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Exact local refinement using Fourier interpolation for nonuniformgrid modeling

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Earth and Planetary Physics 2017年第1期1卷 58-62页

作者： JinHai Zhang ZhenXing Yao Key Laboratory of Earth and Planetary Physics Institute of Geology and Geophysics Chinese Academy of Sciences

Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited.Traditional interpolation methods would fail at high upsampling ratios(say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.

关键词： local refinement varying grid tiny structures fourier interpolation nonuniform grid

A Finite Difference Scheme for a Semiconductor Device Problem on Grids with local refinement in Time and Space

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Numerical Mathematics(Theory,Methods and Applications) 2006年第3期15卷 278-288页

作者： Wei Liu and Yirang Yuan School of Mathematics and System Science, Shandong University, Jinan 250100, China. School of Mathematics and System Science Shandong University Jinan 250100China

The momentary state of a semiconductor device is described by a system of three nonlinear partial differential equations. A finite difference scheme for simulating transient behaviors of a semiconductor device on grids with local refinement in time and space is constructed and studied. Error analysis is presented and is illustrated by numerical examples.

关键词： Semiconductor device local refinement finite difference scheme error estimate.

Isogeometric Analysis with local Adaptivity for Vibration of Kirchhoff Plate

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Computer Modeling in Engineering & Sciences 2022年第5期131卷 949-978页

作者： Peng Yu Weijing Yun Junlei Tang Sheng He College of Civil Engineering and Architecture Key Laboratory of Disaster Prevention and Structural Safety of Ministry of EducationGuangxi Key Laboratory of Disaster Prevention and Structural SafetyGuangxi UniversityNanning530000China

Based on our proposed adaptivity strategy for the vibration of Reissner-Mindlin plate,we develop it to apply for the vibration of Kirchhoff plate.The adaptive algorithm is based on the Geometry-Independent Field approximaTion(GIFT),generalized from Iso-Geometric Analysis(IGA),and it can characterize the geometry of the structure with NURBS(Non-Uniform Rational B-Splines),and independently apply PHT-splines(Polynomial splines over Hierarchical T-meshes)to achieve local refinement in the solution field.TheMAC(Modal AssuranceCriterion)is improved to locate unique,as well as multiple,modal correspondence between different meshes,in order to deal with error estimation.local adaptivity is carried out by sweeping modes from low to high frequency.Numerical examples showthat a proper choice of the spline space in solution field(with GIFT)can deliver better accuracy than using NURBS solution field.In addition,for vibration of heterogeneous Kirchhoff plates,our proposed method indicates that the adaptive local h-refinement achieves a better solution accuracy than the uniform h-refinement.

关键词： Isogeometric analysis local refinement adaptivity vibration kirchhoff plate

RECENT PROGRESS IN INCOMPRESSIBLE REYNOLDSAVERAGED NAVIER-STOKES SOLVERS

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Journal of Hydrodynamics 1996年第1期8卷 13-30页

作者： C. H. Sung T. T. Huang(David Taylor Model Basin,CD/NSWC Bethesda, MD 20084- 5000,USA) David Taylor Model Basin Bethesda United States

A new numerical approach based on a multiblock, multigrid, local refinement method has been developed. The multiblock structure makes grid generation for complex geometries easier,multigrid techniques significantly accelerate the rate of convergence and the local refinement method provides high spatial resolution of boundary lay6r and separated vortical flows with much reduced computer memory and CPU time. Sample three-dimensional flow computations for complex geometries are presented to illustrate the advantages in term of memory savings and reductions of CPU time in obtaining high spatial resolution solutions. High spatial resolution in the inner viscous layer is achieved by using the values of y+ for the first grid centers rom the wall in the order of 1 to 7. The required solution resolution in the dominantly viscous flow region (boundary layer, vortex core, or three-dimensional separated zone) dictates the acceptable spacing of grid cells in that region. It is very desirable to be able to reduce grid spacing locally in the critical region without changing the overall grid. The local refinement technique doubles grid numbers in all three directions for every level of refinement. Multiple levels of local grid refinement with moderate grid stretching can be used to provide fine grid spacing in rapidly changing flow regions such as near the wall, vortex core and separated shear layer. Thus, the method provides the required fine spatial resolution in the dominantly viscous region which is relatively small compared to the entire computational domain. This also avoids the used of excessively large aspect ratios of the grid cells near the rapidly changing now regions thus reduces truncation error and improves robustness. Furthermore, the results of numerical experimentation indicate that the present multigrid local refinement technique provides very effective numerical communications across the fine and coarse grid interfaces because the finer mesh is embedded entirely in the coarse mesh, and the occurrenc

关键词： ultiblock multigrid local refinement

A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Models

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Communications in Computational Physics 2009年第5期5卷 1012-1029页

作者： Xianliang Hu Ruo Li Tao Tang Department of Mathematics Zhejiang UniversityHangzhou 31027China Department of Applied and Computational Mathematics California Institute of TechnologyPasadenaCA 91125USA CAPT LMAM&School of Mathematical SciencesPeking UniversityBeijing 100871China Department of Mathematics Hong Kong Baptist UniversityKowloon TongKowloonHong Kong

In this work,we propose an efficient multi-mesh adaptive finite element method for simulating the dendritic growth in two-and three-dimensions.The governing equations used are the phase field model,where the regularity behaviors of the relevant dependent variables,namely the thermal field function and the phase field function,can be very different.To enhance the computational efficiency,we approximate these variables on different h-adaptive meshes.The coupled terms in the system are calculated based on the implementation of the multi-mesh h-adaptive algorithm proposed by Li(J.Sci.Comput.,pp.321-341,24(2005)).It is illustrated numerically that the multi-mesh technique is useful in solving phase field models and can save storage and the CPU time significantly.

关键词： Multi-mesh local refinement adaptive finite element phase field

Lazy Slicing for State-Space Exploration

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Journal of Computer Science & Technology 2012年第4期27卷 872-890页

作者：黄少滨黄宏涛陈志远吕天阳张涛 College of Computer Science and Technology Harbin Engineering University

CEGAR （Counterexample-guided abstraction refinement）-based slicing is one of the most important techniques in reducing the state space in model checking. However, CEGAR-based slicing repeatedly explores the state space handled previously in case a spurious counterexample is found. Inspired by lazy abstraction, we introduce the concept of lazy slicing which eliminates this repeated computation. Lazy slicing is done on-the-fly, and only up to the precision necessary to rule out spurious counterexamples. It identifies a spurious counterexample by concretizing a path fragment other than the full path, which reduces the cost of spurious counterexample decision significantly. Besides, we present an improved over-approximate slicing method to build a more precise slice model. We also provide the proof of the correctness and the termination of lazy slicing, and implement a prototype model checker to verify safety property. Experimental results show that lazy slicing scales to larger systems than CEGAR-based slicing methods.

关键词： counterexample-guided abstraction refinement spurious counterexample over-approximate slicing local refinement lazy slicing

Extended T-mesh and Data Structure for the Easy Computation of T-spline

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Extended T-mesh and Data Structure for the Easy Computation ...