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Li, Zi-Cai

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Author ID: li.zi-cai Recent zbMATH articles by "Li, Zi-Cai"
Published as: Li, Zi-Cai; Li, Z. C.; Li, Z.-C.; Li, Zi Cai; Li, Zi-cai
Documents Indexed: 162 Publications since 1980, including 4 Books
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Serials

34 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 Computer Methods in Applied Mechanics and Engineering
7 Computing
6 Mathematical and Computer Modelling
5 Numerical Functional Analysis and Optimization
4 Numerical Linear Algebra with Applications
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 Numerical Algorithms
2 Information
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)

Publications by Year

Citations contained in zbMATH Open

137 Publications have been cited 1,029 times in 403 Documents Cited by Year
Trefftz and collocation methods. Zbl 1140.65005
Li, Z.-C.; Lu, T.-T.; Hu, H.-Y.; Cheng, A. H.-D.
76
2008
Combined methods for elliptic equations with singularities, interfaces and infinities. Zbl 0909.65079
Li, Zi Cai
68
1998
Radial basis collocation methods for elliptic boundary value problems. Zbl 1127.65089
Hu, Hsin-Yun; Li, Zi-Cai; Cheng, Alexander H.-D.
51
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.
46
2007
Singularities and treatments of elliptic boundary value problems. Zbl 1042.35524
Li, Z. C.; Lu, T. T.
38
2000
Effective condition number for finite difference method. Zbl 1104.65043
Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai
36
2007
The method of fundamental solutions for annular shaped domains. Zbl 1166.65060
Li, Zi-Cai
28
2009
Highly accurate solutions of Motz’s and the cracked beam problems. Zbl 1074.74655
Lu, T. T.; Hu, H. Y.; Li, Z. C.
25
2004
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
22
2008
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
19
2010
Effective condition number for numerical partial differential equations. Zbl 1212.65410
Li, Z.-C.; Huang, H.-T.
17
2008
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
16
2009
The Trefftz method for the Helmholtz equation with degeneracy. Zbl 1141.65082
Li, Z. C.
16
2008
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
15
2006
Collocation methods for Poisson’s equation. Zbl 1124.65111
Hu, Hsin-Yun; Li, Zi-Cai
15
2006
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
14
2010
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
Study on effective condition number for collocation methods. Zbl 1244.65186
Li, Zi-Cai; Huang, Hung-Tsai
12
2008
The Trefftz method using fundamental solutions for biharmonic equations. Zbl 1222.65131
Li, Zi-Cai; Lee, Ming-Gong; Chiang, John Y.; Liu, Ya Ping
12
2011
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
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.
12
2005
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
10
2011
Computer transformation of digital images and patterns. Zbl 0744.68135
Li, Zi Cai; Bui, Tien Dai; Tang, Yuan Yan; Suen, Ching Y.
10
1989
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
A coupling approach of state-based peridynamics with node-based smoothed finite element method. Zbl 1439.74392
Bie, Y. H.; Cui, X. Y.; Li, Z. C.
10
2018
Penalty combinations of the Ritz-Galerkin and finite difference methods for singularity problems. Zbl 0886.65106
Li, Zi-Cai
10
1997
A radial basis collocation method for Hamilton-Jacobi-Bellman equations. Zbl 1104.49024
Huang, C.-S.; Wang, S.; Chen, C. S.; Li, Z.-C.
10
2006
Boundary penalty finite element methods for blending surfaces. II: Biharmonic equations. Zbl 0942.65134
Li, Zi-Cai
9
1999
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
Effective condition number and its applications. Zbl 1198.65085
Li, Zi-Cai; Huang, Hung-Tsai; Chen, Jeng-Tzong; Wei, Yimin
8
2010
Two-grid discretization schemes for nonlinear Schrödinger equations. Zbl 1135.65361
Chien, C.-S.; Huang, H.-T.; Jeng, B.-W.; Li, Z.-C.
8
2008
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
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
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
7
2011
New expansions of numerical eigenvalues by Wilson’s element. Zbl 1165.65070
Lin, Qun; Huang, Hung-Tsai; Li, Zi-Cai
7
2009
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.
7
2006
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 method of fundamental solutions for the Helmholtz equation. Zbl 1406.65130
Li, Zi-Cai; Wei, Yimin; Chen, Yunkun; Huang, Hung-Tsai
7
2019
An approach combining the Ritz-Galerkin and finite difference methods. Zbl 0686.65075
Li, Zi-Cai
6
1989
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.
6
2014
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
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 for the finite element method using local mesh refinements. Zbl 1180.65150
Li, Zi-Cai; Huang, Hung-Tsai
5
2009
The Trefftz method for solving eigenvalue problems. Zbl 1195.65163
Li, Zi-Cai; Lu, Tzon-Tzer; Tsai, Heng-Shuing; Cheng, Alexander H. D.
5
2006
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-integrating method for inverse transformation of \(n\)-dimensional digital images and patterns. Zbl 0829.68109
Li, Zi-Cai
5
1995
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
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.
5
2013
The simplified hybrid-combined methods for Laplace’s equation with singularities. Zbl 0692.65050
Li, Z. C.; Bui, T. D.
5
1990
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.
5
1988
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
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
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.
5
2017
New error estimates of biquadratic Lagrange elements for Poisson’s equation. Zbl 1091.65111
Huang, Hung-Tsai; Li, Zi-Cai; Zhou, Aihui
4
2006
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 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
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.
4
2013
Penalty-combined method and applications in solving elliptic problems with singularities. Zbl 0762.76057
Li, Z. C.; Bui, T. D.
4
1992
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
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 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
Combinations of the Ritz-Galerkin and finite difference methods. Zbl 0882.65094
Li, Zi-Cai
4
1996
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
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 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
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
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
4
2016
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.
4
2017
Collocation Trefftz methods for the Stokes equations with singularity. Zbl 1364.76158
Li, Zi-Cai; Lee, Ming-Gong; Chiang, John Y.
3
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.
3
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
3
2012
The Schwarz alternating method for singularity problems. Zbl 0813.65129
Li, Zi-Cai
3
1994
The cracked-beam problem solved by the boundary approximation method. Zbl 1067.74067
Lu, T. T.; Li, Z. C.
3
2005
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
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.
3
2020
Splitting-integrating methods for the image transformations \(T\) and \(T^{-1}T\). Zbl 0858.65022
Li, Zi-Cai
3
1996
Effective condition number of Trefftz methods for biharmonic equations with crack singularities. Zbl 1224.65108
Li, Zi-Cai; Lu, Tzon-Tzer; Wei, Yimin
3
2009
A nonconforming combination for solving elliptic problems with interfaces. Zbl 0694.65053
Li, Zi-Cai
3
1989
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
Blending curves for landing problems by numerical differential equations. II: Numerical methods. Zbl 0998.65022
Li, Zi-Cai; Huang, Hung-Tsai
3
2000
Global superconvergence in combinations of Ritz-Galerkin-FEM for singularity problems. Zbl 0933.65125
Li, Zi-Cai; Lin, Qun; Yan, Ning-Ning
3
1999
The finite volume method and application in combinations. Zbl 0930.65127
Li, Zi-Cai; Wang, Song
3
1999
Error analysis of the Trefftz method for solving Laplace’s eigenvalue problems. Zbl 1109.65095
Li, Zi-Cai
3
2007
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
3
2016
The method of fundamental solutions and its combinations for exterior problems. Zbl 1245.65171
Li, Zi-Cai; Lu, Tzon-Tzer; Xie, G. Q.
2
2012
New series expansions for fundamental solutions of linear elastostatics in 2D. Zbl 1231.35005
Li, Zi-Cai; Lee, Ming-Gong; Chen, Jeng-Tzong
2
2011
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
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
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.
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
1
2020
The method of fundamental solutions for the Helmholtz equation. Zbl 1406.65130
Li, Zi-Cai; Wei, Yimin; Chen, Yunkun; Huang, Hung-Tsai
7
2019
A coupling approach of state-based peridynamics with node-based smoothed finite element method. Zbl 1439.74392
Bie, Y. H.; Cui, X. Y.; Li, Z. C.
10
2018
Analysis on the method of fundamental solutions for biharmonic equations. Zbl 1429.65293
Dou, Fangfang; Li, Zi-Cai; Chen, C. S.; Tian, Zhaolu
2
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.
5
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.
4
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
4
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
3
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
2
2016
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
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.
2
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.
6
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.
5
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.
4
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
3
2012
The method of fundamental solutions and its combinations for exterior problems. Zbl 1245.65171
Li, Zi-Cai; Lu, Tzon-Tzer; Xie, G. Q.
2
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
12
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
10
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
7
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.
3
2011
New series expansions for fundamental solutions of linear elastostatics in 2D. Zbl 1231.35005
Li, Zi-Cai; Lee, Ming-Gong; Chen, Jeng-Tzong
2
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
19
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
14
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
8
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
28
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
16
2009
New expansions of numerical eigenvalues by Wilson’s element. Zbl 1165.65070
Lin, Qun; Huang, Hung-Tsai; Li, Zi-Cai
7
2009
Effective condition number for the finite element method using local mesh refinements. Zbl 1180.65150
Li, Zi-Cai; Huang, Hung-Tsai
5
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 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
3
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.
76
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
22
2008
Effective condition number for numerical partial differential equations. Zbl 1212.65410
Li, Z.-C.; Huang, H.-T.
17
2008
The Trefftz method for the Helmholtz equation with degeneracy. Zbl 1141.65082
Li, Z. C.
16
2008
Combinations of method of fundamental solutions for Laplace’s equation with singularities. Zbl 1244.65222
Li, Zi-Cai
13
2008
Study on effective condition number for collocation methods. Zbl 1244.65186
Li, Zi-Cai; Huang, Hung-Tsai
12
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
Two-grid discretization schemes for nonlinear Schrödinger equations. Zbl 1135.65361
Chien, C.-S.; Huang, H.-T.; Jeng, B.-W.; Li, Z.-C.
8
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
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
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
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
Coupling techniques of Trefftz methods. Zbl 1420.65123
Huang, Hung-Tsai; Li, Zi-Cai; Cheng, Alexander H.-D.
1
2008
Superconvergence and stability for boundary penalty techniques of finite difference methods. Zbl 1144.65066
Li, Zi-Cai; Huang, Hung-Tsai; Huang, Jin
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
Trefftz, collocation, and other boundary methods – a comparison. Zbl 1223.65093
Li, Zi-Cai; Lu, Tzon-Tzer; Huang, Hung-Tsai; Cheng, Alexander H.-D.
46
2007
Effective condition number for finite difference method. Zbl 1104.65043
Li, Zi-Cai; Chien, Cheng-Sheng; Huang, Hung-Tsai
36
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
3
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
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
15
2006
Collocation methods for Poisson’s equation. Zbl 1124.65111
Hu, Hsin-Yun; Li, Zi-Cai
15
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.
10
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.
7
2006
The Trefftz method for solving eigenvalue problems. Zbl 1195.65163
Li, Zi-Cai; Lu, Tzon-Tzer; Tsai, Heng-Shuing; Cheng, Alexander H. D.
5
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.
51
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.
12
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.
25
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
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 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
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
Singularities and treatments of elliptic boundary value problems. Zbl 1042.35524
Li, Z. C.; Lu, T. T.
38
2000
Blending curves for landing problems by numerical differential equations. I: Mathematical modelling. Zbl 0998.65021
Li, Zi-Cai
4
2000
Blending curves for landing problems by numerical differential equations. II: Numerical methods. Zbl 0998.65022
Li, Zi-Cai; Huang, Hung-Tsai
3
2000
Global superconvergence for blending surfaces by boundary penalty plus hybrid FEMs. Zbl 0982.65125
Li, Z. C.; Yan, N. N.
2
2000
Global superconvergence of simplified hybrid combinations for elliptic equations with singularities. I: Basic theorem. Zbl 0962.65088
Li, Z.-C.
1
2000
...and 37 more Documents
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Cited by 522 Authors

83 Li, Zi-Cai
42 Huang, Hung-Tsai
21 Lee, Ming-Gong
17 Huang, Jin
13 Wei, Yimin
13 Zhang, Liping
12 Hu, Hsin-Yun
12 Liu, Chein-Shan
11 Chiang, John Y.
10 Chien, Cheng-Sheng
9 Cheng, Alexander H.-D.
9 Wang, Song
8 Fan, Chia-Ming
7 Chen, Wen
7 Dehghan Takht Fooladi, Mehdi
7 Fang, Qing
7 Georgiou, Georgios C.
7 Lin, Qun
7 Lu, Tzontzer
6 Chen, Ching-Shyang
6 Chen, Jiun-Shyan
6 Fu, Zhuojia
6 Jeng, B.-W.
6 Xenophontos, Christos A.
6 Xie, Hehu
5 Chen, Jeng-Tzong
5 Dosiyev, Adigüzel A.
5 Elliotis, Miltiades C.
5 Gu, Yan
5 He, Xiaoming
5 Wang, Lihua
5 Yan, Ningning
5 Yang, Yidu
5 Young, Lih-Jier
4 Bi, Hai
4 Borkowski, Mariusz
4 Boroomand, Bijan
4 Cheng, Pan
4 Chi, Sheng-Wei
4 Cival Buranay, S.
4 Dou, Fangfang
4 Hon, Yiu-Chung
4 Ling, Leevan
4 Marin, Liviu
4 Schaback, Robert
4 Siraj-ul-Islam
3 Aziz, Imran
3 Bernal, Francisco
3 Chen, Yanping
3 Chen, Yung-Wei
3 Chu, Po-Chun
3 Hu, Hanzhang
3 Hu, Jun
3 Huang, Yunqing
3 Jia, Shanghui
3 Karageorghis, Andreas
3 Kindelan, Manuel Segura
3 Kolodziej, Jan Adam
3 Ku, Cheng-Yu
3 Kuo, Chung-Lun
3 Liu, Huipo
3 Maciąg, Artur
3 Min, Chohong
3 Oruç, Ömer
3 Šarler, Božidar
3 Shirzadi, Mohammad
3 Wang, Fajie
3 Wang, Fuzhang
3 Zhang, Yaoming
2 Abbaszadeh, Mostafa
2 Ahn, Soyoung
2 Al-Ali, A. Y.
2 Almutairi, K. H.
2 Alwardi, H.
2 Benrabah, Abderafik
2 Bergen, Bart
2 Borkowska, Dorota
2 Boussetila, Nadjib
2 Brański, Adam
2 Chan, Hsin-Fang
2 Chang, Shing-Lin
2 Chen, Hongtao
2 Chen, Huei-Shuang
2 Chen, I-Lin
2 Chen, Zhen
2 Christodoulou, Evgenia
2 Colbrook, Matthew J.
2 Desmet, Wim
2 Deuring, Paul
2 Duan, Yong
2 Fili, Abdeljalil
2 Flyer, Natasha
2 Fornberg, Bengt
2 Ghaleb, Ahmed Fouad
2 Grabski, Jakub Krzysztof
2 Groza, Ghiocel
2 Grysa, Krzysztof
2 Han, Houde
2 Haq, Sirajul
2 Heydari, Mohammad Hossien
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Cited in 74 Serials

113 Engineering Analysis with Boundary Elements
34 Computers & Mathematics with Applications
32 Journal of Computational and Applied Mathematics
18 Applied Mathematics and Computation
18 Applied Numerical Mathematics
13 Journal of Computational Physics
12 Numerical Methods for Partial Differential Equations
11 Computer Methods in Applied Mechanics and Engineering
10 International Journal for Numerical Methods in Engineering
8 Mathematical Problems in Engineering
7 Journal of Scientific Computing
6 Computing
6 Applied Mathematical Modelling
5 Numerical Functional Analysis and Optimization
5 Computational Mechanics
5 International Journal of Computer Mathematics
5 Science China. Mathematics
4 Numerische Mathematik
4 Applied Mathematics Letters
4 Mathematical and Computer Modelling
4 Applications of Mathematics
4 Advances in Computational Mathematics
3 Mathematics of Computation
3 Automatica
3 Numerical Algorithms
3 Numerical Linear Algebra with Applications
3 Inverse Problems in Science and Engineering
2 Computer Physics Communications
2 Journal of Engineering Mathematics
2 BIT
2 Mathematics and Computers in Simulation
2 Applied Mathematics and Mechanics. (English Edition)
2 Journal of Global Optimization
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 SIAM Journal on Scientific Computing
2 Journal of the Egyptian Mathematical Society
2 Journal of Inverse and Ill-Posed Problems
2 Engineering Computations
2 Journal of Applied Mathematics
1 Calcolo
1 Journal of Approximation Theory
1 SIAM Journal on Numerical Analysis
1 COMPEL
1 SIAM Journal on Matrix Analysis and Applications
1 Japan Journal of Industrial and Applied Mathematics
1 Linear Algebra and its Applications
1 Communications in Numerical Methods in Engineering
1 Computational and Applied Mathematics
1 International Journal of Numerical Methods for Heat & Fluid Flow
1 Complexity
1 Discrete and Continuous Dynamical Systems
1 Mathematics and Mechanics of Solids
1 Abstract and Applied Analysis
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Lobachevskii Journal of Mathematics
1 Journal of Modern Optics
1 Journal of Zhejiang University. Science
1 Discrete and Continuous Dynamical Systems. Series B
1 Computational Methods in Applied Mathematics
1 Advances in Difference Equations
1 Sibirskie Èlektronnye Matematicheskie Izvestiya
1 Boundary Value Problems
1 International Journal for Computational Methods in Engineering Science and Mechanics
1 Advances in Mathematical Physics
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
1 Asian Journal of Control
1 Mathematical Control and Related Fields
1 Mathematical Sciences
1 Journal of Mathematics
1 Journal of Mathematical Modeling
1 AMM. Applied Mathematics and Mechanics. (English Edition)
1 Journal of Siberian Federal University. Mathematics & Physics
1 Journal of Applied Mathematics and Computational Mechanics

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