Research

Publications

In preparation

34. An hp-adaptive Sampling Algorithm for Dispersion Relation Reconstruction of 3D Photonic Crystals, with Y. Wang and R. Craster, submitted, 2024.

33. Gradient-enhanced sparse Hermite polynomial expansions for pricing and hedging high-dimensional American options, with J. Yang, submitted, 2024.

32. Adaptive finite element approximations of the first eigenpair associated with p-Laplacian, with J. Li, J. Merten, Y. Xu and S. Zhu, submitted, 2024.

31. Neural Option Pricing for Rough Bergomi Model, with C. Teng, submitted, 2024.

30. An hp-Adaptive Sampling Algorithm on Dispersion Relation Reconstruction for 2D Photonic Crystals, with Y. Wang, submitted, 2023.

29. On Sparse Grid Interpolation for American Option Pricing with Multiple Underlying Assets, with J. Yang, submitted, 2023.

28. Wavelet-based Edge Multiscale Finite Element Methods for Singularly Perturbed Convection-Diffusion Equations, with S. Fu and E. Chung, submitted, 2023.

27. Quasi-Monte Carlo finite element approximation of the Navier-Stokes equations with initial data modeled by log-normal random fields, with S. Ko and Y.Yu, submitted, 2022

26. On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data, with M. Griebel and C. Rieger, preprint, 2022.

Journal papers

25.  Robust collimated beaming in three-dimensional acoustic sonic crystals, with A. L. Vanel, M. Dubois, C. Tronche, et al., to appear in New Journal of Physics, 2024.

24. Dispersion relation reconstruction for 2D Photonic Crystals based on polynomial interpolation, with Y. Wang, 498,  J. Comput. Phys, 2024.

23. Wavelet-based Edge Multiscale Parareal Algorithm for time fractional diffusion Equations with Heterogeneous Coefficients in a large time domain, To appear, J. Comput. Appl. Math., 2023.

22.  An Edge Multiscale Interior Penalty Discontinuous Galerkin method for heterogeneous Helmholtz problems with large varying wavenumber, with E. Chung and S. Fu,  J. Comput. Phys, 441(15), 2021.

21.  Wavelet-based edge multiscale parareal algorithm for parabolic equations with heterogeneous coefficients and rough initial data, with J. Hu, J. Comput. Phys, 444, 2021.

20. Wavelets-based Edge Multiscale Finite Element Method for Helmholtz problems in perforated domains, with S. Fu, R. Craster and S. Guenneau,  Multiscale Model. Simul., 19(4), 1684-1709, 2021.

19. Homogenization of time-fractional diffusion equations with periodic coefficients, with J. Hu, J. Comput. Phys: 408, 2020.

18.  Edge Multiscale Methods for elliptic problems with heterogeneous coefficients,  with S. Fu and E. Chung,  396,  228-242, J. Comput. Phys, 2019; 

17. Quasi-Optimality of an Adaptive Finite Element Method for Cathodic Protection, with Y. Xu, ESAIM: M2AN, 53(5), 1645-1665, 2019;

16.  On the Convergence Rates of GMsFEMs for Heterogeneous Elliptic Problems without Oversampling Techniques, Multiscale Model. Simul., 17(2), 593 - 619, 2019;

15. On the Degree of Ill-Posedness of Multi-Dimensional Magnetic Particle Imaging, with T. Kluth and B. Jin, Inverse Problems,  34(9), 095006, 26 pp., 2018;

14. Upscaled HDG methods for Brinkman equations with high-contrast heterogeneous coefficient,  with K. Shi, J. Sci. Comput., 77(3), 1780-1800 , 2018.

13. On the decay rate of the singular values of bivariate functions,  with M. Griebel, SIAM J. Numer. Anal., 56(2), 974–993, 2018;

12. Low-Rank Approximation to Heterogeneous Elliptic Problems, Multiscale Model. Simul., 16(1), 477–502, 2018;

11. Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d, with D. Peterseim and M. Schedensack, IMA J. Numer. Anal., 38(3), 1229-1253, 2018;

10. A convergent adaptive finite element method for cathodic protection, with Y. Xu, Computational Methods in Applied Mathematics, 17(1), 105-120, 2017;

9. Sparse Generalized Multiscale Finite Element Methods and their applications,  with E. T. Chung, Y. Efendiev, and W. T. Leung, International Journal for Multiscale Computational Engineering, 14(1), 1-23, 2016;

8. Randomized oversampling for Generalized Multiscale Finite Element Method, with V. Calo, Y. Efendiev and J. Galvis, Multiscale Model. Simul., 14(1), 482-501, 2016;

7. Generalized Multiscale Finite Element Methods for problems in perforated heterogeneous domains,  with E. T. Chung, Y. Efendiev and M. Vasilyeva,  Applicable Analysis, 95(10), 2254-2279, 2016;

6. Hierarchical multiscale modeling for flows in fractured media using Generalized Multiscale Finite Element Method,  with Y. Efendiev, S. Lee, J. Yao, and N. Zhang, GEM -International Journal on Geomathematics 6(2), 141-162, 2015;

5.  Homogenization of High Contrast Brinkman flows,  with D. Brown, Y. Efendiev and V. Savatorova, Multiscale Model. Simul., 13(2), 472-490, 2015;

4.A Generalized Multiscale Finite Element Method for the Brinkman Equation, with J. Galvis and K. Shi,  J. Comput. Appl. Math., 280, 294-309, 2015;

3. Generalized Multiscale Finite Element Methods. Oversampling Strategies, with Y. Efendiev, J. Galvis and M. Presho, International Journal for Multiscale Computational Engineering, 12(6), 465-484, 2014;

2. Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations, with Y. Efendiev, J. Galvis and M. Presho, Commun. Comput. Phys. 15(3), 733-755, 2014;

1.  An adaptive GMsFEM for high-contrast flow problems, with E. T. Chung and Y. Efendiev, J. Comput. Phys., 273, 54-76, 2014;

Refereed Articles in Collections:

1. On metrics for computation of strength of coupling in multiphysics simulation, with A. Wilson, W. Du, A. Moosavi, and C.S. Woodward, Numerical Partial Differential Equations and Scientific Computing, volume 160 of The IMA Volumes in Mathematics and its Applications. Springer New York, 137-176, 2016.

Nonrefereed papers:

2. Multiscale modeling of high contrast Brinkman equations with applications to deformable porous media, with D. Brown, Y. Efendiev, P. Popov and V. Savatorova, Poromechanics V: pp. 1991-1996, 2013.

1. Electrochemical Energy Storage Devices, with A. Hernandez, S. Nguyen, F. Smith, and T. Takhtaganov, IMA Preprint Series #2433, 2014.

Thesis

2. Multiscale model reduction for high-contrast flow problems, PhD thesis, Texas A&M University, 2015.

1. Prediction and optimization in petroleum production, Master thesis, Fudan University, 2011.