簡澄陞 教授 

Cheng-Sheng Chien, Professor

 數值偏微分方程

 numerical partial differential equations

 數值線性代數

 numerical linear algebra

 線性及非線性特徵值問題

 linear and nonlinear eigenvalue problems

 計算物理

•  Ph.D., Colorado State University , 1984.

• Associate professor, (08/1984 ~ 07/1988).

• Professor, (08/1988 ~ ).

• Visiting professor, (03/1994 ~ 08/1994), University of Marburg, Germany.

• Chairman, (08/1991 ~ 07/1993).

• Dean of College of Sciences, (08/2000 ~ 07/2003).

1. Numerical solutions for nonlinear Schrödinger equations

2. Computational Mathematics

3. Scientific computing

(A)  期刊論文 

1.     E.L. Allgower and C.-S. Chien, 1986(7), Continuation and local perturbation for multiple bifurcations, SIAM J. Sci. Stat. Comput., pp.1265-1281.                                                           SCI

2.   C.-S. Chien, 1987(15), Multiple Bifurcations on 3D. eigenvalue problems, Chinese J. Math., pp.181-194.

3.   E.L. Allgower and C.-S. Chien, 1988(14), Bifurcation arising from complexifications of real homotopies, Soochow J. Math., pp.1-10.

4.   C.-S. Chien, 1989(25), Secondary bifurcations in the buckling problem, J. Comput. Appl. Math., pp.277-287.                                                                                                                               JCR

5.   E.L. Allgower, C.-S. Chien and K. Georg, 1989(26), Large sparse continuation problems. J. Comput. Appl. Math., pp.3-21.                                                                                                  JCR

6.   C.-S. Chien, 1990(18), Predictor-corrector methods for large sparse problems, Bull. Inst. Math., Academia Sinica, pp.191-204.

7.   E.L. Allgower, C.-S. Chien and K. Georg and C.-F. Wang, 1991(38), Conjugate gradient methods for continuation problems, J. Comput. Appl. Math., pp.1-16.
計畫編號：NSC 79-0208-M-005-01                                                                                       JCR

8.   E.L. Allgower, C.-S. Chien and W.-C. Lee, 1993(25), Bifurcations of corank greater than two, Computers Math. Appl., pp.51-64.
計畫編號：NSC 82-0208-M-005-039                                                                                     SCI

9.   E.L. Allgower and C.-S. Chien, 1993(25), continuation-minimization methods for stability problems, Computers Math. Appl., pp.65-79.
計畫編號：NSC 82-0208-M-005-039                                                                                     SCI

10. M.-Z. Chen, T.-Z. Chen, C.-S. Chien and M.-S. Yu, A parallel continuation algorithm for nonlinear eigenvalue problems, 1994(27), Computers Math. Appl., pp.83-97.
計畫編號：NSC 83-0208-M-005-026                                                                                     SCI

11. C.-S. Chien, N.-H. Lu, and J.-L. Weng, 1995(62), Conjugate gradient methods for continuation problems II, J. Comput. Appl. Math., pp.197-216.
計畫編號：NSC 83-0208-M-005-026                                                                                     JCR

12. C.-S. Chien, S.-Y. Gong and N.-H. Lu, 1996(20), Some computing techniques for bifurcation problems, Proceedings of the NSC, Part A, pp.360-370.
計畫編號：NSC 85-2121-M-005-002-C

13. C.-S. Chien, J.-L. Weng, and C.-L. Shen, 1997(4), Lanczos type methods for continuation problems, Numer. Linear Algebra Appl., pp.23-41.
計畫編號：NSC 84-2121-M-005-005-MS                                                                              SCI

14. C.-S. Chien and M.-S. Chen, 1997(18), Multiple bifurcation in the von Kármán equations, SIAM J. Sci. Comput., pp.1737-1766.
計畫編號：NSC 84-2121-M-005-MS                                                                                      SCI

15. C.-S. Chien, Z. Mei and C.-L. Shen, 1998(8), Numerical continuation at double bifurcation points of a reaction-diffusion problem, International J. Bifurcation and Chaos, pp.117-139.
計畫編號：NSC 85-2115-M-005-002C                                                                                   SCI

16. C.-S. Chien and M.-H. Chen, 1998(35), Multiple bifurcations in a reaction-diffusion problem, Computers Math. Applics., pp.15-39.
計畫編號：NSC 86-2115-M-005-004                                                                                     SCI

17. C.-S. Chien, Y.-J. Kuo and Z. Mei, 1998(49), Symmetry and scaling properties of the von Kármán equations, J. Appl. Math. Phys. (ZAMP), pp.710-729.
計畫編號：NSC 87-2115-M-005-04.                                                                                      SCI

18. C.-S. Chien, W.-W. Lin and Z. Mei, 1999(37), Conjugate gradient type methods for semilinear elliptic problems with symmetry, Computers Math. Appl., pp.3-22.
計畫編號：NSC 87-2115-M-005-005                                                                                     SCI

19. C.-S. Chien, Y.-J. Kuo and Z. Mei, 1999(38), Bifurcations of the von Kármán equations with Robin boundary conditions, Computers Math. Appl., pp.85-112.
計畫編號：NSC 87-2115-M-005-004                                                                                     SCI

20. C.-S. Chien, H.-S. Chow and B.W. Jeng, 1999(22), A continuation-domain decomposition algorithm for bifurcation problems, Numerical Algorithms, pp.367-383.
計畫編號：NSC 86-2115-M-005-004                                                                                     JCR

21. C.-S. Chien, S.-Y. Gong and Z. Mei, 2000(22), Mode jumping in the von Kármán equations, SIAM J. Sci.  Comput., pp.1354-1385.
計畫編號：NSC 86-2115-M-005-04                                                                                       SCI

22. C.-S. Chien and Y.-S. Liao, 2001(130), Multiple bifurcations generated by mode interactions in a reaction-diffusion system, J. Comput. Appl. Math., pp.345-368.
計畫編號：NSC 88-2115-M-005-005                                                                                     SCI

23. C.-S. Chien, S.-L. Chang and Z. Mei, 2001(136), Tracing the buckling of a rectangular plate with block GMRES method, J. Comput. Appl. Math., pp.199-218.
計畫編號：NSC 88-2115-M-005-005                                                                                     SCI

24. S.-L. Chang and C.-S. Chien, 2003(13), A multigrid-Lanczos algorithm for the numerical solutions of nonlinear eigenvalue problems, Int. J. Bifurcation & Chaos, pp.1217-1228.
計畫編號：NSC 90-2115-M-005-007                                                                1.019 (33%), SCI

25. C.-S. Chien and S.-L. Chang, 2003(10), Application of the Lanczos algorithm for solving the linear systems that occur in continuation problems, Numer. Linear Algebra Appl., pp.335-355.
計畫編號：NSC 89-2115-M-005-011                                                             1.042 (18.3%), SCI

26. S.-L. Chang and C.-S. Chien, 2003(191), Domain decomposition algorithms for fourth order nonlinear elliptic eigenvalue problems, J. Comput. Phys., pp.476-501.
計畫編號：NSC 90-2115-M-005-007                                                               1.777 (7.3%), SCI

27. S.-L. Chang, H.-S. Chen and C.-S. Chien, 2004(14), Multigrid-conjugate gradient type methods for reaction-diffusion systems, Int. J. Bifurcation & Chaos, pp.3587-3605.
計畫編號：NSC 91-2115-M-005-003                                                                1.019 (33%), SCI

28. C.-S. Chien and B.-W. Jeng, 2005(15), No.7, Symmetry reduction and a posteriori finite element error estimators for bifurcation problems, Int. J. Bifurcation & Chaos, pp.2091-2107.
計畫編號：NSC 91-2115-M-005-003                                                                1.019 (33%), SCI

29. S.-L. Chang, C.-S Chien and B.-W. Jeng, 2005(15), No.8, Tracing the solution surface with folds of a two-parameter system, Int. J. Bifuraction & Chaos, pp.2689-2700.
計畫編號：NSC 92-2115-M-005-001                                                                1.019 (33%), SCI

30. C.-S. Chien and B.-W. Jeng, 2006(27), A two-grid discretization scheme for semilinear elliptic eigenvalue problems, SIAM J. Sci. Comput., pp. 1287-1304.
計畫編號：NSC 93-2115-M-005-005                                                                  1.824 (4%), SCI

31. Z.-C. Li, C.-S. Chien and H.-T. Huang, 2007 (198), Effective condition number for finite difference method, J. Comput. Appl. Math., 208-235.

      計畫編號：NSC 94-2115-M-005-001                                                             0.759 (44.6%), SCI

32. S.-L. Chang and C.-S. Chien, 2007（17）, Numerical continuation for nonlinear Schrödinger equations, Int. J. Bifurcation & Chaos, 641-656.

      計畫編號：NSC 94-2115-M-005-001                                                                0.866 (33%), SCI

33. S.-L. Chang, C.-S. Chien and B.-W. Jeng, 2007（205）, An efficient algorithm for the Schrödinger-Poisson eigenvalue problem, J. Comput. Appl. Math., 509-532.

      計畫編號：NSC 93-2115-M-005-005                                                             0.759 (44.6%), SCI

34. S.-L. Chang, C.-S. Chien, and B.-W. Jeng, 2007（29）, Liapunov-Schmidt reduction and continuation for nonlinear Schrödinger equations, SIAM J. Sci. Comput., 729-755.

      計畫編號：NSC 95-2115-M-005-004-NY3                                                         1.824 (4%), SCI

35. S.-L. Chang, C.-S. Chien and B.-W. Jeng, 2007 (226), Computing wave functions of nonlinear Schrödinger equations: a time-independent approach, J. Comput. Phys., 104-130.                                                                 

      計畫編號：NSC 95-2115-M-005-004-NY3                                                      2.372 (7.3%), SCI

36. S.-L. Chang and C.-S. Chien, 2007 (177), Adaptive continuation algorithms for computing energy levels of rotating Bose-Einstein condensates, Comput. Phys. Commun., 707-719.

      計畫編號：NSC 95-2115-M-005-004-MY3                                                   1.842 (29.3%), SCI

37. C.-S. Chien, B.-W. Jeng and Z.C. Li, 2008 (15), A time-independent approach for computing wave functions of the Schrödinger-Poisson system, Numer. Linear Algebra Appl., 55-82.

      計畫編號：NSC 94-2115-M-005-001                                                            0.696 (27.5%), SCI

38. C.-S. Chien, H.-T. Huang, B.-W. Jeng, and Z.C. Li, 2008 (214), Two-grid discretization schemes for nonlinear Schrödinger equations, J. Comput. Appl. Math., 549-571.                

      計畫編號：NSC 94-2115-M-005-001                                                             0.943 (30.9%), SCI

39. Z. C. Li, C.-S. Chien, H.-T. Huang, and B.-W. Jeng, 2008 (18), Superconvergence of FEMs and numerical continuation for parameter-dependent problems with folds, Inter. J. Bifurcatiion and Chaos, 1321-1336.

      計畫編號：NSC 94-2115-M-005-001                                                                0.910 (30%), SCI

40. S.-L. Chang, C.-S. Chien, and Z.-C. Li, 2008 (179), A finite difference continuation method for computing energy levels of Bose-Einstein condensates, Comput. Phys. Commun., 208-226.

      計畫編號：NSC 95-2115-M-005-004-MY3                                                   1.842 (30.2%), SCI

41. S.-L. Chang and C.-S. Chien, 2009 (180), Computing multiple peak solutions for Bose-Einstein condensates in optical lattices, Comput. Phys. Commun., 926-947.

      計畫編號：NSC 95-2115-M-005-004-MY3                                                    1.842 (30.2%), SCI

42. H.-T. Huang, S.-L. Chang, C.-S. Chien, and Z.-C. Li, 2009 (198), Superconvergence of high order FEMs for Schrödinger equations with periodic boundary conditions, Comput. Method Appl. Mech. & Engrg., 2246-2259.

      計畫編號：NSC 95-2115-M-005-004-MY3                                                     1.488 (18.9%), SCI

43. C.-S. Chien, and Y.-T. Shih, 2009 (209), A cubic Hermite finite element and continuation methods for numerical solutions of the von Kármán equations, Appl. Math. Comput., 356-368.

      計畫編號：NSC 95-2115-M-005-004-MY3                                                     0.821 (37.0%), SCI

44. S. L. Chang, H.-S. Chen, C.-S. Chien, and D. J. Han, 2009 (231), An adaptive multigrid scheme for Bose-Einstein condensates in a periodic potential, J. Comput. Appl. Math., 268-287.

      計畫編號：NSC 95-2115-M-005-004-MY3                                                     0.943 (30.9%), SCI

45. Z.-C. Li, C.-S. Chien, H.-T. Huang, and B.-W. Jeng, Superconvergence of bi-k(≧2)-Lagrange elements for eigenvalue problems, Comput. Phys. Commun., to appear.

      計畫編號：NSC 95-2115-M-231-001-MY3                                                     1.842 (30.2%), SCI

46. S.-L. Chang, H.-S. Chen, and C.-S. Chien, 2009 (  ), A multigrid continuation algorithm for multiple peak solutions of the Gross-Pitaevskii equation in a periodic potential, Comput. Phys. Commun., revised.

      計畫編號：NSC 95-2115-M-005-004-MY3                                                     1.842 (30.2%), SCI

47. H.-S. Chen and C.-S. Chien, 2009(  ), Multi-level spectral-Galerkin and continuation methods for nonlinear Schrödinger equations, revised for Multiscale Model. Sim..

      計畫編號：NSC 98-2115-M-005-003-MY3                                                       2.037 (8.1%), SCI

(B)  研討會論文 

1.     C.-S. Chien, 1988, Computer graphic solutions of linear eigenvalue problem, Proc. Symposium on Mathematics, Education, and Computer, Taipei, R.O.C., pp.69-91.

2.   C.-S. Chien, 1989, An efficient continuation algorithm for nonlinear eigenvalue problems, in: R.Gruber, J. Periaux and R.P. Shaw, Eds., Proc. 5th International Symposium on Numerical Methods in Engineering, Computational Mechanics Publications, Springer-Verlag, pp.215-220.

3.   C.-S. Chien, On some derivative-free continuation methods, 1992, Proceedings of the 10th International Conference on Computing Methods in Applied Sciences and Engineering, sponsored by INRIA, Nova Science Publishers, R. Glowinski Ed., pp.679-688.
計畫編號：NSC 80-0208-M-005-032

4.   C.-S. Chien and S.-S. Chien, 1992, On 3D semilinear elliptic eigenvalue Neumann problems II, Proceedings of the 10th International Conference on Computing Methods in Applied Sciences and Engineering, sponsored by INRIA, Nova Science Publishers, R. Glowinski Ed., pp.669-678.
計畫編號：NSC 80-0208-M-005-032

5.   C.-S. Chien, and B.-W. Jeng, Continuation-conjuate gradient algorithms for semilinear elliptic Neumann problems, Proceeding of the Third International Conference on Difference Equations and Applications, pp.137-160, 1997, Gordon & Breach Science Publishers.

6.   C.-S. Chien, M.-S. Chen and S.-L. Chang, Double bifurcation in fourth order clamped plate problem, 1998, Proceeding of the 13th Technological an Vocational Eduation Conference of R.O.C., pp.171-180.

7.   C.-S. Chien, and B.-W. Jeng, 2004. A two-grid finite element discretization scheme for nonlinear eigenvalue problems, Proceedings of the International Conference on Computational Methods, pp. 1951-1955, Singapore, Springer.

8.   C.-S. Chien, and B.-W. Jeng, 2004. Implementing MINRES and SYMMLQ for eigenvalue problems, Proceedings of the International Conference on Computational Methods, pp. 1957-1961, Singapore, Springer.

(C)  研究報告與投稿之論文 

1.     C.-S. Chien, N.-H. Lu, and M.-S. Yu, 1995, Parallel conjugate gradient methods for nonlinear eigenvalue problems, Technical Report of the NSC.
計畫編號：NSC 84-2121-M-005-005-MS

2.   S.-L. Chang, C.-S. Chien, and Biao Wu, Two-stage continuation algorithm for Bloch waves of Bose-Einstein condensates in optical lattices, submitted to SIAM J. Sci. Comput..

      計畫編號：NSC 95-2115-M-005-004-MY3

3.   Y.-S. Wang, C.-S. Chien, and H.-S. Chen, Two-grid continuation algorithms for symmetry-breaking solutions of the Gross-Pitaevskii equation, 2009 (  ), to appear.

      計畫編號：NSC 98-2115-M-005-003-MY3

4.   Z.-C. Li, H.-T. Huang, C.-S. Chien, and Y.-D. Yang, 2009 (  ), Superconvergence of High order FEMs using penalty techniques for eigenvalue problems with periodic boundary conditions, submitted to Computer Method Appl. Mech. & Engrg..

      計畫編號：NSC 95-2115-M-005-004-MY3

5.   Z.-C. Li, S. C. Hu, H.-T. Huang, and C.-S. Chien, 2009 (  ), Spectral collocation methods for semilinear elliptic eigenvalue problems, submitted to J. Sci. Comput..

      計畫編號：NSC 98-2115-M-005-003-MY3

(D) 歷年指導過之碩博士畢業生，( ) 數字代表畢業年度。

   1. 碩士班畢業生

黃士修 (78)，王靜風 (79) (和春技術學院講師)，陳宗仁 (79) (數學教師)，簡碩伸 (80) (屏東普門中學教師)，林明珊 (80) (嘉義協同中學教師)，葉佐欽 (80) (明道中學教師)，李維昌 (81) (數學教師)，陳明哲 (82) (資訊業)，陳明信 (83)，盧南華 (83) (職業軍官)，翁振陵 (84) (金門就業)，龔信有 (85) (資通電腦系統部程式設計師)，沈志龍 (85) (北投國中教師)，郭昱汝 (86) (美國Indiana University助理教授)，陳美華 (86) (竹北高中教師)，鄭博文 (86) (台中教育大學數學教育助理教授)，曹惟勝 (87) (台積電資訊工程師)，廖益賢 (88)，戴佩芬 (88) (中興大學應數系助教)，周修聖 (88) (銀行業)，李一平 (89)，江俊瑩 (91) (中興大學應數系助教)，陳慧霜 (91) (中興大學應數系博士生)，李政軒 (92)，杜慧絹 (92) (台南市國中教師)，古嚴博 (93) (空軍基地)，林雅菁 (93) (彰化縣竹塘國中)，葉政叡 (94) (台南科學中心志邦科技工程師)，林進一 (94) (服役)，尤力廣 (95)，蕭竣中 (95)，王信舜 (98)，白佶弘 (98)，林千資 (98)。

   2. 博士班畢業生

張勝麟 (91)，現職：南台科技大學通識中心教授。

鄭博文 (94)，曾任： 國立交通大學應數系助理教授，

                        現職： 國立台中教育大學數學教育系助理教授。

  3. 博士生

博四：陳慧霜，王允仕。

博三：陳素英。

(E) 最近三年之研究方向

   1. 利用雙重網格法與延續法求解半線性特徵值問題與反應–擴散系統，與       Schrödinger-Poisson 特徵值問題。

   2. 利用 Liapunov-Schmidt reduction與延續法處理非線性的Schrödinger 方程組，及一些反應擴散問題，諸如 Gierer-Meinhardt 與 Schnarkenberg system 等。

 3. 利用spectral methods與 pseudo-spectral methods解nonlinear Schrödinger equations, 探討Bose-Einstein condensates (BEC) 與非線性光學之Bloch waves與symmetry-breaking solutions. 使用之basis functions為 (i) Fourier sine functions, (ii) Legendre polynomials, (iii) Chebyshev polynomials.

(F) 目前合作研究對象：

(1)       張勝麟：南台科技大學通識中心

(2)       鄭博文：國立台中教育大學數學教育系

(3)       吳飆：中國科學院物理所

(4)       李瑞光：清華大學光電所

(5)       郭西川：彰化師範大學物理系

(6)       洪子倫：逢甲大學應數系

(7)       施因澤：中興大學應數系

(8)       李子才：中山大學應數系

(9)       黃宏財：義守大學應數系