On balanced moving mesh methods

Remski, Joan; Zhang, Jingyan; Du, Qiang

doi:10.1016/j.cam.2013.09.041

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…The grid deformation approaches reported in the literature may be grouped into three main categories, namely, algebraic techniques (Karman and Sahasrabudhe, 2007; Liu et al , 2006; Rendall and Allen, 2009; Zhou and Li, 2015), iterative elliptic smoothing techniques (Huang and Kamenski, 2015; Ngo and Huang, 2016; Remski et al , 2014) and physical analogy techniques (Blom, 2000; Clarence, 2004; Degand and Farhat, 2002; Stein et al , 2004; Zeng and Ethier, 2005). The algebraic techniques define the interior grid node movement as an algebraic function of the boundary node positions.…”

Section: Grid Deformation Based On Spring-analogymentioning

confidence: 99%

Parallel algorithms for moving boundary problems by local remeshing

Zheng

et al. 2019

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Purpose The purpose of this paper is to develop parallel algorithms for moving boundary simulations by local remeshing and compose them to a fully parallel simulation cycle for the solution of problems with engineering interests. Design/methodology/approach The moving boundary problems are solved by unsteady flow computations coupled with six-degrees-of-freedom equations of rigid body motion. Parallel algorithms are developed for both computational fluid dynamics (CFD) solution and grid deformation steps. Meanwhile, a novel approach is developed for the parallelization of the local remeshing step. It inputs a distributed mesh after deformation, then marks low-quality elements to be deleted on the respective processors. After that, a parallel domain decomposition approach is used to repartition the hole mesh and then to redistribute the resulting sub-meshes onto all available processors. Then remesh individual sub-holes in parallel. Finally, the element redistribution is rebalanced. Findings If the CFD solver is parallelized while the remaining steps are executed in sequential, the performance bottleneck of such a simulation cycle is observed when the simulation of large-scale problem is executed. The developed parallel simulation cycle, in which all of time-consuming steps have been efficiently parallelized, could overcome these bottlenecks, in terms of both memory consumption and computing efficiency. Originality/value A fully parallel approach for moving boundary simulations by local remeshing is developed to solve large-scale problems. In the algorithm level, a novel parallel local remeshing algorithm is present. It repartitions distributed hole elements evenly onto all available processors and ensures the generation of a well-shaped inter-hole boundary always. Therefore, the subsequent remeshing step can fix the inter-hole boundary involves no communications.

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Section: Grid Deformation Based On Spring-analogymentioning

confidence: 99%

Parallel algorithms for moving boundary problems by local remeshing

Zheng

et al. 2019

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“…Over the years, adaptive zoning (also called adaptive moving mesh method or r-adaptivity) has been used to generate meshes that can help the numerical schemes to attain higher accuracy by producing a higher concentration of mesh points in regions of the domain where a higher resolution is desired [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. An efficient adaptive zoning is relevant for applications that need to model physical quantities characterized by steep gradients that propagate in space over time such as shock waves in a compressible medium.…”

Section: Introductionmentioning

confidence: 99%

A deep learning approach for adaptive zoning

Pasini¹,

Malenica²,

Chong³

et al. 2023

Preprint

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We propose a supervised deep learning (DL) approach to perform adaptive zoning on time dependent partial differential equations that model the propagation of 1D shock waves in a compressible medium. We train a neural network on a dataset composed of different static shock profiles associated with the corresponding adapted meshes computed with standard adaptive zoning techniques. We show that the trained DL model learns how to capture the presence of shocks in the domain and generates at each time step an adapted non-uniform mesh that relocates the grid nodes to improve the accuracy of Lax-Wendroff and fifth order weighted essentially non-oscillatory (WENO5) space discretization schemes. We also show that the surrogate DL model reduces the computational time to perform adaptive zoning by at least a 2x factor with respect to standard techniques without compromising the accuracy of the reconstruction of the physical quantities of interest.

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“…Application range of the method is quite wide, ranging from 1-D single PDEs 28), 29) to multi-dimensional system of PDEs 30), 31) . The MMPDE method solves a parabolic PDE controlling mesh resolution in addition to the equation to be solved 32), 33) , and does not modify the mesh topology, such as linkage of nodes and elements.…”

Section: Introductionmentioning

confidence: 99%

A Petrov-Galerkin Finite Element Scheme for 1-D Time-independent Hamilton-Jacobi-Bellman Equations

Yoshioka

Unami

Fujihara

2015

J. JSCE

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A numerical method for solving 1-D time-independent Hamilton-Jacobi-Bellman equations, which are referred to as 1-D HJBEs, is presented and applied to test cases for assessing its computational performance. An HJBE in this paper is a nonconservative second-order ordinary differential equation having linear diffusion and nonlinear drift terms. This paper applies a regularization method to the drift coefficient of the HJBEs, which helps well-pose the boundary value problems of the equations in the classical sense. A mathematical analysis on consistency errors between the solutions to the original and regularized HJBEs is performed. The derived results of the analysis show that the regularization method is mathematically consistent. The regularized HJBEs are solved with a Petrov-Galerkin finite element scheme, which is referred to as the PGFE scheme. The scheme is based on the fitting technique and is unconditionally stable for linear problems. Application of the scheme with the regularization method to the HJBEs with bounded drift coefficients demonstrates its satisfactory high computational accuracy. The optimal regularization parameter value as a function of the element size is then numerically identified. The computational results show that the PGFE scheme without the regularization method would fail to accurately capture solution profiles even if thousands of elements are used, which is not the case for the scheme with the regularization method even with hundreds of elements. Impacts of incorporating an adaptive re-meshing method, which is the moving mesh partial differential equation method, into the PGFE scheme are also assessed, demonstrating that it can enhance robustness of the scheme with regularization.

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On balanced moving mesh methods

Cited by 6 publications

References 23 publications

Parallel algorithms for moving boundary problems by local remeshing

Parallel algorithms for moving boundary problems by local remeshing

A deep learning approach for adaptive zoning

A Petrov-Galerkin Finite Element Scheme for 1-D Time-independent Hamilton-Jacobi-Bellman Equations

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