Thomas Yizhao Hou

Charles Lee Powell Professor of Applied and Computational Mathematics

[*]
Curriculum Vitae
[*] Recent Publications


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Curriculum Vitae

University Address

Applied and Comput. Math., 9-94
California Institute of Technology
Pasadena, CA 91125
Tel: (626)-395-4546
Fax: (626)-578-0124
Email: hou@cms.caltech.edu

Education

B.S. (Mathematics), South China University of Technology, June 1982
M.S. (Mathematics), UCLA, March, 1985
Ph.D.(Mathematics), UCLA, 1987
Thesis Supervisor: Prof. Bjorn Engquist

Experience

Charles Lee Powell Professor of Applied and Computional Mathematics, Caltech, June 2004- present.

Professor of Applied and Computional Mathematics, Caltech, Feb 1998 - present.

Executive Officer of Applied and Computational Math, Caltech, July 2000 - June, 2006.

Associate Professor of Applied Mathematics, Caltech, June 1993 - Jan. 1998.

Associate Professor of Mathematics, Courant Institute, September 1992 - May1993.

Assstant Professor of Mathematics, Courant Institute, September 1989 - August 1992.

Visiting Member, Courant Institute, July 1987 - August 1989.

Visiting Member, Institute for Advanced Study, HKUST Sept. 2010 -- present.

Distinguished Visiting Professor, the Chinese Academy of Sciences, Beijing, China, Sept. 2002 -- June, 2006.

Visiting Chaired Professor, the Tsinghua University, Beijing, China, April-June, 2004.

Distinguished Visiting Professor, the National University of Singapore, Singapore, Deecember, 2002.

Visiting Professor, Institute for Advanced Study, Hong Kong University of Science and Technology, September 2009 -- present.

Invited Professor, Universite de Paris VI, March 1997 and July 1997.

Invited Visiting Professor, Mittag-Leffler Institute, October 1997.

Invited Professor, Ecole Normale Superieure, Paris, September 1994.

Invited Visiting Professor, Institute for Advanced Study, September 1991 - June 1992.

Research Interests


Homogenization, Multiscale Analysis and Computation;

Vortex Dynamics, Interface Problems, Multi-Phase Flows;

Blow-up or non-Blow-up of 3D Euler and Navier-Stokes Equations ;

Adaptive Data Analysis.

Honors and Awards


Fellow of the American Mathematical Society, 2012

Fellow of the American Academy of Art and Sciences, 2011

Fellow of Society of Industrial and Applied Mathematics, 2009

Computational and Applied Sciences Award, the United States Association of Computational Mechanics, 2005

Morningside Gold Medal in Applied Mathematics, International Congress of Chinese Mathematicians, 2004

Invited Plenary Speaker, International Congress on Industrial and Applied Mathematicians, Sydney, 2003

James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, SIAM, 2001

Invited Speaker, International Congress of Mathematicians, Berlin, 1998

Francois N. Frenkiel Award for 1998, Division of Fluid Dynamics, American Physical Society.

Feng Kang Prize in Scientific Computing, 1997

Afred Sloan Fellow (1990-1992)

Richard C. DiPrima Outstanding Dissertation Prizes, Society of Industrial and Applied Mathematics, 2002 (Gang Hu) and 2006 (Xinwei Yu).

The Aisenstadt Chair, Center de Reserches Mathematiques, Universite de Montreal, 9/04-5/05.

The Aziz Lecturer, University of Maryland, 11/03.


Professional Service and Leadership


Member of SIAM Council, 2009 -- present.

Director of Board of Governors, Institute of Mathematics and its Applications, January 2012 -- present.

Member of Board of Governors, Institute of Mathematics and its Applications, 2010 -- present.

Founding Editor-in-Chiefs


Founding Editor-in-Chief, SIAM Journal on Multiscale Modeling and Simulation, (Jan, 2002 -- Dec. 2007)

Founding Co-Editor-in-Chief, Advances in Adaptive Data Analysis, (Jan, 2009 -- present)

Editorial Boards


Editor Board, SIAM Journal on Multiscale Modeling and Simulation, (Jan, 2002-- present)

Editor Board, SIAM Journal on Numerical Analysis (June, 1992 -- Dec, 1997)

Editor, Mathematical Modelling and Numerical Analysis, (Oct, 1998 - Dec., 2001)

Editorial Board, Int. J. on Multiscale Computational Engineering (Apr. 2004 - present)

Editorial Board, Discrete and Continuous Dynamical Systems, Series B, (Aug, 2000 - present)

Editorial Board, Communications in Mathematical Sciences, (Jan, 2003 - present)

Editorial Board, International Journal for Multiscale Computational Engineering, (April, 2004 - present)

Editorial Board, Applied Mathematics Letters, (Jan, 2012 - present)

Editorial Board, Journal of Computational Mathematics, (Jan, 2008 - present)


Recent Invited Plenary Lectures


Invited speaker and main organizer, IPAM Workshop on Adaptive Data Analysis and Sparsity, IPAM, UCLA. 1/28-2/1/2013,

Invited speaker, CERM Workshop on Uncertainty Quantification, Brown University, 10/9-13/2012,

Co-Organizer and invited speaker, Frontier of Computational and Applied Mathematics, IPAM, UCLA, 6/8-10/2012,

Invited speaker, International Conference on Scientific Computing, Chinese University of Hong Kong, 1/4-7/2012,

Invited speaker and main organizer, IMA Hot-Topic Workshop on Trend and Instantaneous Frequency, IMA, University of Minnesota. 9/7-9/2011.

Invited plenary speaker, the Sixth International Conference of Society for the Foundations of Computational Mathematics, Budapest, Hungary, 7/4-14/2011.

Invited plenary speaker, the 20th International Conference on Domain Decomposition, UCSD, San Diego, 2/7-11/2011.

Invited speaker, IMA Workshop on Numerical Solutions of Partial Differential Equations: Novel Discretization Techniques, Minnesota, 11/1-5/2010.

Invited plenary speaker, Fluid Dynamics, Analysis and Numerics, a conference in honor of J. Thomas Beale, Duke University, North Carolina, 6/28-30/2010.

Invited keynote speaker, Second Intrenational Conference on Nonlinear Waves: Theory and Applications, Tsinghua University, Beijing, China. 6/26-29/2010.

Invited plenary speaker, Advances in Partial Differential Equations and their Applications, Fudan University, Shanghai, China, 5/31-6/4/2010.

Invited speaker and co-organizer, Sparse Representation of Multiscale Data and Images, Nanyang Technological University, Singapore. 12/14-18/2009.

Invited plenary speaker, EPSRC-Warwick Capstone Conference on Chalenges in Sceintific Computing, Warwick University, UK. 6/29-7/3/2009.

Invited plenary speaker, Second International Conference on Hilbert-Huang Transfrom: Theory and Applications, Zhongshan Univerisity, Guangzhou, China. 12/15-17/2008.

Invited Plenary Speaker, International Conference on Applied Mathematics: Modeling, Analysis and Computation, City University of Hong Kong, Hong Kong, May, 2008.

Invited Plenary Speaker, International Workshop on Multiscale Problems. Hong Kong University of Science and Technology, Hong Kong, December, 2007.

Invited Plenary Speaker, International Conference on Partial Differential Equations and Their Numerical Analysis, Beijing, China, July, 2007.

Invited Speaker, Newton Institute Workshop on Effective Computational Methods for Highly Oscillatory Solutions: The Interplay Between Mathematical Theory and Applications, University of Cambridge, July, 2007.

Invited Speaker, International Conference on EULER EQUATIONS: 250 YEARS ON, Aussois, France, June, 2007.

Invited Speaker, International Conference dedicated to the 300th Birthday of Leonard Euler, "Mathematical Hydrodynamics: Euler Equations and Related Topics" Saint Petersburg, Russia, June, 2007.

Invited Plenary Speaker, International Conference on Multiscale Problems, Technical University Munich, Germany, October, 2006.

Invited Semi-Plenary Speaker, Seventh World Congress on Computational Mechanics, Los Angeles, July, 2006.

Invited Plenary Speaker, International Conference on Applied Mathematics and Interdisciplinary Research, Nankai, China, June, 2006.

Invited Plenary Speaker, NCTS International Workshop on Scientific Computing, Taipei, Taiwan, June, 2006.

Invited Speaker, the 2006 Abel Symposium, Mathematics and Computation, a Contemporary View, Norway, May, 2006.

Invited Plenary Speaker, Frontiers in Applied and Computational Mathematics, New Jersey Institute of Technology, New Jersey, May, 2006.

Invited Speaker, the Brown University PDE conference, Brown University, Rhode Island, April, 2006.

Principal Invited Speaker, The Sixth Mississippi State Conference on Differential Equations and Computational Simulations, May, 2005.

Opening Keynote Speaker, The National Computational Fluid Dynamics Conference Taiwan, August, 2004.

Invited Plenary Speaker, the International Congress of Industrial and Applied Mathematics, Sydney, Australia, July, 2003.

Invited Plenary Speaker, the Gordon Research Conference on Flow and Transport in Permeable Media, Andover, USA, August, 2002.

Invited Plenary Speaker, the International Conference of Applied Mathematics in Memory of Jacques-Louis Lions, Paris, France, July, 2002.

Invited Plenary Speaker, the Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, USA, May, 2002.

Invited Plenary Speaker, International Conference on Scientific and Engineering Computation, Singapore, December, 2002.

Invited Plenary Speaker, the First SIAM/EMS Conference on Applied Mathematics in our Changing World, Berlin, Germany, September, 2001.

Invited Plenary Speaker, the Annual Meeting of the German Society for Applied Mathematics and Mechanics (GAMM), Zurich, February, 2001.

Invited Plenary Speaker, International Conference on Scientific and Engineering Computing, Beijing, China, March, 2001.

Invited Plenary Speaker, Conference on Scientific Computing and Differential Equations, Scicade01, Vancouver, August, 2001.

Invited Speaker, The Fourth European Conference on Numerical Mathematics and Advanced Applications, Ischia, Italy, July, 2001.

Invited Plenary Speaker, the Eighth International Conference on Hyperbolic PDEs and Applications, Germany, March, 2000.

Invited Plenary Speaker, the Thirteen International Conference on Domain Decomposition, France, October, 2000.

Invited Plenary Speaker, the Third International Conference on Numerical Modelling in Continuum Mechanics, Prague, July, 2000.

Invited Keynote Speaker, European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona, Spain, September, 2000.

Invited Plenary Speaker, Second International Conference on Boundary Integral Methods: Theory and Applications, Bath, UK, September, 2000.

Invited Plenary Speaker, First International Congress of Chinese Mathematicians, Beijing, Decemebr, 1998

Invited Plenary Speaker, European Science Foundation Conference on Applied Mathematics for Industrial Flows, Spain, October, 1998.

Invited Public Lecture at London Mathematical Society on Mathematical Aspect of Numerical Analysis of PDEs, London, October, 1997.


List of Publications


PUBLICATIONS



  1. Homogenization for Semilinear Hyperbolic Systems with Oscillatory Data, T. Y. Hou, Comm. Pure and Appl. Math. 41, 471-495 (1988).

  2. Particle Method Approximation of Oscillatory Solutions to Hyperbolic Differential Equations, B. Engquist and T. Y. Hou , SIAM J. Numer. Anal., 26, 289-319 (1989).

  3. The Convergence of the Point Vortex Method for the 2-D Euler Equations,  J. Goodman, T. Y. Hou and J. Lowengrub, Comm. Pure and Appl. Math., 43, 415-430(1990).

  4. Homogenization and Convergence of the Vortex Method for 2-D Euler Equations with Oscillatory Vorticity Fields, W. E and T. Y. Hou, Comm. Pure and Appl. Math., 43, 821-855 (1990)

  5. The Convergence of a Point Vortex Method for the 3-D Euler Equations, T. Y. Hou and J. Lowengrub, Comm. Pure and Appl. Math., 43 , 965-981(1990).

  6. Dispersive Approximations in Fluid Dynamics, T. Y. Hou and P. Lax, Comm. Pure and Appl. Math., 44, 1-40 (1991).

  7. Convergence of the Grid Free Point Vortex method for the 3-D Euler Equations, G.H. Cottet, J. Goodman and T. Y. Hou, SIAM J. Numer. Anal., 28, 291-307 (1991).

  8. Geometry Independent Convergence Results for Domain Decomposition Algorithms, T. F. Chan, T. Y. Hou and P. L. Lions SIAM J. Numer. Anal., 28, 378-391 (1991).

  9. Finite Difference Approximations for Partial Differential Equations with Rapidly Oscillating Coefficients, M. Avellaneda, T. Y. Hou and G. Papanicolaou, Mathematical Modelling and Numerical Analysis, 25, 693-710 (1991).

  10. Homogenization of Linear Transport Equations with Oscillatory Vector Fields, T. Y. Hou and X. Xin, SIAM J. Appl. Math., 52, 34-45 (1992).

  11. Convergence of a Finite Difference Scheme for the Navier-Stokes Equations Using Vorticity Boundary Conditions, T. Y. Hou and B. Wetton, SIAM J. Numer. Anal., 29, 615-639 (1992).

  12. Multi-Valued Solutions and Branch Point Singularities for Nonlinear Hyperbolic and Elliptic Systems, . Caflisch, N. Ercolani, T. Y. Hou, Y. Landis, Comm. Pure and Appl. Math., 46 , 453-499 (1993).

  13. Growth Rates for Linearized Motion of Fluid Interfaces Away from Equilibrium, J. T. Beale, T. Y. Hou and J. Lowengrub, Comm. Pure and Appl. Math. , 46 , 1269-1301 (1993).

  14. On the Stability of the Unsmoothed Fourier Method for Hyperbolic Equations, J. Goodman, T. Y. Hou and E. Tadmor, Numer. Math. , 67 , 93-129 (1994).

  15. Removing the Stiffness from Interfacial Flows with Surface Tension ,  T. Y. Hou, J. Lowengrub and M. Shelley, J. Comput Phys. , 114 , 312-338 (1994).

  16. Numerical Solutions to Free Boundary Problems, ,  T. Y. Hou, ACTA Numerica, , 4 , 335-415 (1995).

  17. Eulerian Capturing Methods Based on a Level Set Formulation for Incompressible Fluid Interfaces, ,  Y. C. Chang, T. Y. Hou, B. Merriman, and S. Osher, J. Comput Phys. , 124 , 449-464 (1996).

  18. Convergence of a Boundary Integral Method for Water Waves, J. T. Beale, T. Y. Hou and J. Lowengrub, SIAM J. Numer. Anal., . 33 , 1797-1843(1996).

  19. Well-Posedness of Linearized Motion for 3-D Water Waves Far From Equilibrium, T. Y. Hou, Z.-H. Teng, and P. Zhang, Comm in PDEs , 21 , 1551-1586 (1996).

  20. Converging Methods for the Computation of Propagating Solid-Solid Phase Boundaries, X. Zhong, T. Y. Hou, and P. LeFloch, J. Comput. Phys., 124 , 192-216 (1996).

  21. The Long-Time Motion of Vortex Sheets with Surface Tension ,  T. Y. Hou, J. Lowengrub and M. Shelley, Phys. of Fluid, A, 9 , 1933-1954 (1997).

  22. A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media ,  T. Y. Hou and X. H. Wu, J. Comput Phys. , 134 , 169-189, (1997).

  23. A Hybrid Method for Moving Interface Problems with Application to the Hele-Shaw Flow, T. Y. Hou, Z. Li, S. Osher, and H. Zhao, J. Comput. Phys. , 134 , 236-252, (1997).

  24. Convergence of a Non-Stiff Boundary Integral Method for Interfacial Flows with Surface Tension ,  H. Ceniceros and T. Y. Hou, Math. Comput. , 67 , 137-182 (1998).

  25. Removing the Stiffness of Curvature in Computing 3-D Filaments, T. Y. Hou, I. Klapper and H. Si, J. Comput. Phys. , 143 , 628-664 (1998).

  26. Effect of Scaling Regime and Finite Scaling Range on the Relation between Power Laws in Physical and Spectral Domains, T. Y. Hou, X. H. Wu, S. Y. Chen and Y. Zhou, Phys. Review E. , 58 , 5841- (1998).

  27. Convergence of a Multiscale Finite Element Method for Elliptic Problems With Rapidly Oscillating Coefficients ,  T. Y. Hou, X. H. Wu, and Z.Q. Cai, Math. Comput. , 68 , 913-943, (1999).

  28. Dynamic Generation of Capillary Waves ,  H. Ceniceros and T. Y. Hou, Phys. Fluids, A , 11 (5) , 1042-1050 (1999).

  29. Numerical Study of Hele-Shaw Flow with Suction ,  H. Ceniceros, T. Y. Hou, and H. Si, Phys. Fluids, A , 11 (9) , 2471-2486, (1999).

  30. A Level-Set Approach to the Computation of Twinning and Phase Transition Dynamics, T. Y. Hou, P. Rosakis, and P. LeFloch, J. Comput. Phys. , 150 , 302-331 (1999).

  31. The Singular Perturbation of Surface Tension in Hele-Shaw Flow and The Effect of Noise ,  H. Ceniceros and T. Y. Hou, J. Fluid Mech. , 409 , 251-272 (2000).

  32. Convergence of A Nonconformal Multiscale Finite Element Method ,  Y. R. Efendiev, T. Y. Hou, and X. H. Wu, SIAM J. Numer. Anal. , 37 , 888-910 (2000)..

  33. A Mixed Multiscale Finite Element Method for Elliptic Problems with Oscillating Coefficients ,  Z. Chen and T. Y. Hou, Math. Comput., 72, No. 242 , 541-576, published electronically on June 28, 2002.

  34. An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions ,  H. Ceniceros and T. Y. Hou, J. Comput. Phys. , 172 , 1-31 2001.

  35. Boundary Integral Methods for Multi-Phase Problems in Fluid Dynamics and Materials Science ,  T. Y. Hou, J. Lowengrub, and M. Shelley, in J. Comput. Phys. , 169, No. 2 , 302-362 (2001).

  36. Convergence of A Boundary Integral Method for 3-D Water Waves ,  T. Y. Hou and P. Zhang, Discrete and Continuous Dynamical Systems, Series B , 2(1) , 1-34 (2002).

  37. Analysis of Upscaling Absolute Permeability ,  X. H. Wu, Y. Efendiev, and T. Y. Hou, Discrete and Continuous Dynamical Systems, Series B , 2(2), , 185-204(2002).

  38. Multiscale Domain Decomposition Methods for Elliptic Problems with High Aspect Ratios ,  J. Aarnes and T. Y. Hou, Acta Mathematicae Applicatae Sinica, , 18 No. 1 , 63-76 (2002).

  39. Singularity Formation in 3-D Vortex Sheets ,  T. Y. Hou, G. Hu, and P. Zhang, Phys of Fluids, , 15 No. 1 , 147-172 (2003).

  40. A Nearly Optimal Existence Result for Slightly Perturbed 3D Vortex Sheets ,  T. Y. Hou and G. Hu, Comm. in PDEs , 28, No.1/2, , 155-198 (2003).

  41. Numerical Approximations to Multiscale Solutions in Partial Differential Equations ,  T. Y. Hou, Frontier in Numerical Analysis , ed. J. F. Blowey, A. W. Craig, and T. Shardlow, Springer Publications, 241-302 (2003).

  42. Homogenization of Incompressible Euler Equation ,  T. Y. Hou, D. P. Yang, and K. Wang,

  43. Multiscale Modeling and Computation of Incompressible Flow ,  T. Y. Hou, Applied Mathematics Entering the 21st Century, Invited Talks from the ICIAM2003 Congress, ed. J. M. Hill and R. Moore, SIAM Publications, 177-210 (2004). J. Comput. Math. , 22, No.2, , 220-229 (2004).

  44. Removing the Cell Resonance Error in the Multiscale Finite Element Method via a Petrove-Galerkin Formulation ,  T. Y. Hou, X. H. Wu and Y. Zhang Comm. Math. Sciences, , 2 No. 2 , 185-205 (2004).

  45. Geometric Properties and Non-blowup of 3-D Incompressible Euler Flow ,  J. Deng, T. Y. Hou, and X. Yu, Comm. in PDEs. , 30, No.1, , 225-243 (2005).

  46. Multiscale Numerical Methods for Singularly-Perturbed Convection Diffusion Equations ,  P. Park and T. Y. Hou, International Journal of Computational Methods , 1, No.1, , 17-65 (2004).

  47. Multiscale Finite Element Methods for Nonlinear Problems and Their Applications,  Y. Efendiev, T. Y. Hou, and V. Ginting, Comm. Math. Sci. , 2, No.4, , 553-589 (2004).

  48. A Modified Particle Method for Semilinear Hyperbolic Systems with Oscillatory Solutions ,  R. Fetecau and T. Y. Hou, Methods and Applications of Analysis , 11, No.4, , 573-604 (2004).

  49. Multiscale Analysis in Lagrangian Formulation for the 2-D Incompressible Euler Equation ,  T. Y. Hou, D. P. Yang, and H. Ran, Discrete and Continuous Dynamical Systems, Series A , 13(5) , 1153-1186, 2005.

  50. Global Well-Posedness of the Viscous Boussinesq Equations ,  T. Y. Hou and C. Li, Discrete and Continuous Dynamical Systems, Series A , 12(1), , 1-12, 2005.

  51. Improved Geometric Conditions for Non-blowup of the 3D Incompressible Euler Equation ,  J. Deng, T. Y. Hou, and X. Yu, Comm. in PDEs , 31, No. 2 , 293-306, 2006.

  52. Level Set Dynamics and Non-blowup of the 2D Quasi-Geostrophic Equation,  J. Deng, T. Y. Hou, R. Li, and X. Yu, Methods and Applications of Analysis , 13, No. 2 , 157-180, 2006.

  53. Wiener Chaos Expansions and Numerical Solutions of Randomly Forced Equations of Fluid Mechanics,  T. Y. Hou, W. Luo, B. Rozovskii, and H.M. Zhou, J. Comput. Phys. , 216 , 687-706 (2006).

  54. Coarse-gradient Langevin Algorithms for Dynamic Data Integration and Uncertainty Quantification,  P. Dostert, Y. Efendiev, T. Y. Hou, W. Luo, J. Comput. Phys. , 217 , 123-142 (2006).

  55. Parametric Vertical Coordinate Formulation for Multiscale, Boussinesq, and Non-Boussinesq Ocean Modeling ,  Y. T. Song and T. Y. Hou, Ocean Modeling , 11, , 298-332, 2006.

  56. A Pseudo-spectral Multiscale Method: Interfacial Conditions and Coarse Grid Equations ,  Shaoqiang Tang, T. Y. Hou, Wing Kam Liu, J. Comput. Phys. , 213 , 57-85, 2006.

  57. A Mathematical Framework of the Bridging Scale Method ,  Shaoqiang Tang, T. Y. Hou, Wing Kam Liu, Int. J. Numer. Meth. Engng., 65 , 1688-1713, 2006.

  58. Accurate Multiscale Finite Element Methods for Two-Phase Flow Simulations ,  Y. Efendiev, V. Ginting, T. Y. Hou, and R. Ewing, J. Comput. Phys., 220, , 155-174, 2006.

  59. On Global Well-Posedness of the Lagrangian Averaged Euler Equations ,  T. Y. Hou and C. Li, SIAM J. Math Anal., 38 (3) , 782-794, 2006.

  60. A 3D Numerical Method for Studying Vortex Formation Behind a Moving Plate ,  T. Y. Hou, V.G. Stredie, and T. Y. Wu, Comm. in Comput. Phys., 1 , 207-228, 2006.

  61. Mathematical Modeling and Simulation of Aquatic and Aerial Animal Locomotion ,  T. Y. Hou, V.G. Stredie, and T. Y. Wu, J. Comput. Phys. , 225 , 1603-1631, 2007.

  62. A Level Set Formulation for the 3D Incompressible Euler Equations ,  J. Deng, T. Y. Hou, and X. Yu, Methods and Applications of Analysis , 12 (4) , 427-440, 2005.

  63. Multiscale Computation of Isotropic Homogeneous Turbulent Flow ,  T. Y. Hou, D. P. Yang, and H. Ran, Contemporary Mathematics , 408 , 111-135, 2006. AMS Publ., Inverse Problems, Multi-Scale Analysis, and Effective Medium Theory. ed. H. Ammari and H. Kang.

  64. Preconditioning of Markov Chain Monte Carlo Simulations Using Coarse-Scale Models ,  Y. Efendiev, T. Y. Hou and W. Luo, SIAM J. Sci. Comput. , 28(2) , 776-803, 2006.

  65. Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations ,  T. Y. Hou and R. Li, J. Nonlinear Science , 16(6) , 639-664, 2006.

  66. A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media ,  T. Y. Hou, A. Westhead, and D. P. Yang, SIAM Multiscale Modeling and Simulation , 5(4) , 1087-1127, 2006.

  67. Computing Nearly Singular Solutions Using Pseudo-Spectral Methods ,  T. Y. Hou and R. Li, J. Comput. Phys. , 226 , 379-397, 2007.

  68. Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations ,  T. Y. Hou and R. Li, Discrete and Continuous Dynamical Systems, Series A , 18(4) , 637-642, 2007.

  69. Multiscale Simulations of Porous Media Flows in Flow-Based Coordinate System ,  Y. Efendiev, T. Y. Hou, and T. Strinopoulos, Comput. Geoscience , 12 , 257-272, 2008, DOI 10.1007/s10596-007-9073-7.

  70. Dynamic Stability of the 3D Axi-symmetric Navier-Stokes Equations with Swirl ,  T. Y. Hou and C. Li, Commun. Pure Appl. Math. , 61(5) , 661--697, 2008. Published online Aug 27, 2007, DOI: 10.1002/cpa.20213.

  71. Numerical Study of Nearly Singular Solutions of the 3-D Incompressible Euler Equations ,  T. Y. Hou and R. Li, the Proceedings of 2006 Abel Symposium on Computational Mathematics , H. Munthe-Kaas and B. Owren (Eds.), Springer-Verlag, Berlin Heidelberg, 39--66, 2008.

  72. Multiscale Finite Element Methods for Porous Media Flows and Their Applications ,  Y. Efendiev and T. Y. Hou, Applied Numerical Mathematics , 57 , 577-596, 2007.

  73. Multiscale Analysis and Computation for the 3D Incompressible Navier-Stokes Equations ,  T. Y. Hou, D. P. Yang and H. Ran, SIAM Multiscale Modeling and Simulation , 6 (4) , 1317-1346, 2008, published online on March 26, 2008, DOI: 10.1137/070682046.

  74. Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data ,  T. Y. Hou, Z. Lei and C. Li, Commun PDEs, , 33 (9) , 1622-1637, 2008, DOI: 10.1080/03605300802108057.

  75. Blowup or No Blowup? The Interplay between Theory and Numerics ,  T. Y. Hou and R. Li, Physica D , 237 , 1937-1944, 2008, in the special issue of "Euler Equations: 250 Years On", published online Jan. 25, 2008, DOI:10.1016/j.physd.2008.01.018. .

  76. Flow Based Oversampling Technique for Multiscale Finite Element Methods ,  J. Chu, Y. Efendiev, V. Ginting, and T. Y. Hou, Advances in Water Resources , 31 , 599--608, 2008.

  77. Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations ,  T. Y. Hou and Z. Shi, J. Comput. Phys., , 227 , 9138-9169, 2008, DOI:10.1016/j.jcp.2008.03.002.

  78. An Efficient Semi-Implicit Immersed Boundary Method for the Navier-Stokes Equations ,  T. Y. Hou and Z. Shi, J. Comput. Phys., , 227 , 8968-8991, 2008, DOI:10.1016/j.jcp.2008.07.005.

  79. On the Stabilizing Effect of Convection in 3D Incompressible Flow ,  T. Y. Hou and Z. Lei, Commun. Pure Appl. Math. , 62(4) , 501--564, 2009. Published online June 10, 2008, DOI: 10.1002/cpa.20254.

  80. On the Partial Regularity of a 3D Model of the Navier-Stokes Equations ,  T. Y. Hou and Z. Lei, Commun. Math. Phys. , Commun. Math. Phys., 287(2) , 589--612, 2009. Published online on Nov. 20, 2008, DOI:10.1007/s00220-008-0689-9.

  81. Multiscale Analysis for Convection Dominated Transport Equations ,  T. Y. Hou and D. Liang, DCDS-A , 23 , 281-298, 2009, doi:10.3934/dcds.2009.23.281.

  82. Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations ,  T. Y. Hou, Acta Numerica , 18 , 277-346, 2009, doi: 10.1017/S0962492906420018.

  83. Stable Fourth-Order Stream-Function Methods for Incompressible Flows with Boundaries ,  T. Y. Hou and B. Wetton, J. Comput. Math. , 27 (4) , 441-458, 2009.

  84. A Variant of the EMD Method for Multiscale Data, ,  T. Y. Hou, M. P. Yan, and Z. Wu, AADA , 1 (4) , 483-516, 2009.

  85. A New Multiscale Finite Element Method for High-Contrast Elliptic Interface Problems ,  C.-C. Chu, I. G. Graham, and T. Y. Hou, Math. Comput., 79 , 1915-1955, 2010.

  86. On Singularity Formation of a Nonlinear Nonlocal System ,  T. Y. Hou, C. Li, Z. Shi, S. Wang, and X. Yu, ARMA , 199 , 117-144, 2011.

  87. Adaptive Data Analysis via Sparse Time-Frequency Representation ,  T. Y. Hou and Z. Shi, Advances in Adaptive Data Analysis , 3 (1&2), 1-28, 2011. DOI: 10.1142/S1793536911000647.

  88. On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations ,  T. Y. Hou, Z. Shi, and S. Wang, Advances in Mathematics , 230, 607-641, 2012.

  89. Dynamic Growth Estimates of Maximum Vorticity for 3D Incompressible Euler Equations and the SQG Model ,  T. Y. Hou and Z. Shi, DCDS-A, 32 (5) , 1449-1463, 2012.

  90. Multiscale Modeling of Incompressible Turbulent Flows ,  T. Y. Hou, X. Hu, and F. Hussain, JCP , 232 , 383-396, 2013. DOI: 10.1016/j.jcp.2012.08.029.

  91. Data-Driven Time-Frequency Analysis ,  T. Y. Hou and Z. Shi, Applied and Comput. Harmon. Anal., Vol. 35(2), pp. 284–308, 2013, http://dx.doi.org/10.1016/j.acha.2012.10.001.

  92. A Decadal Microwave Record of Tropical Air Temperature from AMSU-A/Aqua Observations ,  Y. Shi, K. F. Li, Y. L. Yung, H. H. Aumann, Z. Shi, and T. Y. Hou, Climate Dynamics , 41 (5-6) , 1385-1405, 2013. DOI: 10.1007/s00382-013-1696-x.

  93. Numerical Simulation of Water Resources Problems: Models, Methods, and Trends ,  C. T. Miller, C. N. Dawsonb, M. W. Farthing, T. Y. Hou, J.F. Huange, C. E. Kees, C.T. Kelley, H. P. Langtangen, Advances in Water Resources , 51 , 405-437, 2013. DOI: 10.1016/j.advwatres.2012.05.008.

  94. A Dynamically Bi-Orthogonal Method for Time-Dependent Stochastic Partial Differential Equations I: Derivation and Algorithms ,  M. Cheng, T. Y. Hou, and Z. Zhang, JCP , 242 , 843-868, 2013. DOI:10.1016/j.jcp.2013.02.033.

  95. A Dynamically Bi-Orthogonal Method for Time-Dependent Stochastic Partial Differential Equations II: Adaptivity and Generalizations ,  M. Cheng, T. Y. Hou, and Z. Zhang, JCP , 242 , 753-776, 2013. DOI: 10.1016/j.jcp.2013.02.020.

  96. On Finite Time Singularity and Global Regularity of an Axisymmetric Model for the 3D Euler Equations, ,  T. Y. Hou, Z. Lei, G. Luo, S. Wang, and C. Zou, ARMA , , 2014. DOI: 10.1007/s00205-013-0717-6.

  97. Generalized Multiscale Finite Element Methods (GMsFEM) ,  Y. Efendiev, J. Galvis, and T. Y. Hou, JCP , 251 , 116-135, 2013. DOI: 10.1016/j.jcp.2013.04.045.

  98. A Multiscale Model Reduction Method for Partial Differential Equations, ,  M. Ci, T. Y. Hou and Z. Shi. M2AN , 48 , 449-474, 2014. DOI: 10.1051/m2an/2013115.

  99. Convergence of a Data-Driven Time-Frequency Analysis Method, ,  T. Y. Hou, Z. Shi, and P. Tavallali. Applied and Comput. Harmonic Analysis , 37 , 235-270, 2014. Doi: 10.1016/j.acha.2013.12.004 .

  100. A Data-driven Stochastic Method for Elliptic PDEs with Random Coefficients, ,  M. Cheng, T. Y. Hou, M. Yan, and Z. Zhang. SIAM/ASA J. Uncertainty Quantificatin , 1 , 452-493, 2013. DOI: 10.1137/130913249.

  101. Sparse Time Frequency Representation of Nonlinear and Nonstationary Data.,  T. Y. Hou and Z. Shi. Science China, Mathematics , 56 (No. 12) , 2489-2506, 2013. DOI: 10.1007/s11425-013-4733-7.

  102. Sparse Time Frequency Representation and Dynamical Systems. ,  T. Y. Hou, Z. Shi and P. Tavallali. Accepted by Commun. Math. Sci., 2014.

  103. Potentially Singular Solutions of the 3D Incompressible Euler Equations, ,  G. Luo and T. Y. Hou. arXiv:1310.0497v2 [physics.flu-dyn], 2013.

  104. Potentially Singular Solutions of the 3D Axisymmetric Euler Equations,,  G. Luo and T. Y. Hou. PNAS , 2014. www.pnas.org/cgi/doi/10.1073/pnas.1405238111.

  105. Toward the Finite-Time Blowup of the 3D Incompressible Euler Equations: a Numerical Investigation,,  G. Luo and T. Y. Hou. SIAM MMS , 2014. Accepted.

  106. On the Finite Time Blowup of a 1D Model for the 3D Incompressible Euler Equations. ,  T. Y. Hou and G. Luo. arXiv:1311.2613v1 [math.AP], 2013

  107. On the Finite Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations, ,  K. Choi, T. Y. Hou, A. Kiselev, G. G. Luo, V. Sverak, and Y. Yao. arXiv:1407.4776v1 [math.AP], 2014.

  108. Self-Similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations, ,  T. Y. Hou and P. Liu. arXiv:1407.5740v1 [math.AP], 2014.

  109. Extraction of Intrawave Signals Using the Sparse Time-Frequency Representation Method. ,  P. Tavallali, T. Y. Hou, and Z. Shi. SIAM MMS , 12 (No. 4) , 1458-1493, 2014. DOI: 10.1137/140957767.

  110. A Heterogeneous Stochastic FEM Framework for Elliptic PDEs, ,  T. Y. Hou and P. Liu. JCP , 281 , 942-969, 2015. DOI: http://dx.doi.org/10.1016/j.jcp.2014.10.020.

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