Advanced methods of boundary integral equations for Laplace's equation: Relations to method of fundamental solutions.

Zi-Cai Li

Liping Zhang 0005 Zi-Cai Li Hung-Tsai Huang Ming-Gong Lee Advanced methods of boundary integral equations for Laplace's equation: Relations to method of fundamental solutions. 117135 2026 476 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2025.117135 db/journals/jcam/jcam476.html#ZhangLHL26 streams/journals/jcam

Hung-Tsai Huang Zi-Cai Li Yimin Wei 0001 Ching Yee Suen Face Boundary Formulation for Harmonic Models: Face Image Resembling. 14 2024 11 J. Imaging 1 https://doi.org/10.3390/jimaging11010014 db/journals/jimaging/jimaging11.html#HuangLWS24 streams/journals/jimaging

Liping Zhang 0005 Zi-Cai Li Ming-Gong Lee Hung-Tsai Huang Lower and upper bounds of condition number for Vandermonde-wise matrices and method of fundamental solutions using pseudo radial-lines. 2023 March 30 Numer. Linear Algebra Appl. 2 https://doi.org/10.1002/nla.2466 https://www.wikidata.org/entity/Q114235386 db/journals/nla/nla30.html#ZhangLLH23

Li-Ping Zhang Zi-Cai Li Ming-Gong Lee Hung-Tsai Huang Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace's equation: better pseudo-boundaries. 1183-1222 2022 89 Numer. Algorithms 3 https://doi.org/10.1007/s11075-021-01150-5 db/journals/na/na89.html#ZhangLLH22

Liping Zhang 0005 Zi-Cai Li Yimin Wei 0001 Hung-Tsai Huang Spurious eigenvalue-free algorithms of the method of fundamental solutions for solving the Helmholtz equation in bounded multiply connected domains. 895-932 2022 91 Numer. Algorithms 2 https://doi.org/10.1007/s11075-022-01286-y db/journals/na/na91.html#ZhangLWH22

Liping Zhang 0005 Zi-Cai Li Hung-Tsai Huang Zhen Chen 0016 Super-exponential growth rates of condition number in the boundary knot method for the Helmholtz equation. 106333 2020 105 Appl. Math. Lett. https://doi.org/10.1016/j.aml.2020.106333 https://www.wikidata.org/entity/Q115597807 db/journals/appml/appml105.html#ZhangLHC20

Fang-Fang Dou Liping Zhang 0005 Zi-Cai Li C. S. Chen Source nodes on elliptic pseudo-boundaries in the method of fundamental solutions for Laplace's equation; selection of pseudo-boundaries. 112861 2020 377 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2020.112861 db/journals/jcam/jcam377.html#DouZLC20

Fang-Fang Dou Zi-Cai Li C. S. Chen Zhaolu Tian Analysis on the method of fundamental solutions for biharmonic equations. 346-366 2018 339 Appl. Math. Comput. https://doi.org/10.1016/j.amc.2018.07.016 db/journals/amc/amc339.html#DouLCT18

Zhaolu Tian Zi-Cai Li Hung-Tsai Huang C. S. Chen Analysis of the method of fundamental solutions for the modified Helmholtz equation. 262-281 2017 305 Appl. Math. Comput. https://doi.org/10.1016/j.amc.2017.01.063 db/journals/amc/amc305.html#TianLHC17

S.-Y. Chen Zi-Cai Li Y.-S. Wang Cheng-Sheng Chien Efficient spectral collocation and continuation methods for symmetry-breaking solutions of rotating Bose-Einstein condensates. 651-670 2013 90 Int. J. Comput. Math. 3 https://doi.org/10.1080/00207160.2012.736615 db/journals/ijcm/ijcm90.html#ChenLWC13

Zi-Cai Li Hung-Tsai Huang Ming-Gong Lee John Y. Chiang Error analysis of the method of fundamental solutions for linear elastostatics. 133-153 2013 251 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2013.03.018 db/journals/jcam/jcam251.html#LiHLC13

Jin Huang 0011 Guang Zeng Xiaoming He Zi-Cai Li Splitting extrapolation algorithm for first kind boundary integral equations with singularities by mechanical quadrature methods. 79-97 2012 36 Adv. Comput. Math. 1 https://doi.org/10.1007/s10444-011-9181-8 db/journals/adcm/adcm36.html#HuangZHL12

Zi-Cai Li Ming-Gong Lee Jeng-Tzong Chen New series expansions for fundamental solutions of linear elastostatics in 2D. 199-224 2011 92 Computing 3 https://doi.org/10.1007/s00607-010-0137-5 db/journals/computing/computing92.html#LiLC11

Zi-Cai Li S.-Y. Chen Cheng-Sheng Chien Huei-Shuang Chen A spectral collocation method for a rotating Bose-Einstein condensation in optical lattices. 1215-1234 2011 182 Comput. Phys. Commun. 6 https://doi.org/10.1016/j.cpc.2011.02.002 db/journals/cphysics/cphysics182.html#LiCCC11

Zi-Cai Li John Y. Chiang Ching Y. Suen New splitting algorithms for geometric transformations of digital images and their error analysis. 323-335 2011 21 Int. J. Imaging Syst. Technol. 4 https://doi.org/10.1002/ima.20298 db/journals/imst/imst21.html#LiCS11

Zi-Cai Li Ming-Gong Lee John Y. Chiang Ya-Ping Liu The Trefftz method using fundamental solutions for biharmonic equations. 4350-4367 2011 235 J. Comput. Appl. Math. 15 https://doi.org/10.1016/j.cam.2011.03.024 db/journals/jcam/jcam235.html#LiLCL11

Zi-Cai Li Hung-Tsai Huang Yimin Wei 0001 Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations. 205-221 2011 18 Numer. Linear Algebra Appl. 2 https://doi.org/10.1002/nla.766 db/journals/nla/nla18.html#LiHW11

Zi-Cai Li Jin Huang Hung-Tsai Huang Stability analysis of method of fundamental solutions for mixed boundary value problems of Laplace's equation. 1-29 2010 88 Computing 1-2 https://doi.org/10.1007/s00607-010-0081-4 db/journals/computing/computing88.html#LiHH10

Zi-Cai Li Hung-Tsai Huang Jeng-Tzong Chen Yimin Wei 0001 Effective condition number and its applications. 87-112 2010 89 Computing 1-2 https://doi.org/10.1007/s00607-010-0098-8 db/journals/computing/computing89.html#LiHCW10

Zi-Cai Li John Y. Chiang Ching Y. Suen Face Transformation With Harmonic Models by the Finite-Volume Method With Delaunay Triangulation. 1543-1554 2010 40 IEEE Trans. Syst. Man Cybern. Part B 6 https://doi.org/10.1109/TSMCB.2010.2042955 https://www.wikidata.org/entity/Q51573451 db/journals/tsmc/tsmcb40.html#LiCS10

Zi-Cai Li Cheng-Sheng Chien H.-T. Huang Bor-Wen Jeng Superconvergence of bi-k-Lagrange elements for eigenvalue problems. 2268-2282 2009 180 Comput. Phys. Commun. 11 https://doi.org/10.1016/j.cpc.2009.07.015 db/journals/cphysics/cphysics180.html#LiCHJ09

Zi-Cai Li Qing Fang Hung-Tsai Huang Yimin Wei 0001 On solution uniqueness of elliptic boundary value problems. 293-307 2009 233 J. Comput. Appl. Math. 2 https://doi.org/10.1016/j.cam.2009.07.040 db/journals/jcam/jcam233.html#LiFHW09

Zi-Cai Li Tzon-Tzer Lu Yimin Wei 0001 Effective condition number of Trefftz methods for biharmonic equations with crack singularities. 145-171 2009 16 Numer. Linear Algebra Appl. 2 https://doi.org/10.1002/nla.613 db/journals/nla/nla16.html#LiLW09

Zi-Cai Li Heng-Shuing Tsai Song Wang 0004 John J. H. Miller Accurate and approximate analytic solutions of singularly perturbed differential equations with two-dimensional boundary layers. 2602-2622 2008 55 Comput. Math. Appl. 11 https://doi.org/10.1016/j.camwa.2007.10.027 https://www.wikidata.org/entity/Q59416194 db/journals/cma/cma55.html#LiTWM08

Shing-Lin Chang Cheng-Sheng Chien Zi-Cai Li A finite difference continuation method for computing energy levels of Bose-Einstein condensates. 208-226 2008 179 Comput. Phys. Commun. 4 https://doi.org/10.1016/j.cpc.2008.02.014 db/journals/cphysics/cphysics179.html#ChangCL08

Cheng-Sheng Chien H.-T. Huang Bor-Wen Jeng Zi-Cai Li Superconvergence of Fems and Numerical Continuation for Parameter-Dependent Problems with Folds. 1321-1336 2008 18 Int. J. Bifurc. Chaos 5 https://doi.org/10.1142/S0218127408021014 db/journals/ijbc/ijbc18.html#ChienHJL08

Qun Lin 0001 Hung-Tsai Huang Zi-Cai Li New expansions of numerical eigenvalues for -Δu = λρu by nonconforming elements. 2061-2084 2008 77 Math. Comput. 264 https://doi.org/10.1090/S0025-5718-08-02098-X db/journals/moc/moc77.html#LinHL08

Cheng-Sheng Chien Bor-Wen Jeng Zi-Cai Li A time-independent approach for computing wave functions of the Schrödinger-Poisson system. 55-82 2008 15 Numer. Linear Algebra Appl. 1 https://doi.org/10.1002/nla.564 db/journals/nla/nla15.html#ChienJL08

Zi-Cai Li Hung-Tsai Huang Effective condition number for numerical partial differential equations. 575-594 2008 15 Numer. Linear Algebra Appl. 7 https://doi.org/10.1002/nla.584 db/journals/nla/nla15.html#LiH08

Chieh-Sen Huang Song Wang 0004 C. S. Chen Zi-Cai Li A radial basis collocation method for Hamilton-Jacobi-Bellman equations. 2201-2207 2006 42 Autom. 12 https://doi.org/10.1016/j.automatica.2006.07.013 https://www.wikidata.org/entity/Q59416202 db/journals/automatica/automatica42.html#HuangWCL06

Zi-Cai Li Y. L. Chan Georgios C. Georgiou Christos Xenophontos Special boundary approximation methods for laplace equation problems with boundary singularities - Applications to the motz problem. 115-142 2006 51 Comput. Math. Appl. 1 https://doi.org/10.1016/j.camwa.2005.01.030 db/journals/cma/cma51.html#LiCGX06

Hsin-Yun Hu Zi-Cai Li Combinations of collocation and finite-element methods for Poisson's equation. 1831-1853 2006 51 Comput. Math. Appl. 12 https://doi.org/10.1016/j.camwa.2005.10.018 db/journals/cma/cma51.html#HuL06

Tzon-Tzer Lu Zi-Cai Li The cracked-beam problem solved by the boundary approximation method. 11-16 2005 18 Appl. Math. Lett. 1 https://doi.org/10.1016/j.aml.2004.07.017 db/journals/appml/appml18.html#LuL05

Hsin-Yun Hu Zi-Cai Li Verification of Reduced Convergence Rates. 67-73 2005 74 Computing 1 https://doi.org/10.1007/s00607-004-0079-x db/journals/computing/computing74.html#HuL05

Hung-Tsai Huang Zi-Cai Li Blending curves for landing problems by numerical differential equations, III. Separation techniques. 1351-1374 2004 40 Math. Comput. Model. 11-12 https://doi.org/10.1016/j.mcm.2005.01.024 db/journals/mcm/mcm40.html#HuangL04

Zi-Cai Li Huaiqing Wang Stephen S. Y. Liao Numerical algorithms for image geometric transformations and applications. 132-149 2004 34 IEEE Trans. Syst. Man Cybern. Part B 1 https://doi.org/10.1109/TSMCB.2003.809230 https://www.wikidata.org/entity/Q35888202 db/journals/tsmc/tsmcb34.html#LiWL04

Song Wang 0004 Zi-Cai Li A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation. 1689-1709 2003 72 Math. Comput. 244 db/journals/moc/moc72.html#WangL03 https://doi.org/10.1090/S0025-5718-03-01516-3

Zi-Cai Li J. Y. Lin Ching Y. Suen H. Wang New Algorithm for Geometric Transformations of Digital Images and Patterns. 315-318 2002 conf/icpr/2002 ICPR (3) https://doi.org/10.1109/ICPR.2002.1047856 https://doi.ieeecomputersociety.org/10.1109/ICPR.2002.1047856 db/conf/icpr/icpr2002-3.html#LiLSW02

Zi-Cai Li Global Superconvergence of Simplified Hybrid Combinations for Elliptic Equations with Singularities, I. Basic Theorem. 27-44 2000 65 Computing 1 https://doi.org/10.1007/PL00021411 db/journals/computing/computing65.html#Li00

Zi-Cai Li Ching Y. Suen The partition-combination method for recognition of handwritten characters. 701-720 2000 21 Pattern Recognit. Lett. 8 https://doi.org/10.1016/S0167-8655(00)00037-4 db/journals/prl/prl21.html#LiS00

Zi-Cai Li Ching Y. Suen Crucial combinations for the recognition of handwritten letters. 873-898 2000 21 Pattern Recognit. Lett. 10 https://doi.org/10.1016/S0167-8655(00)00047-7 db/journals/prl/prl21.html#LiS00a

Ching Y. Suen Zi-Cai Li Crucial Combinations for the Recognition of Handwritten Letters. 19-39 1997 conf/bsdia/1997 BSDIA db/conf/bsdia/bsdia1997.html#SuenL97 https://doi.org/10.1007/3-540-63791-5_2

Zi-Cai Li Analysis of discrete techniques for image transformation. 225-263 1996 13 Numer. Algorithms 2 https://doi.org/10.1007/BF02207696 db/journals/na/na13.html#Li96

Zi-Cai Li Splitting-integrating method for inverse transformation of<i>n</i>-dimensional digital images and patterns. 181-198 1995 9 Numer. Algorithms 2 https://doi.org/10.1007/BF02141587 db/journals/na/na9.html#Li95

Zi-Cai Li Ching Y. Suen J. Guo A regional decomposition method for recognizing handprinted characters. 998-1010 1995 25 IEEE Trans. Syst. Man Cybern. 6 https://doi.org/10.1109/21.384265 db/journals/tsmc/tsmc25.html#LiSG95

Zi-Cai Li The Schwarz Alternating Method for Singularity Problems. 1064-1082 1994 15 SIAM J. Sci. Comput. 5 https://doi.org/10.1137/0915065 db/journals/siamsc/siamsc15.html#Li94

Ching Y. Suen J. Guo Zi-Cai Li Analysis and recognition of alphanumeric handprints by parts. 614-631 1994 24 IEEE Trans. Syst. Man Cybern. 4 db/journals/tsmc/tsmc24.html#SuenGL94 https://doi.org/10.1109/21.286382

Zi-Cai Li Ching Y. Suen J. Guo Hierarchical Model for Analysis and Recognition of Handwritten Characters. 149-174 1993 10 Ann. Math. Artif. Intell. 1-2 db/journals/amai/amai10.html#LiSG93 https://doi.org/10.1007/BF01530947

Zi-Cai Li Ching Y. Suen Tien D. Bui Quan Lin Gu Harmonic models of shape transformations in digital images and patterns. 198-209 1992 54 CVGIP Graph. Model. Image Process. 3 https://doi.org/10.1016/1049-9652(92)90051-X db/journals/cvgip/cvgip54.html#LiSBG92

Zi-Cai Li Ching Y. Suen Tien Dai Bui Yuan Yan Tang Quan Lin Gu Splitting-Integrating Method for Normalizing Images by Inverse Transformations. 678-686 1992 14 IEEE Trans. Pattern Anal. Mach. Intell. 6 https://doi.org/10.1109/34.141558 http://doi.ieeecomputersociety.org/10.1109/34.141558 db/journals/pami/pami14.html#LiSBTG92

Ching Y. Suen J. Guo Zi-Cai Li Analysis and recognition of alphanumeric handprints by parts. 338-341 1992 ICPR (2) https://doi.org/10.1109/ICPR.1992.201787 conf/icpr/1992-2 db/conf/icpr/icpr1992-2.html#SuenGL92

Zi-Cai Li Tien Dai Bui Coupling strategy for matching different methods in solving singularity problems. 311-319 1990 45 Computing 4 https://doi.org/10.1007/BF02238799 db/journals/computing/computing45.html#LiB90

Zi-Cai Li Yuan Yan Tang Tien Dai Bui Ching Y. Suen Shape Transformation Models and their Applications in Pattern Recognition. 65-94 1990 4 Int. J. Pattern Recognit. Artif. Intell. 1 https://doi.org/10.1142/S021800149000006X db/journals/ijprai/ijprai4.html#LiTBS90

Zi-Cai Li Tien Dai Bui Ching Y. Suen Yuan Yan Tang Splitting-Shooting Methods for Nonlinear Transformations of Digitized Patterns. 671-682 1990 12 IEEE Trans. Pattern Anal. Mach. Intell. 7 https://doi.org/10.1109/34.56210 http://doi.ieeecomputersociety.org/10.1109/34.56210 db/journals/pami/pami12.html#LiBST90

Zi-Cai Li Discrete techniques for computer transformations of digital images and patterns. 1249-1273 1990 23 Pattern Recognit. 11 https://doi.org/10.1016/0031-3203(90)90120-A db/journals/pr/pr23.html#Li90

Zi-Cai Li Quan Lin Gu Ching Y. Suen Tien D. Bui A comparative study of nonlinear shape models for digital image processing and pattern recognition. 858-871 1990 20 IEEE Trans. Syst. Man Cybern. 4 https://doi.org/10.1109/21.105085 db/journals/tsmc/tsmc20.html#LiGSB90

Zi-Cai Li Ching Y. Suen Tien Dai Bui Quan Lin Gu Harmonic models of shape transformations in digital images and patterns. 1-7 1990 ICPR (2) https://doi.org/10.1109/ICPR.1990.119319 conf/icpr/1990-2 db/conf/icpr/icpr1990-2.html#LiSBG90 Zi-Cai Li Tien D. Bui Yuan Yan Tang Ching Y. Suen Computer Transformation of Digital Images and Patterns World Scientific 1989 1-276 World Scientific Series in Computer Science 17 978-9971-5-0951-4 978-981-4522-11-3 https://doi.org/10.1142/0890

Zi-Cai Li Tien Dai Bui A new kind of combinations between the Ritz-Galerkin and finite element methods for singularity problems. 29-50 1988 40 Computing 1 https://doi.org/10.1007/BF02242188 db/journals/computing/computing40.html#LiB88

Tien D. BuiTien Dai Bui Y. L. Chan Shing-Lin Chang C. S. Chen Huei-Shuang Chen Jeng-Tzong Chen S.-Y. Chen Zhen Chen 0016 John Y. Chiang Cheng-Sheng Chien Fangfang DouFang-Fang Dou Qing Fang Georgios C. Georgiou Quan Lin Gu J. Guo Xiaoming He Hsin-Yun Hu Chieh-Sen Huang H.-T. Huang Hung-Tsai Huang Jin Huang Jin Huang 0011 Bor-Wen Jeng Ming-Gong Lee Stephen Shaoyi LiaoStephen S. Y. Liao J. Y. Lin Qun Lin 0001 Ya-Ping Liu Tzon-Tzer Lu John J. H. Miller Ching Y. SuenChing Yee Suen Yuan Yan Tang Zhaolu Tian Heng-Shuing Tsai H. Wang Huaiqing Wang Song Wang 0004 Y.-S. Wang Yimin Wei 0001 Christos Xenophontos Guang Zeng Li-Ping Zhang Liping Zhang 0005