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multiresolution method for bending of plates with complex shapes

Applied Mathematics and Mechanics(English Edition) 2023年第4期44卷 561-582页

作者： Jizeng WANG Yonggu FENG Cong XU Xiaojing LIU Youhe ZHOU Key Laboratory of Mechanics on Disaster and Environment in Western China(Lanzhou University) the Ministry of EducationLanzhou 730000China College of Civil Engineering and Mechanics Lanzhou UniversityLanzhou 730000China

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular *** realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex *** the solution of differential equations,various derivatives of the unknown function are denoted as new ***,the integral relations between these functions are applied in terms of wavelet approximation of multiple ***,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order *** the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse *** examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various *** comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth *** solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of *** addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

关键词： multiresolution generalized Coiflet wavelet integral collocation method irregular domain complex shape high accuracy plate bending

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multiresolution and multimaterial topology optimization of fail-safe structures under B-spline spaces

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Frontiers of Mechanical Engineering 2023年第4期18卷 149-163页

作者： Yingjun WANG Zhenbiao GUO Jianghong YANG Xinqing LI National Engineering Research Center of Novel Equipment for Polymer Processing South China University of TechnologyGuangzhou 510641China The Key Laboratory of Polymer Processing Engineering of the Ministry of Education South China University of TechnologyGuangzhou 510641China Guangdong Provincial Key Laboratory of Technique and Equipment for Macromolecular Advanced Manufacturing South China University of TechnologyGuangzhou 510641China State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and TechnologyWuhan 430074China

This study proposes a B-spline-based multiresolution and multimaterial topology optimization(TO)design method for fail-safe structures(FSSs),aiming to achieve efficient and lightweight structural design while ensuring safety and facilitating the postprocessing of topological *** approach involves constructing a multimaterial interpolation model based on an ordered solid isotropic material with penalization(ordered-SIMP)that incorporates failsafe *** reduce the computational burden of finite element analysis,we adopt a much coarser analysis mesh and finer density mesh to discretize the design domain,in which the density field is described by the B-spline *** B-spline can efficiently and accurately convert optimized FSSs into computer-aided design *** 2D and 3D numerical examples demonstrate the significantly enhanced computational efficiency of the proposed method compared with the traditional SIMP approach,and the multimaterial TO provides a superior structural design scheme for ***,the postprocessing procedures are significantly streamlined.

关键词： multiresolution multimaterial topology optimization fail-safe structure B-spline

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An Adaptive multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear Schrödinger Equations

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Communications on Applied Mathematics and Computation 2022年第1期4卷 60-83页

作者： Zhanjing Tao Juntao Huang Yuan Liu Wei Guo Yingda Cheng School of Mathematics Jilin UniversityJilin 130012China Department of Mathematics Michigan State UniversityEast LansingMI 48824USA Department of Mathematics Statistics and PhysicsWichita State UniversityWichitaKS 67260USA Department of Mathematics and Statistics Texas Tech UniversityLubbockTX 70409USA Department of Mathematics Department of Computational MathematicsScience and EngineeringMichigan State UniversityEast LansingMI 48824USA

This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger *** solutions to such equations often exhibit solitary wave and local structures,which make adaptivity essential in improving the simulation *** scheme uses the ultra-weak discontinuous Galerkin(DG)formulation and belongs to the framework of adaptive multiresolution *** numerical experiments are presented to demon-strate the excellent capability of capturing the soliton waves and the blow-up phenomenon.

关键词： multiresolution Sparse grid Ultra-weak discontinuous Galerkin method Schrödinger equation Adaptivity

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multiresolution Isogeometric Topology Optimisation Using Moving Morphable Voids

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Computer Modeling in Engineering & Sciences 2020年第3期122卷 1119-1140页

作者： Bingxiao Du Yong Zhao Wen Yao Xuan Wang Senlin Huo College of Aerospace Science and Engineering National University of Defense TechnologyChangsha410073China. National Innovation Institute of Defense Technology Chinese Academy of Military ScienceBeijing100000China. School of Civil Engineering Hefei University of TechnologyHefei230009China.

A general and new explicit isogeometric topology optimisation approach with moving morphable voids(MMV)is *** this approach,a novel multiresolution scheme with two distinct discretisation levels is developed to obtain high-resolution designs with a relatively low computational *** material model based on Greville abscissae collocation scheme is utilised to represent both the Young’s modulus of the material and the density *** benchmark examples are tested to illustrate the effectiveness of the proposed *** results show that high-resolution designs can be obtained with relatively low computational cost,and the optimisation can be significantly improved without introducing additional DOFs.

关键词： Isogeometric analysis(IGA) multiresolution moving morphable voids(MMV) topology optimisation.

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multiresolution analysis of density fluctuation in supersonic mixing layer

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Science China(Technological Sciences) 2010年第2期53卷 584-591页

作者： ZHAO YuXin1, YI ShiHe, TIAN LiFeng, HE Lin & CHENG ZhongYu College of Aerospace and Material Engineering, National University of Defense Technology, Changsha 410073, China College of Aerospace and Material Engineering National University of Defense Technology Changsha China

Due to the difficulties in measuring supersonic density field, the multiresolution analysis of supersonic mixing layer based on experimental images is still a formidable challenge. By utilizing the recently developed nanoparticle based planar laser scattering method, the density field of a supersonic mixing layer was measured at high spatiotemporal resolution. According to the dynamic behavior of coherent structures, the multiresolution characteristics of density fluctuation signals and density field images were studied based on Taylor’s hypothesis of space-time conversion and wavelet analysis. The wavelet coefficients reflect the characteristics of density fluctuation signals at different scales, and the detailed coefficients reflect the differences of approximation at adjacent levels. The density fluctuation signals of supersonic mixing layer differ from the periodic sine signal and exhibit similarity to the fractal Koch signal. The similarity at different scales reveals the fractal characteristic of mixing layer flowfield. The two-dimensional wavelet decomposition and reconstruction of density field images extract the approximate and detailed signals at different scales, which effectively resolve the characteristic structures of the flowfield at different scales.

关键词： supersonic mixing layer density fluctuation multiresolution analysis

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multiresolution SYMPLECTIC SCHEME FOR WAVE PROPAGATION IN COMPLEX MEDIA

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Applied Mathematics and Mechanics(English Edition) 2004年第5期25卷 573-579页

作者：马坚伟杨慧珠 Department of Engineering Mechanics Tsinghua University

A fast adaptive symplectic algorithm named multiresolution Symplectic Scheme (MSS) was first presented to solve the problem of the wave propagation (WP) in complex media, using the symplectic scheme and Daubechies' compactly supported orthogonal wavelet transform to respectively discretise the time and space dimension of wave equation. The problem was solved in multiresolution symplectic geometry space under the conservative Hamiltonian system rather than the traditional Lagrange system. Due to the fascinating properties of the wavelets and symplectic scheme, MSS is a promising method because of little computational burden, robustness and reality of long-time simulation.

关键词： wavelet transform multiresolution symplectic wave propagation

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HAT AVERAGE multiresolution WITH ERROR CONTROL IN 2-D

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Journal of Computational Mathematics 2004年第6期22卷 777-790页

作者： SergioAmat DepartamentodeMatemdticaAplicadayEstadística UniversidadPolitdcnicadeCartagenaSpain

multiresolution representations of data are a powerful tool in data compression. For a proper adaptation to the singularities, it is crucial to develop nonlinear methods which are not based on tensor product. The hat average framework permets develop adapted schemes for all types of singularities. In contrast with the wavelet framework these representations cannot be considered as a change of basis, and the stability theory requires different considerations. In this paper, non separable two-dimensional hat average multiresolution processing algorithms that ensure stability are introduced. Explicit error bounds are presented.

关键词： Stability Hat average multiresolution Non separable

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multiresolution Terrian Model in GIS

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测绘学报 2002年第Z1期31卷 92-98页

作者： ZHANG Jin 1,TONG Xiao hua 2 (1. Department of Surveying and Mapping, Taiyuan University of Technology, Taiyuan 030024,China 2. Department of Surveying and Geo informatics, Tongji University, Shanghai 200092,China) Department of Surveying and Mapping Taiyuan University of Technology Taiyuan 030024 Department of Surveying and Geo-informatics Tongji University 上海 200092

DEM, which becomes a major component of geographic information processing in earth and engineering sciences, has been studied in the GIS literature for a long time. We use DEM to represent the terrain in GIS. The more data are available, the better representations of a terrain can be built. But not all tasks in the framework of a given application necessarily require the same accuracy, and even a single task may need different levels of accuracy in different areas of the domain. multiresolution models, such as LOD, offer the possibility of representing and analyzing a terrain at a range of different levels of detail. In this paper, some key issues in multiresolution DEM model are studied. Three main models are focused on Hierarchical TIN(HTIN), multiresolution terrain model based Delaunay and Hierarchical Dynamic Simplification. The advantages and disadvantages of these methods are analyzed. The technology of tile to tile edge match is studied to maintain the consistency between adjacent edges and tile edges in HTIN model. And the Hypergraph based Objected oriented Model(HOOM) is presented to divide and code spatial area and describe the terrain feature in adding and deleting points based on Delaunay rule retriangulating. The conclusions have been drawn in the end.

关键词： DEM multiresolution LOD GIS

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HOUSE EXTRACTION WITH multiresolution ANALYSIS AND INFORMATION FUSION

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Geo-Spatial Information Science 1998年第1期1卷 6-12页

作者： LI Deren[a] SHAO Juliang [a] WTUSM Wuhan China 430079

Houses are key elements both in aerial photographs and *** extraction has significance not only to military,but also to automatical rela-tive orientation,automatical absolute orientation,feature-based matching,sys-tematic description,automatic data aquisition,structure analysis,image under-standing,digital mapping,and construction of urban geographic information sys-tem（UGIS）.For this purpose,this paper mainly addresses:（1）a brief introduc-tion to the multiresolution analysis of wavelet theory and its difference formLaplacian pyramid,（2）how to generate the multiresolution images and edge fea-tures,and（3）how to employ these multiresolution images and edge features toextract the houses from aerial photographs by multiresolution structure and infor-mation fusion.

关键词： wavelet theory multiresolution analysis: house extraction information fusion

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A novel vague set approach for selective contrast enhancement of mammograms using multiresolution

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Journal of Biomedical Science and Engineering 2009年第8期2卷 575-581页

作者： Arpita Das Mahua Bhattacharya Institute of Radio Physics & Electronics University of Calcutta Kolkata India

The proposed algorithm introduces a novel vague set approach to develop a selective but robust, flexible and intelligent contrast enhancement technique for mammograms. Wavelet based filtering analysis can produce Low Frequency (LF) and High Frequency (HF) subbands of the original input images. The extremely small size microcalcifications become visible under multiresolution techniques. LF subband is then fuzzified by conventional fuzzy c-means clustering (FCM) algorithm with justified number of clusters. HF components, representing the narrow protrusions and other fine details are also fuzzified by FCM with justified number of clusters. Vague set approach captures the hesitancies and uncertainties of truly affected masses/other breast abnormalities with normal glandular tissues. After highlighting the masses/microcalcifications accurately, both LF and HF subbands are transformed back to the original resolution by inverse wavelet transform. The results show that the proposed method can successfully enhance the selected regions of mammograms and provide better contrast images for visual interpretation.

关键词： multiresolution Vague Set Approach True- membership Functions False-Membership Functions

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