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| 1 | Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators显示文摘 | Ting Wei Y.C. Hon Leevan Ling | 2006 | Engineering Analysis with Boundary Elements2006，，4： | 1 |
| 2 | Results on meshless collocation techniques 显示文摘 | Ling Leevan Opfer Roland Schaback Robert | 2006 | Engineering Analysis with Boundary Elements2006，30，4： | 1 |
| 3 | Method of fundamental solutions with regulaxization techniques for Cauchy problems of elliptic operators显示文摘 | WEI Ting HON Y C LING Leevan | | 0，，04： | 1 |
| 4 | Numerical Simulations of 2D Fractional Subdiffusion Problems显示文摘 | HERMANN BRUNNERA LEEVAN LINGA MASAHIRO YAMAMOTO | 2010 | Journal Computational Physics2010，229，18： | 1 |
| 5 | Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs显示文摘This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin(MLPG)method with radial basis function(RBF)kernels generated trial spaces.Local weak-form testings are done with stepfunctions.It is proved that subject to sufficiently many appropriate testings,solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed.Moreover,an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation.Numerical results(in double precision)give good agreement with the provided theory. | Ahmad Shirzadi Leevan Ling | 2013 | Advances in Applied Mathematics and Mechanics2013，5，1： | 0 |
| 6 | An Energy Regularization for Cauchy Problems of Laplace Equation in Annulus Domain显示文摘Detecting corrosion by electrical field can be modeled by a Cauchy problem of Laplace equation in annulus domain under the assumption that the thickness of the pipe is relatively small compared with the radius of the pipe.The interior surface of the pipe is inaccessible and the nondestructive detection is solely based on measurements from the outer layer.The Cauchy problem for an elliptic equation is a typical ill-posed problem whose solution does not depend continuously on the boundary data.In this work,we assume that the measurements are available on the whole outer boundary on an annulus domain.By imposing reasonable assumptions,the theoretical goal here is to derive the stabilities of the Cauchy solutions and an energy regularization method.Relationship between the proposed energy regularization method and the Tikhonov regularization with Morozov principle is also given.A novel numerical algorithm is proposed and numerical examples are given. | Houde Han Leevan Ling Tomoya Takeuchi | 2011 | Communications in Computational Physics2011，9，4： | 0 |
| 7 | On Convergence of a Least-Squares Kansa’s Method for the Modified Helmholtz Equations显示文摘We analyze a least-squares asymmetric radial basis function collocation method for solving the modified Helmholtz equations.In the theoretical part,we proved the convergence of the proposed method providing that the collocation points are sufficiently dense.For numerical verification,direct solver and a subspace selection process for the trial space(the so-called adaptive greedy algorithm)is employed,respectively,for small and large scale problems. | Ting-On Kwok Leevan Ling | 2009 | Advances in Applied Mathematics and Mechanics2009，1，3： | 0 |
| 8 | Point Sources Identification Problems for Heat Equations显示文摘We considered the point source identification problems for heat equations from noisy observation data taken at the minimum number of spatially fixed measurement points.We aim to identify the unknown number of sources and their locations along with their strengths.In our previous work,we proved that minimum measurement points needed under the noise-free setting.In this paper,we extend the proof to cover the noisy cases over a border class of source functions.We show that if the regularization parameter is chosen properly,the problem can be transformed into a poles identification problem.A reconstruction scheme is proposed on the basis of the developed theoretical results.Numerical demonstrations in 2D and 3D conclude the paper. | Leevan Ling Tomoya Takeuchi | 2009 | Communications in Computational Physics2009，5，5： | 0 |
| 9 | Preface Special Issue for SCPDE08: Numerical Methods and Analysis for PDEs and Inverse Problems显示文摘The Third International Conference on Scientific Computing and Partial Differential Equations(SCPDE)was held from December 8 to December 12,2008 at China Hong Kong Baptist University.It was a sequel to similar conferences held in Hong Kong region(2002 and 2005).The conference aims to promote research interests in scientific computation.In SCPDE 2008,there were 118 participants from seventeen countries and regions participated in the conference.The Programme included seventeen plenary addresses,thirty invited talks,twenty five contributed talks and seven poster presentations. | C.S.Chen Ming-Chih Lai Leevan Ling Jichun Li Masahiro Yamamoto | 2009 | Advances in Applied Mathematics and Mechanics2009，1，6： | 0 |
| 10 | Preface Special Issue for SCPDE11显示文摘The Fourth International Conference on Scientific Computing and Partial Differential Equations(SCPDE)was held at Hong Kong Baptist University from December 5 to December 9,2011(http://gffzz68f5171dc6a242c7h0wnb95bo6cpf6vvp.ffgz.tsg.suse.edu.cn/SCPDE11/).It was a sequel to similar conferences held in Hong Kong(2002,2005 and 2008).The conference aims to promote research interests in scientific computation.In SCPDE 2011,there were over 100 participants from several countries and regions participated in the conference.The Programme included sixteen plenary speakers,thirty invited talks,thirty five contributed talks.Four main themes were organized to review recent scientific developments and explore exciting new directions in mathematical modeling and computational methods;in particular,they are Numerical Analysis and Applications of Volterra Functional Equations,Stochastic Computations,Electromagnetic and Acoustic Scattering,and Numerical Partial Differential Equations. | Leevan Ling Zhonghua Qiao Tao Tang | 2012 | Advances in Applied Mathematics and Mechanics2012，4，6： | 0 |
| 11 | Complex Pattern Formations by Spatial Varying Parameters显示文摘Pattern formations by Gierer-Meinhardt(GM)activator-inhibitor model are considered in this paper.By linear analysis,critical value of bifurcation parameter can be evaluated to ensure Turing instability.Numerical simulations are tested by using second order semi-implicit backward difference methods for time discretization and the meshless Kansa method for spatially discretization.We numerically show the convergence of our algorithm.Pattern transitions in irregular domains are shown.We also provide various parameter settings on some irregular domains for different patterns appeared in nature.To further simulate patterns in reality,we construct different kinds of animal type domains and obtain desired patterns by applying proposed parameter settings. | Siqing Li Leevan Ling | 2020 | Advances in Applied Mathematics and Mechanics2020，12，6： | 0 |
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