IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Zhu Wang

  • Assistant Professor
  • Department of Mathemtics
  • University of South Carolina


Education

Ph.D. Mathematics Virginia Tech 2012
M.S. Computational Mathematics Sichuan University, China 2006
B.A. Information & Computational Mathematics Sichuan University, China 2003

Experience

2014 – Present Assistant Professor Department of Mathematics, Univ. of South Carolina
2012 – 2014 Industrial Postdoc IMA, Univ. of Minnesota
2011 Givens Associate Argonne Natinal Laboratory
2010 Givens Associate Argonne National Laboratory

Research

Research Interests

My research centers around the development of mathematically justified models and corresponding efficient, accurate algorithms for grand challenge problems at the frontier of computational science and engineering. Topics include: Scientific Computing, Numerical Analysis, Reduced-Order Modeling, Climate Modeling, Large Eddy Simulation, Numerical Solutions to PDEs.

Current Projects

  • Reduced-order modeling for complex systems - Reduced-order modeling is a powerful technique to decrease the tremendous computational cost required in many real-world problems, e.g., the control of turbulent flows. The proper orthogonal decomposition (POD) combined with Galerkin method has been widely used to generate reduced-order models (ROMs) for flows. However, this methodology breaks down when the complexity of the flow increases. To address the lack of physical accuracy of standard POD-ROMs, novel POD closure models were introduced for structurally dominated turbulent flows. The new models have been applied to the airflow control in energy efficient buildings and uncertainty analysis in nuclear engineering.
  • Variational approaches to inverse photolithograph - Optical lithography is a typical process utilized in producing microchips, which transfers a layout pattern from a photomask to a substrate, under an ultraviolet light source. Along with the growing demand for circuit components with smaller and smaller scales, the classic manufacturing method is not able to resolve the fine details of the circuit components. As a result, the pattern on the substrate may have wrong spots connected. We develop a variational approach to design an appropriate photomask such that the final pattern after a complete lithography process remains as close as possible to the target pattern.

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Teaching Activities

Current Courses

  • MATH 142: Calculus II
  • MATH 344: Applied Linear Algebra

Previous Courses

  • MATH 141: Calculus I
  • MATH 520: Differential Equations
  • Courses taught while at Va Tech: Calculus, Elementary Calculus with Trig II, Vector Geometry Recitation.

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Honors and Other Special Scientific Recognition

  • SIAM CSE 3rd BGCE Student Paper Prize Finalist, Reno, NV, 2011
  • Winner of the 34th SIAM SEAS Conference Student Paper Competition, Raleigh, NC, 2010
  • C. B. Ling Scholarship, Virginia Tech, 2008-2009

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5 Selected Publications

  • T. Iliescu and Z. Wang, Are the Snapshot Difference Quotients Needed in the Proper Orthogonal Decomposition?, SIAM J. Sci. Comput., vol. 36 (3), 2014, pp. A1221-A1250.
  • T. Iliescu and Z. Wang, Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations, Numer. Meth. Partial. Diff. Eqs., vol. 30, 2014, pp. 641-663.
  • Z. Wang, B. McBee and T. Iliescu, Approximate Partitioned Methods of Snapshots for POD, J. Comput. Appl. Math., vol. 307, 2016, pp. 374-384.
  • L. Rondi, F. Santosa and Z. Wang, A Variational Approach to the Inverse Photolithography Problem, SIAM J. Appl. Math., vol. 76 (1), 2016, pp. 110-137.
  • Z. Wang, Nonlinear Model Reduction Based on the Finite Element Method With Interpolated Coefficients: Semilinear Parabolic Equations, Numer. Meth. Partial. Diff. Eqs., vol. 31 (6), 2015, pp. 1713-1741.

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Curriculum Vitae

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