Wu, Chin-Tien

Ph.D. Applied Mathematics and Scientific Computation,

University of Maryland, College Park, USA.

Associate Professor, Department of Applied Mathematics,

National Chiao-Tung University, Taiwan

Contact information:


Department of Applied Mathematics

Institute of Mathematical Modeling and Scientific Computing

National Chiao-Tung University,

No. 1001, Ta Shueh Rd., Hsinchu 300, Taiwan

Phone: 03-5712121-ext-56424

email: ctw@math.nctu.edu.tw

Research interests

Multigrid and finite element methods in computational fluid dynamics and computational mechanics.

Research Projects:

2018~2019 多尺度多頻譜影像之人工智慧機器學習。 經緯科技亞洲矽谷計畫(第二期)委託研究

2017 衛星影像去雜訊處理。 太空計畫中心產學合作

2017 多尺度多頻譜影像之人工智慧機器學習。 經緯科技亞洲矽谷計畫(第一期)委託研究

2017~2018 高精度共形參數化及其在曲面篇微分方程計算的應用(106-2115-M-009 -002 -)

2017~2018 拓樸光子晶體上的三維馬克斯威爾方程之快速演算法(1/4) 共同主持人

2016 影像時間軸補償修正 太空計畫中心產學合作

2016 智慧籃球之感測器偏心調教及飛行路徑校正 仁寶工業電腦產學合作

2016~2017 LDDMM於三維影像型變對應與註冊的應用(105-2115-M-009-006-)

2015~2016 離散形格林函數與混合形變模型於MRI影像對應的應用(104-2115-M-009-002-)

2014~2015 自由曲面於成像光學的應用(103-2115-M-009-003-)

2013~2017計算共形幾何與其應用(1~4) (102-2628-M-009 -002 - , 103-2628-M-009 -005 - , 104-2628-M-009-001-,105-2628-M-009-001-)

(共同主持人: 負責臉部淚水流動建模與模擬)

2013~2014 高精度有限原之三維自由曲面重建(102-2115-M-009-011-)

2012~2013 折射與反射式光學曲面重建與其應用(101-2115-M-009-003-)

2011~2012 光學設計中Monge-Ampere 方程的數值計算(100-2115-M-009-001)

2009~2012 Sox1篩選之人類神經幹細胞對帕金森氏症模型大鼠之效果:應用非侵入性的核磁共振技術追蹤幹細胞並評估多巴胺神經系統的復原 (98-2321-B-001-042-)

(共同主持人: 負責MR signal processing based on spectroscopy with SVD)

2010~2011 沉浸有限元素法於彈性界面與流構耦合問題的計算與誤差估計 (99-2115-M-009-001)

2009~2010 流構耦合的多尺度數值模擬與特徵值問題的探討(98-2115-M-009-010-)

2008~2009 多重網格法與保結構二次特徵值問題計算對預測壓電材料裂縫成長的重要性(97-2119-M-009-006-)

2007~2008 流體與結構於區域移動網格上的動態數值模擬(96-2115-M-009-014-)

2005~2006 不可壓縮流的有限元後驗估計與多重網格計算(94-2119-M-009-003-)


Referred papers:

1. C. T. Wu and H. C. Elman, Analysis and comparison of geometric and algebraic multigrid for convection-diffusion equations. SIAM Sci. Comput. Vol. 28, No. 6, 2006, p.2208-2228.

2. M. C. Lai, C. T. Wu and Yu-Hou, Tseng, An efficient semi-coarsening multigrid method for variable diffusion problems in cylindrical coordinates. Applied Numerical Mathematics, Vol. 57, 2007, p.801-810.

3. Eric Chu, T. M. Hwang, W. W. Lin and C. T. Wu, Vibration of Fast Trains, Palindromic Eigenvalue Problems and Structure-Preserving Doubling Algorithms. J. Comp. and Appl. Math. Vol. 219, 2008, p.237-252.

4. K. Lee, C. T. Wu, G. V. Clarke and S. W. Lee, Computational Modeling of a Lightweight Composite Space Reflector using Geometrically Nonlinear Solid Shell Elements. CMES, Vol 33, No. 1, p. 109-129, 2008.

5. G. Uhlmann, J. N. Wang, C. T. Wu, Reconstruction of inclusions in an elastic body. J. Math. Pures Appl. Vol. 91 No. 6, p. 569-582, 2009.

6. Z. T. Huang, H. C. Hsu, C. L. Chang, C. T. Wu and T.F. Jiang, Momentum-time flux method for one-dimensional wave equations. Computer Physics Communications, Vol. 181, No. 3, p.473-480, 2010.

7. Eric King-wah Chu*, Tsung-Min Hwang, Wen-Wei Lin and Chin-Tien Wu, Palindromic Eigenvalue problems: a Brief Survey, Taiwaness Journal of Mathematics, Vol. 14, No. 3, 2010.

8. Chin-Tien Wu*, Zhilin. Li and Ming-Chih Lai, Adaptive mesh refinement for the elliptic interface problems using immersed finite element method. Int. J. Num. Anal. and Mod. Vol. 8, No. 3, p.466~p.483, 2011.

9. Tsung-Min Hwang, Wen-Wei Lin and Chin-Tien Wu*, Structure Preserving Arnoldi-type for solving Palindromic Quadratic Eigenvalue Problems in Leaky Surface Wave Propagation. Applied Mathematics and Computation, Vol. 219 No. 19, p. 9947-9958, 2013.

10. Tsung-Min Hwang, Chin-Tien Wu* and Tiexiang Li, Numerical studies on structure-preserving algorithms for surface acoustic wave simulations. Applied Mathematics and Computation, Volume 244, p.140–154, 2013.

11. Yu-Lin Tsai, Ming-Chen Chiang, Ray Chang, Chung-Hao Tien, and Chin-Tien Wu, A new approach to construct freeform surface by numerically differential formulation, Optical Engineering, Vol. 53(3), 031307, 2014.

12. Yu-Lin Tsai , Ming-Chen Chiang, Chung-Hao Tien and Chin-Tien Wu*, A Reconstruction Algorithm for the inverse problem arising from optical freeform design, submitted to ESAIM: Mathematical Modelling and Numerical Analysis. 2014 (under review).

13. Mei-Heng Yueh, Wen-Wei Lin, Chin-Tien Wu, Shing-Tung Yau, An Efficient Energy Minimization for Conformal Parameterizations, J.S.C. Vol. 73, P. 203-227, 2017.

Conference papers and reports:

Keejoo Lee, C. T. Wu and Sung W. Lee, Geometrically nonlinearly analysis of a lightweight composite space reflector using solid shell elements based on the assumed strain formulation, Technical Report in Goddard Space Flight Center, USA, 2000.

C. T. Wu and H. C. Elman, A comparison of geometric and algebraic multigrid for discrete convection-diffusion equations. Presented in 8th Copper Mountain Conference on Iterative methods, 2004.

C. T. Wu, Stopping criteria for iterative methods in solving convection-diffusion equations on adaptive meshes. Presented in the third International Congress of Chinese Mathematicians, 2004.

Yu-Lin Tsai, Chin-Tien Wu, and Chung-Hao Tien, An approach to construct freeform surface by solving Monge-Ampere equation, Freeform Optics Tucson, Arizona United States, November 3-7, 2013.

Jian-Jia Su, Yu-Lin Tsai, Zi-Yang Huang, Chin-Tien Wu, Chung-Hao Tien, Skew Freeform Reflectors for Two-Dimensional Illuminance. OSA’s Optical Design and Fabrication Congress, Denver, USA, 2017.

Recently invited and joined conferences:

The 6th study group on industrial and applied mathematics, Nanjin China, 2007.

Taiwan-Japan Joint workshop on Numerical Analysis and Scientific Computation, Taipei, Taiwan, 2007.

The 6th international conference on scientific computing and applications, Busan, Korea, 2008.

Taiwan-Japan Joint workshop on inverse problem, Taipei, Taiwan, 2008.

Conference in Differential equation, Taipei, Taiwan, 2010

The Sixth East Asia SIAM Conference, Kuala Lumpur, Malaysia, 2010.

第一屆海峽兩岸計算數學研討會, 廈門, 中國, 2010.

The 19th workshop on Differential equations and its applications, Tainan, Taiwan, 2011.

The Seventh East Asia SIAM Conference, Waseda University Kitakyushu Campus, Japan, 2011.

3D Geometry/Imaging, 昆明理工大學, 雲南, 中國, 2012.

第二屆海峽兩岸計算數學研討會, 高雄, 台灣, 2012.

The 22nd Annual Workshop on Differential Equations, Shinchu, Taiwan, 2014.

The tenth East Asia SIAM Conference, Ambassador City Jomtien, Pattaya, Chonburi, Thailand June 23-25, 2014.


An efficient multigrid solver of transient 2-D Navier-Stokes equations for incompressible flows. In preparation.

C. T. Wu, On the implementation of an accurate and efficient solver for convection-diffusion equations. PhD thesis, University of Maryland, MD, USA, 2003.

C. T. Wu, Existence and regularity of capillary surface over unbounded domain, Master thesis, National Tsing-Hua University, Taiwan, 1993.

Lecture Notes

1.An introduction of multigrid method for large scale computation, Lecture note in Scientific Computing, Winter School National Center for Theoretical Sciences, Tsing-Hua University, Taiwan, 2005.

2.An introduction of Maltab programming for scientific computations, Lecture note in Dept. Applied Math. NCTU, Taiwan, 2006.

3.Scientific Computing, Applied Math. NCTU, Taiwan, 2008.

4.Finite Element Method, Applied Math. NCTU, Taiwan, 2009.

5.A Few Topics on Micro-Pump Simulations, Institute of Mathematical Modeling and Scientific Computing, 2010

Computational Mechanics:

A test case for nonlinear finite element: cantilevel beam with end moment


(1) bar length = 12, width and height of the cross section=1,

(2) end moment M=mf, here f varies from 0 to 2 and m=654761.9

(3) Young’s modulus = 3.0e+07, Poisson ratio=0,

Original configuration

bar under 1M end moment

bar under 2M end moment

Application of nonlinear finite element for the load analysis of a composite space reflector:

Physical composite space reflector

Finite element model of the reflector

load v.s. displacement

Computational Fluid Mechanics:

Some results from my 2D Navier-Stokes Calculation:

Driven Cavity (DC) : Driven Cavity Flow with Renold's number 400


Driven Cavity (DC) : Driven Cavity Flow with Renold's number 5000

BFS at Renold's number 100

BFS at Renold's number 1000

Karman Vortex Street (KVS): Renold's number 100

Karman Vortex Street (KVS): Renold's number 1000

Airfoil NACA0012 : Renold's number 3e+06


Pressure Coefficient

Airfoil NACA0012 with 20 attack angle: Renold's number 1e+06


Pressure Contour Plot

Fluid structure interaction (FSI):

(1) Flow past an cross-flow oscillating cylinder:

l Flow past an cross-flow oscillating cylinder with Reynold’s number 200, oscillating frequency=0.1 and oscillating amplitude=0.4

History of changing of the drag and lift coefficients:

Numerical PDE on Evolution Surface:

Heating on a rotating surface: