Edit Profile (opens in new tab) Li, Zi-Cai Co-Author Distance Author ID: li.zi-cai Published as: Li, Zi-Cai; Li, Z. C.; Li, Z.-C.; Li, Zi Cai more...less Documents Indexed: 167 Publications since 1980, including 4 Books Co-Authors: 48 Co-Authors with 110 Joint Publications 1,471 Co-Co-Authors all top 5 Co-Authors 33 single-authored 58 Huang, Hung-Tsai 27 Lee, Ming-Gong 18 Zhang, Liping 12 Chiang, John Y. 12 Wei, Yimin 11 Hu, Hsin-Yun 11 Huang, Jin 9 Cheng, Alexander H.-D. 9 Chien, Cheng-Sheng 9 Lu, Tzontzer 9 Wang, Song 8 Fang, Qing 5 Yan, Ningning 5 Young, Lih-Jier 4 Chen, Ching-Shyang 4 Jeng, B.-W. 4 Lin, Qun 4 Suen, Ching-Yun 3 Chu, Po-Chun 3 Huang, Chieh-Sen 3 Yamamoto, Tetsuro 2 Bui, Tien Dai 2 Chang, Chia-Shen 2 Chang, Shing-Lin 2 Chen, Jeng-Tzong 2 Chen, Zhen 2 Dai, E. 2 Dou, Fangfang 2 Lempert, Anna Anan’evna 2 Liu, Yaping 2 Lü, Tao 2 Tian, Zhaolu 2 Tsai, Heng-Shuing 2 Zeng, Guang 2 Zhou, Aihui 1 Bai, Zhi-Dong 1 Cao, Zhiyuan 1 Chang, Chia-Ming 1 Chen, Huei-Shuang 1 Chen, I-Lin 1 Chen, Yunkun 1 Cheng, Pan 1 Georgiou, Georgios C. 1 Gu, Quanlin 1 He, Xiaoming 1 Hsu, Chung-Hua 1 Kazakov, Aleksandr Leonidovich 1 Liaw, Cai-Pin 1 Ling, Leevan 1 Miller, John James Henry 1 Nashed, M. Zuhair 1 Oishi, Shin’ichi 1 Tang, Yuanyan 1 Tsai, Wu-Chung 1 Xenophontos, Christos A. 1 Yu, Chung-Sheng 1 Zhu, Rui all top 5 Serials 35 Engineering Analysis with Boundary Elements 22 Journal of Computational and Applied Mathematics 13 Applied Numerical Mathematics 10 Computers & Mathematics with Applications 8 Numerical Methods for Partial Differential Equations 7 Computing 6 Computer Methods in Applied Mechanics and Engineering 6 Mathematical and Computer Modelling 5 Numerical Functional Analysis and Optimization 5 Numerical Linear Algebra with Applications 4 Numerical Algorithms 3 Computer Physics Communications 3 Applied Mathematics Letters 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Mathematics of Computation 2 Applied Mathematics and Computation 2 International Journal for Numerical Methods in Engineering 2 SIAM Journal on Numerical Analysis 2 Information 2 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 1 Journal of Computational Physics 1 Automatica 1 Mathematica Numerica Sinica 1 Acta Mechanica Sinica 1 Journal of Scientific Computing 1 CAD. Computer-Aided Design 1 IEEE Transactions on Systems, Man, and Cybernetics 1 International Journal of Computer Mathematics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 SIAM Journal on Scientific Computing 1 Advances in Computational Mathematics 1 Abstract and Applied Analysis 1 Taiwanese Journal of Mathematics 1 Journal of Computational Analysis and Applications 1 Computer Assisted Mechanics and Engineering Sciences 1 CMES. Computer Modeling in Engineering & Sciences 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Mathematics and its Applications (Dordrecht) 1 Series in Computer Science all top 5 Fields 148 Numerical analysis (65-XX) 87 Partial differential equations (35-XX) 26 Mechanics of deformable solids (74-XX) 11 Computer science (68-XX) 7 Fluid mechanics (76-XX) 6 Ordinary differential equations (34-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Potential theory (31-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Special functions (33-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 142 Publications have been cited 930 times in 491 Documents Cited by ▼ Year ▼ Trefftz and collocation methods. Zbl 1140.65005 Li, Z.-C.; Lu, T.-T.; Hu, H.-Y.; Cheng, A. H.-D. 98 2008 Combined methods for elliptic equations with singularities, interfaces and infinities. Zbl 0909.65079 Li, Zi Cai 69 1998 Radial basis collocation methods for elliptic boundary value problems. Zbl 1127.65089 Hu, Hsin-Yun; Li, Zi-Cai; Cheng, Alexander H.-D. 61 2005 Trefftz, collocation, and other boundary methods – a comparison. Zbl 1223.65093 Li, Zi-Cai; Lu, Tzon-Tzer; Huang, Hung-Tsai; Cheng, Alexander H.-D. 52 2007 Singularities and treatments of elliptic boundary value problems. Zbl 1042.35524 Li, Z. C.; Lu, T. T. 46 2000 Effective condition number for finite difference method. Zbl 1104.65043 Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai 38 2007 The method of fundamental solutions for annular shaped domains. Zbl 1166.65060 Li, Zi-Cai 34 2009 New expansions of numerical eigenvalues for \(-\delta u=\lambda \rho u\) by nonconforming elements. Zbl 1198.65228 Lin, Qun; Huang, Hung-Tsai; Li, Zi-Cai 29 2008 Highly accurate solutions of Motz’s and the cracked beam problems. Zbl 1074.74655 Lu, T. T.; Hu, H. Y.; Li, Z. C. 28 2004 Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace’s equation. Zbl 1223.65085 Li, Zi-Cai; Huang, Jin; Huang, Hung-Tsai 22 2010 Effective condition number for numerical partial differential equations. Zbl 1212.65410 Li, Z.-C.; Huang, H.-T. 19 2008 The Trefftz method for the Helmholtz equation with degeneracy. Zbl 1141.65082 Li, Z. C. 18 2008 Two-grid discretization schemes for nonlinear Schrödinger equations. Zbl 1135.65361 Chien, C.-S.; Huang, H.-T.; Jeng, B.-W.; Li, Z.-C. 18 2008 Collocation methods for Poisson’s equation. Zbl 1124.65111 Hu, Hsin-Yun; Li, Zi-Cai 17 2006 Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs. Zbl 1175.65142 Huang, Jin; Lü, Tao; Li, Zi Cai 17 2009 Combined Trefftz methods of particular and fundamental solutions for corner and crack singularity of linear elastostatics. Zbl 1267.74128 Lee, Ming-Gong; Young, Lih-Jier; Li, Zi-Cai; Chu, Po-Chun 16 2010 Effective condition number and superconvergence of the Trefftz method coupled with high-order FEM for singularity problems. Zbl 1195.65151 Huang, Hung-Tsai; Li, Zi-Cai 16 2006 The Trefftz method using fundamental solutions for biharmonic equations. Zbl 1222.65131 Li, Zi-Cai; Lee, Ming-Gong; Chiang, John Y.; Liu, Ya Ping 15 2011 Particular solutions of Laplace’s equations on polygons and new models involving mild singularities. Zbl 1104.65114 Li, Zi-Cai; Lu, Tzon-Tzer; Hu, Hsin-Yun; Cheng, Alexander H. D. 13 2005 Study on effective condition number for collocation methods. Zbl 1244.65186 Li, Zi-Cai; Huang, Hung-Tsai 13 2008 Combinations of method of fundamental solutions for Laplace’s equation with singularities. Zbl 1244.65222 Li, Zi-Cai 13 2008 Comparisons of fundamental solutions and particular solutions for Trefftz methods. Zbl 1244.65187 Li, Zi-Cai; Young, Lih-Jier; Huang, Hung-Tsai; Liu, Ya-Ping; Cheng, Alexander H.-D. 13 2010 Superconvergence of solution derivatives for the Shortley-Weller difference approximation of Poisson’s equation. II: Sigularity problems. Zbl 1031.65118 Li, Zi-Cai; Hu, Hsin-Yun; Fang, Qing; Yamamoto, Tetsuro 13 2003 A radial basis collocation method for Hamilton-Jacobi-Bellman equations. Zbl 1104.49024 Huang, C.-S.; Wang, S.; Chen, C. S.; Li, Z.-C. 12 2006 Superconvergence of solution derivatives for the Shortley–Weller difference approximation of Poisson’s equation. I: Smoothness problems. Zbl 1030.65108 Li, Zi-Cai; Yamamoto, Tetsuro; Fang, Qing 12 2003 Effective condition number and its applications. Zbl 1198.65085 Li, Zi-Cai; Huang, Hung-Tsai; Chen, Jeng-Tzong; Wei, Yimin 12 2010 The collocation Trefftz method for biharmonic equations with crack singularities. Zbl 1106.74418 Li, Zi-Cai; Lu, Tzon-Tzer; Hu, Hsin-Yun 11 2004 Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations. Zbl 1249.65087 Li, Zi-Cai; Huang, Hung-Tsai; Wei, Yimin 11 2011 The method of fundamental solutions for the Helmholtz equation. Zbl 1406.65130 Li, Zi-Cai; Wei, Yimin; Chen, Yunkun; Huang, Hung-Tsai 11 2019 Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson’s equation with singularities on polygonal domains. Zbl 1139.65072 Li, Zi-Cai; Hu, Hsin-Yun; Wang, Song; Fang, Qing 10 2008 Computer transformation of digital images and patterns. Zbl 0744.68135 Li, Zi Cai; Bui, Tien Dai; Tang, Yuan Yan; Suen, Ching Y. 10 1989 Penalty combinations of the Ritz-Galerkin and finite difference methods for singularity problems. Zbl 0886.65106 Li, Zi-Cai 10 1997 Boundary penalty finite element methods for blending surfaces. II: Biharmonic equations. Zbl 0942.65134 Li, Zi-Cai 9 1999 New expansions of numerical eigenvalues by Wilson’s element. Zbl 1165.65070 Lin, Qun; Huang, Hung-Tsai; Li, Zi-Cai 9 2009 Neumann problems of 2D Laplace’s equation by method of fundamental solutions. Zbl 1368.65254 Li, Zi-Cai; Lee, Ming-Gong; Huang, Hung-Tsai; Chiang, John Y. 9 2017 The null-field method of Dirichlet problems of Laplace’s equation on circular domains with circular holes. Zbl 1245.74098 Li, Zi-Cai; Huang, Hung-Tsai; Liaw, Cai-Pin; Lee, Ming-Gong 8 2012 Special boundary approximation methods for Laplace equation problems with boundary singularities–applications to the Motz problem. Zbl 1094.65119 Li, Z. C.; Chan, Y. L.; Georgiou, G. C.; Xenophontos, C. 8 2006 Algorithm singularity of the null-field method for Dirichlet problems of Laplace’s equation in annular and circular domains. Zbl 1297.74147 Lee, Ming-Gong; Li, Zi-Cai; Zhang, Liping; Huang, Hung-Tsai; Chiang, John Y. 8 2014 A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation. Zbl 1024.65109 Wang, Song; Li, Zi-Cai 8 2003 Source nodes on elliptic pseudo-boundaries in the method of fundamental solutions for Laplace’s equation; selection of pseudo-boundaries. Zbl 1437.65223 Dou, Fangfang; Zhang, Li-Ping; Li, Zi-Cai; Chen, C. S. 8 2020 Mixed types of boundary conditions at corners of linear elastostatics and their numerical solutions. Zbl 1259.74087 Lee, Ming-Gong; Young, Lih-Jier; Li, Zi-Cai; Chu, Po-Chun 8 2011 Models of corner and crack singularity of linear elastostatics and their numerical solutions. Zbl 1267.74050 Li, Zi-Cai; Chu, Po-Chun; Young, Lih-Jier; Lee, Ming-Gong 7 2010 The Trefftz method for solving eigenvalue problems. Zbl 1195.65163 Li, Zi-Cai; Lu, Tzon-Tzer; Tsai, Heng-Shuing; Cheng, Alexander H. D. 7 2006 Stability analysis for the penalty plus hybrid and the direct Trefftz methods for singularity problems. Zbl 1195.65153 Li, Zi-Cai; Huang, Hung-Tsai; Huang, Jin; Ling, Leevan 7 2007 A new kind of combinations between the Ritz-Galerkin and finite element methods for singularity problems. Zbl 0638.65078 Li, Z. C.; Bui, T. D. 6 1988 An approach combining the Ritz-Galerkin and finite difference methods. Zbl 0686.65075 Li, Zi-Cai 6 1989 Global superconvergence of Adini’s elements coupled with the Trefftz method for singular problems. Zbl 1033.65094 Huang, Hung-Tsai; Li, Zi-Cai 6 2003 New error estimates of Adini’s elements for Poisson’s equation. Zbl 1069.65119 Huang, Hung-Tsai; Li, Zi-Cai; Yan, Ningning 6 2004 Cauchy problems of Laplace’s equation by the methods of fundamental solutions and particular solutions. Zbl 1297.65137 Zhang, Liping; Li, Zi-Cai; Wei, Yimin; Chiang, John Y. 6 2013 Conservative schemes and degenerate scale problems in the null-field method for Dirichlet problems of Laplace’s equation in circular domains with circular holes. Zbl 1351.74168 Lee, Ming-Gong; Li, Zi-Cai; Huang, Hung-Tsai; Chiang, John Y. 6 2013 Analysis on the method of fundamental solutions for biharmonic equations. Zbl 1429.65293 Dou, Fangfang; Li, Zi-Cai; Chen, C. S.; Tian, Zhaolu 6 2018 Analysis of the method of fundamental solutions for the modified Helmholtz equation. Zbl 1411.78011 Tian, Zhaolu; Li, Zi-Cai; Huang, Hung-Tsai; Chen, C. S. 6 2017 Six combinations of the Ritz-Galerkin and finite element methods for elliptic boundary value problems. Zbl 0662.65095 Li, Z. C.; Bui, T. D. 5 1988 Splitting-integrating method for inverse transformation of \(n\)-dimensional digital images and patterns. Zbl 0829.68109 Li, Zi-Cai 5 1995 The simplified hybrid-combined methods for Laplace’s equation with singularities. Zbl 0692.65050 Li, Z. C.; Bui, T. D. 5 1990 Effective condition number for the finite element method using local mesh refinements. Zbl 1180.65150 Li, Zi-Cai; Huang, Hung-Tsai 5 2009 Coupling strategy for matching different methods in solving singularity problems. Zbl 0718.65073 Li, Z. C.; Bui, T. D. 5 1990 On nonconforming combinations of various finite element methods for solving elliptic boundary value problems. Zbl 0726.65126 Li, Zi-Cai 5 1991 Penalty-combined approaches to the Ritz-Galerkin and finite element methods for singularity problems of elliptic equations. Zbl 0749.65076 Li, Zi-Cai 5 1992 Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods. Zbl 1381.45005 Huang, Jin; Zeng, Guang; He, Xiaoming; Li, Zi-Cai 5 2012 Effective condition number for simplified hybrid Trefftz methods. Zbl 1244.65185 Li, Zi-Cai; Huang, Hung-Tsai 5 2008 Advanced quadrature methods and splitting extrapolation algorithms for first kind boundary integral equations of Laplace’s equation with discontinuity solutions. Zbl 1244.65201 Huang, Jin; Li, Zi-Cai; Chen, I-Lin; Cheng, Alexander H. D. 5 2010 Effective condition number of the Hermite finite element methods for biharmonic equations. Zbl 1163.65086 Li, Zi Cai; Huang, Hung-Tsai; Huang, Jin 5 2008 An analysis of a conforming exponentially fitted finite element method for a convection-diffusion problem. Zbl 1008.65081 Wang, Song; Li, Zi-Cai 5 2002 Boundary methods for Dirichlet problems of Laplaces equation in elliptic domains with elliptic holes. Zbl 1403.65208 Li, Zi-Cai; Zhang, Li-Ping; Wei, Yimin; Lee, Ming-Gong; Chiang, John Y. 5 2015 Boundary methods for mixed boundary problems of Laplace’s equation in elliptic domains with elliptic holes. Zbl 1403.74289 Zhang, Li-Ping; Li, Zi-Cai; Lee, Ming-Gong 5 2016 The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals. Zbl 1477.65264 Zhang, Li-Ping; Li, Zi-Cai; Huang, Hung-Tsai; Wei, Yimin 5 2019 Superconvergence of solution derivatives of the Shortley-Weller difference approximation to elliptic equations with singularities involving the mixed type of boundary conditions. Zbl 1139.65071 Li, Zi-Cai; Fang, Qing; Wang, Song; Hu, Hsin-Yun 4 2008 A combined method for solving elliptic problems on unbounded domains. Zbl 0688.73052 Li, Zi-Cai 4 1989 Boundary penalty finite element methods for blending surfaces. III: Superconvergence and stability and examples. Zbl 0957.65008 Li, Zi-Cai; Chang, Chia-Shen 4 1999 Superconvergence of high-order FEMs for eigenvalue problems with periodic boundary conditions. Zbl 1229.81010 Huang, H.-T.; Chang, S.-L.; Chien, C.-S.; Li, Z.-C. 4 2009 Error analysis of Trefftz methods for Laplace’s equations and its applications. Zbl 1231.65231 Li, Z. C.; Lu, T. T.; Huang, H. T.; Cheng, A. H.-D. 4 2009 Effective condition number of Trefftz methods for biharmonic equations with crack singularities. Zbl 1224.65108 Li, Zi-Cai; Lu, Tzon-Tzer; Wei, Yimin 4 2009 Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs. Zbl 0989.65135 Li, Zi Cai; Yan, Ningning 4 2001 Blending curves for landing problems by numerical differential equations. I: Mathematical modelling. Zbl 0998.65021 Li, Zi-Cai 4 2000 Global superconvergence of simplified hybrid combinations of the Ritz–Galerkin and FEMs for elliptic equations with singularities. II: Lagrange elements and Adini’s elements. Zbl 1022.65121 Li, Z. C.; Huang, H. T. 4 2002 New error estimates of biquadratic Lagrange elements for Poisson’s equation. Zbl 1091.65111 Huang, Hung-Tsai; Li, Zi-Cai; Zhou, Aihui 4 2006 Error analysis of the Trefftz method for solving Laplace’s eigenvalue problems. Zbl 1109.65095 Li, Zi-Cai 4 2007 Penalty-combined method and applications in solving elliptic problems with singularities. Zbl 0762.76057 Li, Z. C.; Bui, T. D. 4 1992 Combinations of the Ritz-Galerkin and finite difference methods. Zbl 0882.65094 Li, Zi-Cai 4 1996 Stability analysis of Trefftz methods for the stick-slip problem. Zbl 1244.65176 Lu, Tzon-Tzer; Chang, Chia-Ming; Huang, Hung-Tsai; Li, Zi-Cai 4 2009 New error estimates of bi-cubic Hermite finite element methods for biharmonic equations. Zbl 1005.65123 Li, Zi Cai; Yan, Ningning 4 2002 Neumann problems of Laplace’s equation in circular domains with circular holes by methods of field equations. Zbl 1403.65168 Lee, Ming-Gong; Li, Zi-Cai; Huang, Hung-Tsai; Chiang, John Y. 4 2015 The interior field method for Laplace’s equation in circular domains with circular holes. Zbl 1403.74308 Li, Zi-Cai; Chiang, John Y.; Huang, Hung-Tsai; Lee, Ming-Gong 4 2016 Interior field methods for Neumann problems of Laplace’s equation in elliptic domains, comparisons with degenerate scales. Zbl 1403.65207 Li, Zi-Cai; Zhang, Li-Ping; Lee, Ming-Gong 4 2016 Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis. Zbl 1464.65277 Zhang, Li-Ping; Li, Zi-Cai; Huang, Hung-Tsai; Lee, Ming-Gong 4 2021 Error analysis of the method of fundamental solutions for linear elastostatics. Zbl 1290.74017 Li, Zi-Cai; Huang, Hung-Tsai; Lee, Ming-Gong; Chiang, John Y. 4 2013 A spectral collocation method for a rotating Bose-Einstein condensation in optical lattices. Zbl 1259.82012 Li, Z.-C.; Chen, S.-Y.; Chien, C.-S.; Chen, H.-S. 4 2011 Effective condition number for weighted linear least squares problems and applications to the Trefftz method. Zbl 1259.65174 Wei, Yi-Min; Lu, Tzon-Tzer; Huang, Hung-Tsai; Li, Zi-Cai 4 2012 New expansions of numerical eigenvalues by finite elements. Zbl 1147.65090 Huang, Hung-Tsai; Li, Zi-Cai; Lin, Qun 3 2008 The method of fundamental solutions and its combinations for exterior problems. Zbl 1245.65171 Li, Zi-Cai; Lu, Tzon-Tzer; Xie, G. Q. 3 2012 The finite volume method and application in combinations. Zbl 0930.65127 Li, Zi-Cai; Wang, Song 3 1999 Blending curves for landing problems by numerical differential equations. II: Numerical methods. Zbl 0998.65022 Li, Zi-Cai; Huang, Hung-Tsai 3 2000 New series expansions for fundamental solutions of linear elastostatics in 2D. Zbl 1231.35005 Li, Zi-Cai; Lee, Ming-Gong; Chen, Jeng-Tzong 3 2011 Global superconvergence in combinations of Ritz-Galerkin-FEM for singularity problems. Zbl 0933.65125 Li, Zi-Cai; Lin, Qun; Yan, Ning-Ning 3 1999 Particular solutions of singularly perturbed partial differential equations with constant coefficients in rectangular domains. I: Convergence analysis. Zbl 1041.65085 Li, Zi-Cai; Hu, Hsin-Yun; Hsu, Chung-Hua; Wang, Song 3 2004 The cracked-beam problem solved by the boundary approximation method. Zbl 1067.74067 Lu, T. T.; Li, Z. C. 3 2005 A nonconforming combination for solving elliptic problems with interfaces. Zbl 0694.65053 Li, Zi-Cai 3 1989 Splitting-integrating methods for the image transformations \(T\) and \(T^{-1}T\). Zbl 0858.65022 Li, Zi-Cai 3 1996 The Schwarz alternating method for singularity problems. Zbl 0813.65129 Li, Zi-Cai 3 1994 Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries. Zbl 1496.65234 Zhang, Li-Ping; Li, Zi-Cai; Lee, Ming-Gong; Huang, Hung-Tsai 1 2022 Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis. Zbl 1464.65277 Zhang, Li-Ping; Li, Zi-Cai; Huang, Hung-Tsai; Lee, Ming-Gong 4 2021 Dual null field method for Dirichlet problems of Laplace’s equation in circular domains with circular holes. Zbl 1473.65177 Lee, Ming-Gong; Zhang, Li-Ping; Li, Zi-Cai; Kazakov, Alexander. L. 2 2021 Singularity problems from source functions as source nodes located near boundaries; numerical methods and removal techniques. Zbl 1521.74272 Zhang, Li-Ping; Li, Zi-Cai; Huang, Hung-Tsai; Lee, Ming-Gong 2 2021 Source nodes on elliptic pseudo-boundaries in the method of fundamental solutions for Laplace’s equation; selection of pseudo-boundaries. Zbl 1437.65223 Dou, Fangfang; Zhang, Li-Ping; Li, Zi-Cai; Chen, C. S. 8 2020 Super-exponential growth rates of condition number in the boundary knot method for the Helmholtz equation. Zbl 1436.65204 Zhang, Li-Ping; Li, Zi-Cai; Huang, Hung-Tsai; Chen, Zhen 3 2020 The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions. Zbl 1437.35184 Zhang, Li-Ping; Li, Zi-Cai; Chen, Zhen; Huang, Hung-Tsai 3 2020 The method of fundamental solutions for the Helmholtz equation. Zbl 1406.65130 Li, Zi-Cai; Wei, Yimin; Chen, Yunkun; Huang, Hung-Tsai 11 2019 The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals. Zbl 1477.65264 Zhang, Li-Ping; Li, Zi-Cai; Huang, Hung-Tsai; Wei, Yimin 5 2019 Analysis on the method of fundamental solutions for biharmonic equations. Zbl 1429.65293 Dou, Fangfang; Li, Zi-Cai; Chen, C. S.; Tian, Zhaolu 6 2018 Neumann problems of 2D Laplace’s equation by method of fundamental solutions. Zbl 1368.65254 Li, Zi-Cai; Lee, Ming-Gong; Huang, Hung-Tsai; Chiang, John Y. 9 2017 Analysis of the method of fundamental solutions for the modified Helmholtz equation. Zbl 1411.78011 Tian, Zhaolu; Li, Zi-Cai; Huang, Hung-Tsai; Chen, C. S. 6 2017 Boundary methods for mixed boundary problems of Laplace’s equation in elliptic domains with elliptic holes. Zbl 1403.74289 Zhang, Li-Ping; Li, Zi-Cai; Lee, Ming-Gong 5 2016 The interior field method for Laplace’s equation in circular domains with circular holes. Zbl 1403.74308 Li, Zi-Cai; Chiang, John Y.; Huang, Hung-Tsai; Lee, Ming-Gong 4 2016 Interior field methods for Neumann problems of Laplace’s equation in elliptic domains, comparisons with degenerate scales. Zbl 1403.65207 Li, Zi-Cai; Zhang, Li-Ping; Lee, Ming-Gong 4 2016 Boundary methods for Dirichlet problems of Laplaces equation in elliptic domains with elliptic holes. Zbl 1403.65208 Li, Zi-Cai; Zhang, Li-Ping; Wei, Yimin; Lee, Ming-Gong; Chiang, John Y. 5 2015 Neumann problems of Laplace’s equation in circular domains with circular holes by methods of field equations. Zbl 1403.65168 Lee, Ming-Gong; Li, Zi-Cai; Huang, Hung-Tsai; Chiang, John Y. 4 2015 Algorithm singularity of the null-field method for Dirichlet problems of Laplace’s equation in annular and circular domains. Zbl 1297.74147 Lee, Ming-Gong; Li, Zi-Cai; Zhang, Liping; Huang, Hung-Tsai; Chiang, John Y. 8 2014 Cauchy problems of Laplace’s equation by the methods of fundamental solutions and particular solutions. Zbl 1297.65137 Zhang, Liping; Li, Zi-Cai; Wei, Yimin; Chiang, John Y. 6 2013 Conservative schemes and degenerate scale problems in the null-field method for Dirichlet problems of Laplace’s equation in circular domains with circular holes. Zbl 1351.74168 Lee, Ming-Gong; Li, Zi-Cai; Huang, Hung-Tsai; Chiang, John Y. 6 2013 Error analysis of the method of fundamental solutions for linear elastostatics. Zbl 1290.74017 Li, Zi-Cai; Huang, Hung-Tsai; Lee, Ming-Gong; Chiang, John Y. 4 2013 Collocation Trefftz methods for the Stokes equations with singularity. Zbl 1364.76158 Li, Zi-Cai; Lee, Ming-Gong; Chiang, John Y. 3 2013 The null-field method of Dirichlet problems of Laplace’s equation on circular domains with circular holes. Zbl 1245.74098 Li, Zi-Cai; Huang, Hung-Tsai; Liaw, Cai-Pin; Lee, Ming-Gong 8 2012 Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods. Zbl 1381.45005 Huang, Jin; Zeng, Guang; He, Xiaoming; Li, Zi-Cai 5 2012 Effective condition number for weighted linear least squares problems and applications to the Trefftz method. Zbl 1259.65174 Wei, Yi-Min; Lu, Tzon-Tzer; Huang, Hung-Tsai; Li, Zi-Cai 4 2012 The method of fundamental solutions and its combinations for exterior problems. Zbl 1245.65171 Li, Zi-Cai; Lu, Tzon-Tzer; Xie, G. Q. 3 2012 The Trefftz method using fundamental solutions for biharmonic equations. Zbl 1222.65131 Li, Zi-Cai; Lee, Ming-Gong; Chiang, John Y.; Liu, Ya Ping 15 2011 Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations. Zbl 1249.65087 Li, Zi-Cai; Huang, Hung-Tsai; Wei, Yimin 11 2011 Mixed types of boundary conditions at corners of linear elastostatics and their numerical solutions. Zbl 1259.74087 Lee, Ming-Gong; Young, Lih-Jier; Li, Zi-Cai; Chu, Po-Chun 8 2011 A spectral collocation method for a rotating Bose-Einstein condensation in optical lattices. Zbl 1259.82012 Li, Z.-C.; Chen, S.-Y.; Chien, C.-S.; Chen, H.-S. 4 2011 New series expansions for fundamental solutions of linear elastostatics in 2D. Zbl 1231.35005 Li, Zi-Cai; Lee, Ming-Gong; Chen, Jeng-Tzong 3 2011 Effective condition number of finite difference method for Poisson’s equation involving boundary singularities. Zbl 1416.65404 Li, Zi-Cai; Huang, Hung-Tsai; Huang, Chien-Sen; Lu, Tzon-Tzer; Fang, Qing 1 2011 Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace’s equation. Zbl 1223.65085 Li, Zi-Cai; Huang, Jin; Huang, Hung-Tsai 22 2010 Combined Trefftz methods of particular and fundamental solutions for corner and crack singularity of linear elastostatics. Zbl 1267.74128 Lee, Ming-Gong; Young, Lih-Jier; Li, Zi-Cai; Chu, Po-Chun 16 2010 Comparisons of fundamental solutions and particular solutions for Trefftz methods. Zbl 1244.65187 Li, Zi-Cai; Young, Lih-Jier; Huang, Hung-Tsai; Liu, Ya-Ping; Cheng, Alexander H.-D. 13 2010 Effective condition number and its applications. Zbl 1198.65085 Li, Zi-Cai; Huang, Hung-Tsai; Chen, Jeng-Tzong; Wei, Yimin 12 2010 Models of corner and crack singularity of linear elastostatics and their numerical solutions. Zbl 1267.74050 Li, Zi-Cai; Chu, Po-Chun; Young, Lih-Jier; Lee, Ming-Gong 7 2010 Advanced quadrature methods and splitting extrapolation algorithms for first kind boundary integral equations of Laplace’s equation with discontinuity solutions. Zbl 1244.65201 Huang, Jin; Li, Zi-Cai; Chen, I-Lin; Cheng, Alexander H. D. 5 2010 The method of fundamental solutions for annular shaped domains. Zbl 1166.65060 Li, Zi-Cai 34 2009 Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs. Zbl 1175.65142 Huang, Jin; Lü, Tao; Li, Zi Cai 17 2009 New expansions of numerical eigenvalues by Wilson’s element. Zbl 1165.65070 Lin, Qun; Huang, Hung-Tsai; Li, Zi-Cai 9 2009 Effective condition number for the finite element method using local mesh refinements. Zbl 1180.65150 Li, Zi-Cai; Huang, Hung-Tsai 5 2009 Superconvergence of high-order FEMs for eigenvalue problems with periodic boundary conditions. Zbl 1229.81010 Huang, H.-T.; Chang, S.-L.; Chien, C.-S.; Li, Z.-C. 4 2009 Error analysis of Trefftz methods for Laplace’s equations and its applications. Zbl 1231.65231 Li, Z. C.; Lu, T. T.; Huang, H. T.; Cheng, A. H.-D. 4 2009 Effective condition number of Trefftz methods for biharmonic equations with crack singularities. Zbl 1224.65108 Li, Zi-Cai; Lu, Tzon-Tzer; Wei, Yimin 4 2009 Stability analysis of Trefftz methods for the stick-slip problem. Zbl 1244.65176 Lu, Tzon-Tzer; Chang, Chia-Ming; Huang, Hung-Tsai; Li, Zi-Cai 4 2009 Superconvergence of solution derivatives for the Shortley-Weller difference approximation for parabolic problems. Zbl 1190.65134 Li, Z.-C.; Fang, Q.; Wang, S. 1 2009 Trefftz and collocation methods. Zbl 1140.65005 Li, Z.-C.; Lu, T.-T.; Hu, H.-Y.; Cheng, A. H.-D. 98 2008 New expansions of numerical eigenvalues for \(-\delta u=\lambda \rho u\) by nonconforming elements. Zbl 1198.65228 Lin, Qun; Huang, Hung-Tsai; Li, Zi-Cai 29 2008 Effective condition number for numerical partial differential equations. Zbl 1212.65410 Li, Z.-C.; Huang, H.-T. 19 2008 The Trefftz method for the Helmholtz equation with degeneracy. Zbl 1141.65082 Li, Z. C. 18 2008 Two-grid discretization schemes for nonlinear Schrödinger equations. Zbl 1135.65361 Chien, C.-S.; Huang, H.-T.; Jeng, B.-W.; Li, Z.-C. 18 2008 Study on effective condition number for collocation methods. Zbl 1244.65186 Li, Zi-Cai; Huang, Hung-Tsai 13 2008 Combinations of method of fundamental solutions for Laplace’s equation with singularities. Zbl 1244.65222 Li, Zi-Cai 13 2008 Superconvergence of solution derivatives of the Shortley-Weller difference approximation to Poisson’s equation with singularities on polygonal domains. Zbl 1139.65072 Li, Zi-Cai; Hu, Hsin-Yun; Wang, Song; Fang, Qing 10 2008 Effective condition number for simplified hybrid Trefftz methods. Zbl 1244.65185 Li, Zi-Cai; Huang, Hung-Tsai 5 2008 Effective condition number of the Hermite finite element methods for biharmonic equations. Zbl 1163.65086 Li, Zi Cai; Huang, Hung-Tsai; Huang, Jin 5 2008 Superconvergence of solution derivatives of the Shortley-Weller difference approximation to elliptic equations with singularities involving the mixed type of boundary conditions. Zbl 1139.65071 Li, Zi-Cai; Fang, Qing; Wang, Song; Hu, Hsin-Yun 4 2008 New expansions of numerical eigenvalues by finite elements. Zbl 1147.65090 Huang, Hung-Tsai; Li, Zi-Cai; Lin, Qun 3 2008 Accurate and approximate analytic solutions of singularly perturbed differential equations with two-dimensional boundary layers. Zbl 1142.65385 Li, Zi-Cai; Tsai, Heng-Shuing; Wang, Song; Miller, John J. H. 3 2008 Superconvergence and stability for boundary penalty techniques of finite difference methods. Zbl 1144.65066 Li, Zi-Cai; Huang, Hung-Tsai; Huang, Jin 2 2008 Superconvergence of FEMs and numerical continuation for parameter-dependent problems with folds. Zbl 1147.65324 Chien, C.-S.; Huang, H.-T.; Jeng, B.-W.; Li, Z.-C. 2 2008 A time-independent approach for computing wave functions of the Schrödinger-Poisson system. Zbl 1212.65433 Chien, C.-S.; Jeng, B.-W.; Li, Z.-C. 2 2008 A finite difference continuation method for computing energy levels of Bose-Einstein condensates. Zbl 1197.65119 Chang, S.-L.; Chien, C.-S.; Li, Z.-C. 2 2008 Coupling techniques of Trefftz methods. Zbl 1420.65123 Huang, Hung-Tsai; Li, Zi-Cai; Cheng, Alexander H.-D. 1 2008 Discretization principles for linear two-point boundary value problems. III. Zbl 1169.65075 Yamamoto, Tetsuro; Oishi, Shin’ichi; Nashed, M. Zuhair; Li, Zi-Cai; Fang, Qing 1 2008 Splitting extrapolations for solving boundary integral equations of mixed boundary conditions on polygons by mechanical quadrature methods. Zbl 1176.65142 Huang, Jin; Li, Zi Cai; Lü, Tao; Zhu, Rui 1 2008 Trefftz, collocation, and other boundary methods – a comparison. Zbl 1223.65093 Li, Zi-Cai; Lu, Tzon-Tzer; Huang, Hung-Tsai; Cheng, Alexander H.-D. 52 2007 Effective condition number for finite difference method. Zbl 1104.65043 Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai 38 2007 Stability analysis for the penalty plus hybrid and the direct Trefftz methods for singularity problems. Zbl 1195.65153 Li, Zi-Cai; Huang, Hung-Tsai; Huang, Jin; Ling, Leevan 7 2007 Error analysis of the Trefftz method for solving Laplace’s eigenvalue problems. Zbl 1109.65095 Li, Zi-Cai 4 2007 Stability analysis and superconvergence for the penalty Trefftz method coupled with FEM for singularity problems. Zbl 1195.65152 Li, Zi-Cai; Huang, Hung-Tsai; Huang, Jin 2 2007 Collocation methods for Poisson’s equation. Zbl 1124.65111 Hu, Hsin-Yun; Li, Zi-Cai 17 2006 Effective condition number and superconvergence of the Trefftz method coupled with high-order FEM for singularity problems. Zbl 1195.65151 Huang, Hung-Tsai; Li, Zi-Cai 16 2006 A radial basis collocation method for Hamilton-Jacobi-Bellman equations. Zbl 1104.49024 Huang, C.-S.; Wang, S.; Chen, C. S.; Li, Z.-C. 12 2006 Special boundary approximation methods for Laplace equation problems with boundary singularities–applications to the Motz problem. Zbl 1094.65119 Li, Z. C.; Chan, Y. L.; Georgiou, G. C.; Xenophontos, C. 8 2006 The Trefftz method for solving eigenvalue problems. Zbl 1195.65163 Li, Zi-Cai; Lu, Tzon-Tzer; Tsai, Heng-Shuing; Cheng, Alexander H. D. 7 2006 New error estimates of biquadratic Lagrange elements for Poisson’s equation. Zbl 1091.65111 Huang, Hung-Tsai; Li, Zi-Cai; Zhou, Aihui 4 2006 Combinations of collocation and finite-element methods for Poisson’s equation. Zbl 1134.65083 Hu, Hsin-Yun; Li, Zi-Cai 2 2006 Radial basis collocation methods for elliptic boundary value problems. Zbl 1127.65089 Hu, Hsin-Yun; Li, Zi-Cai; Cheng, Alexander H.-D. 61 2005 Particular solutions of Laplace’s equations on polygons and new models involving mild singularities. Zbl 1104.65114 Li, Zi-Cai; Lu, Tzon-Tzer; Hu, Hsin-Yun; Cheng, Alexander H. D. 13 2005 The cracked-beam problem solved by the boundary approximation method. Zbl 1067.74067 Lu, T. T.; Li, Z. C. 3 2005 Interior boundary conditions in the Schwarz alternating method for the Trefftz method. Zbl 1182.74255 Li, Zi-Cai; Huang, Chieh-Sen; Chen, Ren C. 2 2005 Verification of reduced convergence rates. Zbl 1068.65121 Hu, Hsin-Yun; Li, Zi-Cai 1 2005 Highly accurate solutions of Motz’s and the cracked beam problems. Zbl 1074.74655 Lu, T. T.; Hu, H. Y.; Li, Z. C. 28 2004 The collocation Trefftz method for biharmonic equations with crack singularities. Zbl 1106.74418 Li, Zi-Cai; Lu, Tzon-Tzer; Hu, Hsin-Yun 11 2004 New error estimates of Adini’s elements for Poisson’s equation. Zbl 1069.65119 Huang, Hung-Tsai; Li, Zi-Cai; Yan, Ningning 6 2004 Particular solutions of singularly perturbed partial differential equations with constant coefficients in rectangular domains. I: Convergence analysis. Zbl 1041.65085 Li, Zi-Cai; Hu, Hsin-Yun; Hsu, Chung-Hua; Wang, Song 3 2004 Superconvergence of solution derivatives for the Shortley-Weller difference approximation of Poisson’s equation. II: Sigularity problems. Zbl 1031.65118 Li, Zi-Cai; Hu, Hsin-Yun; Fang, Qing; Yamamoto, Tetsuro 13 2003 Superconvergence of solution derivatives for the Shortley–Weller difference approximation of Poisson’s equation. I: Smoothness problems. Zbl 1030.65108 Li, Zi-Cai; Yamamoto, Tetsuro; Fang, Qing 12 2003 A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation. Zbl 1024.65109 Wang, Song; Li, Zi-Cai 8 2003 Global superconvergence of Adini’s elements coupled with the Trefftz method for singular problems. Zbl 1033.65094 Huang, Hung-Tsai; Li, Zi-Cai 6 2003 An analysis of a conforming exponentially fitted finite element method for a convection-diffusion problem. Zbl 1008.65081 Wang, Song; Li, Zi-Cai 5 2002 Global superconvergence of simplified hybrid combinations of the Ritz–Galerkin and FEMs for elliptic equations with singularities. II: Lagrange elements and Adini’s elements. Zbl 1022.65121 Li, Z. C.; Huang, H. T. 4 2002 New error estimates of bi-cubic Hermite finite element methods for biharmonic equations. Zbl 1005.65123 Li, Zi Cai; Yan, Ningning 4 2002 Global superconvergence of finite element methods for biharmonic equations and blending surfaces. Zbl 1057.65072 Li, Z. C.; Lu, T. T. 1 2002 Recognition of handwritten characters by parts with multiple orientations. Zbl 1002.68150 Li, Z. C.; Li, H. J.; Suen, C. Y.; Wang, H. Q.; Liao, S. Y. 1 2002 Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs. Zbl 0989.65135 Li, Zi Cai; Yan, Ningning 4 2001 Superconvergence of coupling techniques in combined methods for elliptic equations with singularities. Zbl 0987.65107 Li, Zi-Cai 2 2001 Exact numerical methods and their applications to blending curves. Zbl 1019.65061 Li, Zi-Cai; Chang, Chia-Shen; Bui, T. D. 1 2001 ...and 42 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 657 Authors 89 Li, Zi-Cai 47 Huang, Hung-Tsai 25 Lee, Ming-Gong 18 Huang, Jin 18 Zhang, Liping 14 Hu, Hsin-Yun 14 Wei, Yimin 13 Liu, Chein-Shan 11 Chen, Wen 11 Chiang, John Y. 10 Chien, Cheng-Sheng 10 Fan, Chia-Ming 9 Cheng, Alexander H.-D. 9 Wang, Song 8 Chen, Jeng-Tzong 8 Fu, Zhuojia 8 Wang, Lihua 8 Xie, Hehu 7 Boroomand, Bijan 7 Chen, Jiun-Shyan 7 Dehghan Takht Fooladi, Mehdi 7 Fang, Qing 7 Georgiou, Georgios C. 7 Gu, Yan 7 Lin, Qun 7 Lu, Tzontzer 6 Chen, Ching-Shyang 6 Chen, Yanping 6 Jeng, B.-W. 6 Oruç, Ömer 6 Tian, Zhikun 6 Wang, Fajie 6 Wang, Jianyun 6 Xenophontos, Christos A. 6 Young, Der-Liang 5 Dosiyev, Adigüzel A. 5 Elliotis, Miltiades C. 5 He, Xiaoming 5 Lin, Ji 5 Schaback, Robert 5 Shi, Dongyang 5 Yan, Ningning 5 Yang, Yidu 5 Young, Lih-Jier 4 Bi, Hai 4 Borkowski, Mariusz 4 Cheng, Pan 4 Chi, Sheng-Wei 4 Cival Buranay, S. 4 Dou, Fangfang 4 Hon, Yiu-Chung 4 Hu, Jun 4 Huang, Yunqing 4 Lee, Ying-Te 4 Ling, Leevan 4 Maciąg, Artur 4 Marin, Liviu 4 Noormohammadi, Nima 4 Qian, Zhihao 4 Siraj-ul-Islam 3 Abbasbandy, Saeid 3 Aslefallah, Mohammad 3 Aziz, Imran 3 Benrabah, Abderafik 3 Bernal, Francisco 3 Chen, Chuin-Shan 3 Chen, Yung-Wei 3 Chu, Po-Chun 3 Colbrook, Matthew J. 3 Haq, Sirajul 3 Hu, Hanzhang 3 Hussain, Manzoor 3 Jia, Shanghui 3 Kao, Shing-Kai 3 Karageorghis, Andreas 3 Kindelan, Manuel Segura 3 Kolodziej, Jan Adam 3 Ku, Cheng-Yu 3 Kuo, Chung-Lun 3 Liao, Xin 3 Liu, Huipo 3 Min, Chohong 3 Nawaz, Rashid 3 Noorizadegan, Amir 3 Qu, Wenzhen 3 Šarler, Božidar 3 Shirzadi, Mohammad 3 Shivanian, Elyas 3 Tsai, Chia-Cheng 3 Wang, Fuzhang 3 Xi, Qiang 3 Zhang, Yaoming 3 Zhou, Yueting 2 Abbaszadeh, Mostafa 2 Ahn, Soyoung 2 Al-Ali, A. Y. 2 Almutairi, K. H. 2 Alwardi, H. 2 Antunes, Pedro Ricardo Simão 2 Bateniparvar, Omid ...and 557 more Authors all top 5 Cited in 95 Serials 122 Engineering Analysis with Boundary Elements 39 Computers & Mathematics with Applications 34 Journal of Computational and Applied Mathematics 22 Applied Mathematics and Computation 19 Applied Numerical Mathematics 17 Numerical Methods for Partial Differential Equations 15 Journal of Computational Physics 14 Computer Methods in Applied Mechanics and Engineering 11 International Journal for Numerical Methods in Engineering 8 Journal of Scientific Computing 8 Applied Mathematical Modelling 8 Mathematical Problems in Engineering 7 Numerical Algorithms 7 Advances in Applied Mathematics and Mechanics 6 Computing 6 International Journal of Computer Mathematics 5 Numerical Functional Analysis and Optimization 5 Computational Mechanics 5 Applied Mathematics Letters 5 Inverse Problems in Science and Engineering 5 Science China. 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