and hr adaptivity with applications in numerical ocean modelling
The purpose of this article is to introduce techniques for performing h, r, and hr adaptivity in the context of numerical ocean modelling. These supplements to a standard numerical discretizationExpand
Reliable error estimation and mesh adaptation for the finite element method
TLDR
Experimental results for a particular nonlinear two-point boundary-value problem show that the combination of continuation, error estimation, and adaptive mesh construction should be an extremely effective approach to the computational solution of many practical engineering problems. Expand
...
1
2
3
4
...