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Application of radial basis functions to evolution equations arising in image segmentation

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Chinese Physics B 2014年第2期23卷 583-588页

作者：李淑玲李小林 College of Mathematics Science Chongqing Normal University

In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method.

关键词： radial basis functions evolution equations image segmentation re-initialization

Performance of Compact radial basis functions in the Direct Interpolation Boundary Element Method for Solving Potential Problems

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Computer Modeling in Engineering & Sciences 2017年第3期113卷 367-387页

作者： C.F.Loeffle L.Zamprogno W.J.Mansur A.Bulcao DEM/PPGEM Federal University of Espírito Santo PGSU Petrobras PEC/LAMEMO/COPPE/Federal University of Rio de Janeiro CENPES Petrobras

This study evaluates the effectiveness of a new technique that transforms doma in integrals into boundary integrals that is applicable to the boundary element *** mulations were conducted in which two-dimensional surfaces were approximated by inter polation using radial basis functions with full and compact *** involving Poisson’s equation are presented using the boundary element method and the proposed te chnique with compact radial basis *** advantages and the disadvantages are e xamined through *** effects of internal poles,the boundary mesh refinemen t and the value for the support of the radial basis functions on performance are assessed.

关键词： Interpolations radial basis functions boundary element method Poisson’s equation

The Partition of Unity Method for High-Order Finite Volume Schemes Using radial basis functions Reconstruction

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Numerical Mathematics(Theory,Methods and Applications) 2009年第2期2卷 153-179页

作者： Serena Morigi Fiorella Sgallari Department of Mathematics University of BolognaP.zza Porta San Donato5BolognaItaly CIRAM University of BolognaVia Saragozza8BolognaItaly

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential *** unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis *** methodology proposed is applied to the noise removal problem in functional surfaces and *** results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

关键词： Finite volume discretization radial basis functions optimal recovery regularization image and surface denoising.

Comparative Study of radial basis functions for PDEs with Variable Coefficients

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Journal of Harbin Institute of Technology(New Series) 2021年第6期28卷 91-96页

作者： Fuzhang Wang Congcong Li Kehong Zheng School of Mathematics and Statistics Xuzhou University of TechnologyXuzhou 221018JiangsuChina School of Mathematical Sciences Huaibei Normal UniversityHuaibei 235000AnhuiChina Department of Mathematics University of MacaoMacao 999078China College of Water Conservancy and Ecological Engineering Nanchang Institute of TechnologyNanchang 330099China

The radial basis functions(RBFs)play an important role in the numerical simulation processes of partial differential *** the radial basis functions are meshless algorithms,its approximation is easy to implement and mathematically *** this paper,the commonly⁃used multiquadric RBF,conical RBF,and Gaussian RBF were applied to solve boundary value problems which are governed by partial differential equations with variable *** results were provided to show the good performance of the three RBFs as numerical tools for a wide range of *** is shown that the conical RBF numerical results were more stable than the other two radial basis *** the comparison of three commonly⁃used RBFs,one may obtain the best numerical solutions for boundary value problems.

关键词： radial basis functions partial differential equations variable coefficient

Patient-specific modeling of facial soft tissue based on radial basis functions transformations of a standard three-dimensional finite element model

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Chinese Medical Journal 2012年第22期125卷 4066-4071页

作者： LOU Hang-di CHEN Si CHEN Gui XU Tian-min RONG Qi-guo Peking Univ Coll Engn Beijing 100081 Peoples R China Peking Univ Sch Stomatol Beijing 100081 Peoples R China

Background An important purpose of orthodontic treatment is to gain the harmonic soft tissue profile. This article describes a novel way to build patient-specific models of facial soft tissues by transforming a standard finite element （FE） model into one that has two stages： a first transformation and a second transformation, so as to evaluate the facial soft tissue changes after orthodontic treatment for individual patients. Methods The radial basis functions （RBFs） interpolation method was used to transform the standard FE model into a patient-specific one based on landmark points. A combined strategy for selecting landmark points was developed in this study： manually for the first transformation and automatically for the second transformation. Four typical patients were chosen to validate the effectiveness of this transformation method. Results The results showed good similarity between the transformed FE models and the computed tomography （CT） models. The absolute values of average deviations were in the range of 0.375-0.700 mm at the lip-mouth region after the first transformation, and they decreased to a range of 0.116-0.286 mm after the second transformation. Conclusions The modeling results show that the second transformation resulted in enhanced accuracy compared to the first transformation. Because of these results, a third transformation is usually not necessary.

关键词： finite element model facial soft tissue model transformation radial basis functions landmark points

Direct collocation method for identifying the initial conditions in the inverse wave problem using radial basis functions

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Direct collocation method for identifying the initial condit...

A meshfree method for inverse wave propagation using collocation and radial basis functions

第十一届南方计算力学学术会议（SCCM-11）

作者： Zhihao Qian Lihua Wang Zhen Wang Yukui Gao School of Aerospace Engineering and Applied Mechanics Tongji University

A direct collocation method associated with explicit time integration using radial basis functions is proposed for identifying the initial conditions in the inverse problem of wave propagation. Optimum weights for the boundary conditions and additional condition are derived based on Lagrange’s multiplier method to achieve the prime convergence. Tikhonov regularization is introduced to improve the stability for the ill-posed system resulting from the noise, and the L-curve criterion is employed to select the optimum regularization parameter. No iteration scheme is required during the direct collocation computation which promotes the accuracy and stability for the solutions, while Galerkin-based methods demand the iteration procedure to deal with the inverse problems. High accuracy and good stability of the solution at very high noise level make this method a superior scheme for solving inverse problems.

关键词： direct collocation method radial basis functions initial conditions inverse wave problem ill-posed system

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A meshfree method for inverse wave propagation using colloca...

A simulation-based software to support the real-time operational parameters selection of tunnel boring machines

第十一届南方计算力学学术会议（SCCM-11）

作者： Lihua Wang Zhen Wang Zhihao Qian School of Aerospace Engineering and Applied Mechanics Tongji University

A stable and highly accurate meshfree scheme based on strong form collocation associated with radial basis functions and explicit time integration is proposed to solve ill-posed inverse wave propagation problems. Tikhonov regularization technique and the L-curve criterion are employed to deal with the noise measurement data before solving the governing equation to get a stable solution. Appropriate weights are first derived for imposing boundary conditions and known conditions from the measurement data to yield the optimal convergence for inverse problems. Compared to the required iterative procedures in common methods, no iteration is needed in the proposed method which leads to the time-saving computation and avoids the instability resulting from the iterative methods. Dispersion analysis describes that this method has much less dispersion error than the classical finite element method(FEM) and popular weak form meshfree methods, and stability analysis is performed to predict the critical time step for the explicit time integration. Another outstanding advantage of this method is it’s effortless to extend the solution scheme of one-dimensional inverse problem to high-dimensional inverse problems. Furthermore, the influences of the high noise into measurement data are evaluated, which demonstrate that even handling with very high noise in the input data the proposed algorithm can achieve stable and high-accuracy solutions.

关键词： strong form collocation radial basis functions ill-posed inverse wave propagation problem Tikhonov regularization dispersion analysis stability analysis

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Underground Space 2024年第1期14卷 176-196页

作者： Yaman Zendaki Ba Trung Cao Abdullah Alsahly Steffen Freitag Gunther Meschke Institute for Structural Mechanics Ruhr University BochumBochum 44801Germany Institute for Structural Analysis Karlsruhe Institute of TechnologyKarlsruhe 76131Germany

With the fact that the main operational parameters of the construction process in mechanized tunneling are currently selected based on monitoring data and engineering experience without exploiting the advantages of computer methods,the focus of this work is to develop a simulation-based real-time assistant system to support the selection of operational *** choice of an appropriate set of these parameters(i.e.,the face support pressure,the grouting pressure,and the advance speed)during the operation of tunnel boring machines(TBM)is determined by evaluating different tunneling-induced soil-structure interactions such as the surface settlement,the associated risks on existing structures and the tunnel lining *** evaluate soil-structure behavior,an advanced process-oriented numerical simulation model based on the finite cell method is *** enable the real-time prediction capability of the simulation model for a practical application during the advancement of TBMs,surrogate models based on the Proper Orthogonal Decomposition and radial basis functions(POD-RBF)are *** proposed approach is demonstrated through several synthetic numerical examples inspired by the data of real tunnel *** developed methods are integrated into a user-friendly application called SMART to serve as a support platform for tunnel engineers at construction *** to each user adjustment of the input parameters,i.e.,each TBM driving scenario,approximately two million outputs of soil-structure interactions are quickly predicted and visualized in seconds,which can provide the site engineers with a rough estimation of the impacts of the chosen scenario on structural responses of the tunnel and above ground structures.

关键词： Numerical simulation Surrogate model Real-time prediction Proper orthogonal decomposition radial basis functions TBM operation Smart construction

基于径向基函数的微分求积区域分裂法及其应用

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高等学校计算数学学报 2005年第S1期 165-169页

作者：杜慧静吴雄华同济大学应用数学系同济大学应用数学系上海 200092

1 引言本文提出的基于径向基函数的微分求积区域分裂法是以径向基函数(RBFs)作为微分求积法(DQM)的基函数,并结合区域分裂法(DDM)提出的,结合了上述三种方法的优点,对解决不规则区域上的问题有很高的实用价值．

关键词： radial basis functions differential quadrature method domain decomposition method irregular domains partial differential equations.