My research interests broadly speaking are in numerical methods for time harmonic wave propagation and elliptic interface problems, wavelet methods for numerical PDEs and data science, numerical linear algebra, and scientific machine learning. You can find more about my research on Google Scholar.

Preprints/submitted articles:

1. B. Han and M. Michelle, Wavelet-based Galerkin Scheme with Arbitrarily High-Order Convergence for 1D Elliptic Interface Problems, arXiv:2603.21394 (2026).

2. Q, Feng, B. Han, M. Michelle, and J. Sim, High-order, compact, and symmetric finite difference methods for a d-dimensional hypercube, arXiv:2510.03927 (2025).

3. A. Maiti, M. Michelle, and H. Yang, Optimal neural network approximation for high-dimensional continuous functions. arXiv:2409.02363 (2024).

4. B. Han and M. Michelle, Galerkin scheme using biorthogonal wavelets on intervals for elliptic interface problems, arXiv:2410.16596 (2024).

Accepted articles:

5. M. Michelle, X. Ou, and J. Xia, A stable matrix version of the wideband fast multipole method for the 2D Helmholtz kernel. SIAM Journal on Scientific Computing 48 (2026), no. 3, A1399-A1429.

6. B. Han and M. Michelle, Wavelet Galerkin method for an electromagnetic scattering problem. Journal of Scientific Computing (2025), 104:19, 1-40.

7. X. Ou, M. Michelle, and J. Xia, A stable matrix version of the fast multipole method: the 2D version. SIAM Journal on Matrix Analysis and Applications 46 (2025), no. 1, 530-560.

8. Q. Feng, B. Han, and M. Michelle, Sixth order compact finite difference method for 2D Helmholtz equations with singular sources and reduced pollution effect. Communications in Computational Physics 34 (2023), 672-712.

9. B. Han and M. Michelle, Sharp wavenumber-explicit stability bounds for 2D Helmholtz equations. SIAM Journal on Numerical Analysis 60 (2022), no. 4, 1985-2013.

10. B. Han, M. Michelle, and Y. S. Wong, Dirac assisted tree method for 1D heterogeneous Helmholtz equations with arbitrary variable wave numbers. Computers and Mathematics with Applications 97 (2021), 416-438.

11. B. Han and M. Michelle, Wavelets on intervals derived from arbitrary compactly supported biorthogonal multiwavelets. Applied and Computational Harmonic Analysis 53 (2021), 270-331.

12. B. Han and M. Michelle, Derivative-orthogonal Riesz wavelets in Sobolev spaces with applications to differential equations. Applied and Computational Harmonic Analysis 47 (2019), no. 3, 759-794.

13. B. Han and M. Michelle, Construction of wavelets and framelets on a bounded interval. Analysis and Applications 16 (2018), no. 6, 807-849.

14. E. Braverman and M. Michelle. Stability of time-dependent dynamic monopoly with concentrated and distributed delays. Dynamic Systems and Applications 26 (2017) 347-366.

Conference papers:

15. Q. Li, M. Michelle, B. Han, and X. Zhuang, Wavelets on intervals for image denoising, 2025 International Conference on Sampling Theory and Applications (SAMPTA), Vienna, Austria.

16. B. Han, M. Michelle, and Y. S. Wong, Wavelet-based methods for numerical solutions of differential equations. Proceedings of the 8th International Congress of Chinese Mathematicians (2019).

University of Alberta:   

Course instructor: 

• MATH 201 (Differential Equations) Winter 2026

• MATH 336 (Honours Ordinary Differential Equations) Winter 2026

• MATH 134 (Calculus for Life Sciences I) Fall 2021

Lab Instructor (2015-2021):

• STAT 151 (Introduction to Applied Statistics I)

• STAT 235 (Introductory Statistics for Engineering)

• STAT 252 (Introduction to  Applied Statistics II)

Purdue University:

Course instructor:

• MA 303 (Differential Equations and Partial Differential Equations for Engineering and the Sciences) Fall 2023, Spring 2024, Fall 2024, Spring 2025

• MA 266 (Ordinary Differential Equations) Fall 2022, Spring 2023

• 2026 SIAM Annual Meeting, July 6-10, 2026, Cleveland, OH, USA. 

• Scientific Computing and Differential Equations SciCADE 2026, June 29-July 3, 2026, Edinburgh, UK.

• The 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation, June 22-26, 2026, Montreal, QC, Canada.

• Innovative Solutions for Interface Problems using Adaptive Methods and Machine Learning 26w5559, May 24-29, 2026, Hangzhou, China.

• The 9th International Conference on Computational Harmonic Analysis 2026 at Vanderbilt University, May 18-22, 2026, Nashville, TN, USA. 

• Department of Mathematical and Statistical Sciences Colloquium at the University of Alberta, Jan 16, 2026, Edmonton, AB, Canada. 

• Applied Math Seminar at the University of Arkansas, Nov 4, 2025, online. 

• The Third Joint SIAM/CAIMS Annual Meetings, Jul 28-Aug 1, 2025, Montreal, QC, Canada. 

• International Undergraduate Summer Enrichment Program in Mathematics, Jul 22, 2025, Edmonton, AB, Canada. 

• 29th International Conference on Domain Decomposition Methods, Jun 23-27, 2025, Milan, Italy. 

• Department of Mathematics and Statistics Colloquium at Binghamton University, Feb 7, 2025, Binghamton, NY, USA. 

• Department of Mathematics and Statistics Colloquium at the University of Vermont, Feb 3, 2025, Burlington, VT, USA. 

• Department of Mathematics Colloquium at Augusta University, Jan 27, 2025, Augusta, GA, USA.

• Department of Mathematics Colloquium at Baylor University, Jan 23, 2025, Waco, TX, USA. 

• Department of Mathematics and Statistics Colloquium at the University of Maine, Jan 21, 2025, Orono, ME, USA.

• Department of Mathematical and Statistical Sciences Colloquium at the University of Alberta, Jan 10, 2025, Edmonton, AB, Canada. 

• Department of Mathematics Colloquium at California State University Fullerton, Dec 6, 2024, Fullerton, CA, USA. 

• SIAM Conference on Applied Linear Algebra, May 13-17, 2024. Paris, France.

• Department of Mathematics Colloquium at Embry-Riddle Aeronautical University, Feb 12, 2024, Daytona Beach, FL, USA.

• Department of Mathematics Colloquium at Syracuse University, Jan 29, 2024, Syracuse, NY, USA. 

• Department of Mathematics and Computer Science Colloquium at Santa Clara University, Jan 18, 2024, Santa Clara, CA, USA. 

• Conference on Fast Direct Solvers, Nov 4-5, 2023, West Lafayette, IN. 

• Geo-Mathematical Imaging Group 2023 Project Review, May 22, 2023, online. 

• Midwest Numerical Analysis Day, Apr 29, 2023, Ames, IA. 

• SIAM Great Lakes Section Annual Meeting, Sept 24, 2022, Detroit, MI. 

• Curves and Surfaces 2022, Jun 20-24, 2022, Arcachon, France. 

• The Canadian Applied and Industrial Mathematics (CAIMS) Annual Meeting, Jun 12-16, 2022, online. 

• Applied Mathematics Institute (AMI) Seminar Series, Apr 1, 2022, Edmonton, AB. 

• Applied Mathematics Institute (AMI) Seminar Series, Nov 19, 2021, Edmonton, AB. 

• Online International Conference on Computational Harmonic Analysis, Sept 13-17, 2021, online. 

• PIMS-AMI Workshop on Applied Harmonic Analysis and Statistical Learning, Aug 2-3, 2018, Edmonton, AB. 

• Calgary Applied and Industrial Mathematical Sciences Conference, May 21-22, 2017, Calgary, AB. 

NSF Computational Mathematics PI Meeting, Jul 15-17, 2024. Seattle, WA. 

ICERM Modern Applied and Computational Analysis, Jun 26-30, 2023. Providence, RI. 

Foundations of Computational Mathematics, Jun 12-21, 2023. Paris, France. 

CBMS Conference: Deep Learning and Numerical PDEs, Jun 19-23, 2023. Baltimore, MD.