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partition of unity Finite Element Analysis of Nonlinear Transient Diffusion Problems Using p-Version Refinement

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Computer Modeling in Engineering & Sciences 2020年第7期124卷 61-78页

作者： Abdelkarim El Kahoui Mustapha Malek Nouh Izem MShadi Mohamed Mohammed Seaid Laboratory of Engineering Sciences Faculty of ScienceIbn Zohr UniversityAgadirMorocco School of Energy GeoscienceInfrastructure and SocietyHeriot-Watt UniversityEdinburghEH144ASUK Department of Engineering Durham UniversityDurhamDH13LEUK International Water Research Institute University Mohammed VI PolytechnicBenguerirMorocco

We propose a high-order enriched partition of unity finite element method for linear and nonlinear time-dependent diffusion *** solution of this class of problems often exhibits non-smooth features such as steep gradients and boundary layers which can be very challenging to recover using the conventional low-order finite element methods.A class of steady-state exponential functions has been widely used for enrichment and its performance to numerically solve these challenges has been ***,these enrichment functions have been used only in context of the standard h-version refinement or the so-called q-version *** this paper we demonstrate that the p-version refinement can also be a very attractive option in terms of the efficiency and the accuracy in the enriched partition of unity finite element ***,the transient diffusion problem is integrated in time using a semi-implicit scheme and the semi-discrete problem is then integrated in space using the p-version enriched finite *** results are presented for three test examples of timedependent diffusion problems in both homogeneous and heterogeneous *** computed results show the significant improvement when using the p-version refined enriched approximations in the finite element *** addition,these results support our expectations for a robust and high-order accurate enriched partition of unity finite element method.

关键词： partition of unity finite element method p-version refinement

GALERKIN MESHLESS METHODS BASED ON partition of unity QUADRATURE

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Applied Mathematics and Mechanics(English Edition) 2005年第7期26卷 893-899页

作者：曾清红卢德唐 Department of Mechanics and Mechanic Engineering University of Science and Technology of China Hefei 230027 P.R.China

Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature （PUQ）,for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are “truly” meshless methods.

关键词： Galerkin meshless method finite cover partition of unity numerical quadrature

Two-grid partition of unity method for second order elliptic problems

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Applied Mathematics and Mechanics(English Edition) 2008年第4期29卷 527-533页

作者：王琤黄自萍李立康 Department of Mathematics Tongji University Chinese-German College Tongji University Department of Mathematics Fudan University

A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.

关键词： second order elliptic problems two-grid method partition of unity

Boundary-representable partition of unity for image magnification

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Science China(Information Sciences) 2013年第11期56卷 216-227页

作者： NAGAI Yukie OHTAKE Yutaka YOKOTA Hideo SUZUKI Hiromasa School of Engineering The University of Tokyo153-8904 Japan Bio-Research Infrastructure Construction Team ASI RIKEN 351-0198 Japan RCAST The University of Tokyo153-8904 Japan

This paper proposes a simple yet efective algorithm to magnify 2D/3D images with preserving discontinuities of *** algorithm is based on the partition of unity(PU)approximation,which ofers many advantages such as smooth representation,noise-robustness,and precise ***,PU encounters difculties when scaling images and maintaining boundaries within images owing to the nature of its *** overcome this problem,we propose an approximation that preserves *** is realized by dividing the local spherical support of PU into two parts along a locally detected discontinuity and by individually approximating intensities on each side of the *** algorithm is suitable for magnifying a variety of images,including scanned documents,pictures,and CT-scanned *** demonstrate the efectiveness of the proposed method,we show some experimental results for 2D/3D images.

关键词： image approximation partition of unity piecewise smooth function volume data magnification

Control synthesis for a class of nonlinear systems based on partition of unity

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控制理论与应用（英文版） 2007年第2期5卷 145-151页

作者： Dongfang HAN Yinhe WANG Siying ZHANG Science College Shantou University Shantou Guangdong 515063 China College of Information Science and Engineering Northeastern University Shenyang Liaoning 110006 China

A partition-of-unity-based approach is proposed to derive an approximate model for a class of nonlinear systems. The precision of the approximate model is analyzed by using the modulus of continuity of continuous functions. The system stability of the approximate model is analyzed by using Lyapunov stability theory. A design algorithm for constructing tracking controllers with tracking performance related to tracking error is given based on the approximate model and the partition of unity method.

关键词： partition of unity Approximate model Modulus of continuity H∞ tracking controller

On the Linear Independence and partition of unity of Arbitrary Degree Analysis-Suitable T-splines

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Communications in Mathematics and Statistics 2015年第3期3卷 353-364页

作者： Jingjing Zhang Xin Li School of Mathematical Science USTCHefeiAnhuiChina

Analysis-suitable T-splines are a topological-restricted subset of T-splines,which are optimized to meet the needs both for design and analysis(Li and Scott ModelsMethods Appl Sci 24:1141-1164,2014;Li et *** Aided Geom Design 29:63-76,2012;Scott et *** Methods Appl Mech Eng 213-216,2012).The paper independently derives a class of bi-degree(d_(1),d_(2))T-splines for which no perpendicular T-junction extensions intersect,and provides a new proof for the linearly independence of the blending *** also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation.

关键词： T-splines Analysis-suitable T-splines Linear independence partition of unity Isogeometric analysis

Approximation property of partition of unity and its applications

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控制理论与应用（英文版） 2004年第3期2卷 267-275页

作者： YinheWANG ZhiyuanLI SiyingZHANG ScienceCollege ShantouUniversityShantouGuangdong515063China DepartmentofMathematics InnerMongoliaNormalUniversityHuhhotInnerMongolia010022China DepartmentofAutomaticControl NortheasternUniversityShenyangLiaoning110006China

The linear combination of certain partition of unity, subordinate to certain open covering of a compact set, is proved to be capable of approximating to a continuous function at arbitrarily precision. By using proper open covering and partition of unity, the robust nonlinear controllers and adaptive laws are designed for a class of nonlinear systems with uncertainties. The states and parameters of the closed-loop systems can be stabilized in the meaning of UUB ( uniformly ultimately bounded) via the robust nonlinear controllers and adaptive laws. Finally, an example shows the validity of method in this paper.

关键词： partition of unity Approximating theorem Uncertain system UUB

Stable Adaptive Control for a Class of Nonlinear Systems Based on partition of unity

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Stable Adaptive Control for a Class of Nonlinear Systems Bas...

Control Synthesis for a Class of MIMO Nonlinear Systems Based on partition of unity

2010 Chinese Control and Decision Conference

作者： Liang Luo~1,Yinhe Wang~1,Junmin Hu~1,Xiao Wang~1,Yun Zhang~1 1.Faculty of Automation,Guangdong University of Technology,Guangzhou 510006

＜正＞In this paper,the robust tracking controllers with adaptive laws are designed for a class of nonlinear systems based on partition of *** results show that the tracking errors converge to a small neighborhood of zero and states in the closed-loop system are bounded via the ***,the simulations show the validity of the method adopted in this paper.

关键词： partition of unity adaptive tracking control nonlinear systems

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Control Synthesis for a Class of MIMO Nonlinear Systems Base...