My research interests broadly speaking are in numerical partial differential equations (PDEs), applications of wavelets to PDEs and data science, and numerical linear algebra. In particular, I am interested in finite difference methods and wavelet finite element methods (FEMs) for solving the Helmholtz equation, which models wave propagation in the time harmonic setting.  You can find more about my research on ResearchGate and Google Scholar.

Preprints/submitted articles:

1. X. Ou, M. Michelle, and J. Xia, A stable matrix version of the fast multipole method for the 2D Helmholtz kernel, preprint (2023), 19 pages.

2. X. Ou, M. Michelle, and J. Xia, A stable matrix version of the fast multipole method: the 2D version, preprint (2023), 24 pages.

3. B. Han and M. Michelle, Wavelet Galerkin method for an electromagnetic scattering problem. arXiv:2303.06770 (2023), 24 pages.

Accepted articles:

4.  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.

5. 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.

6. 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.

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

8. 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.

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

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

Purdue University:

Course instructor:

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

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

University of Alberta:   

Course instructor: 

• 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)

Conference on Fast Direct Solvers, Nov 4-5, 2023, West Lafayette, IN. Talk: A Stable Matrix Version of the 2D Fast Multipole Method

Geo-Mathematical Imaging Group 2023 Project Review, May 22, 2023, online. Talk: A Stable Matrix Version of the Fast Multipole Method for the 2D Helmholtz Kernel. 

Midwest Numerical Analysis Day, Apr 29, 2023, Ames, IA. Talk: Wavelet Galerkin Method for an Electromagnetic Scattering Problem.

SIAM Great Lakes Section Annual Meeting, Sept 24, 2022, Detroit, MI. Talk: Sixth Order Compact Finite Difference Method for 2D Helmholtz Equations.

Curves and Surfaces 2022, Jun 20-24, 2022, Arcachon, France. Talk: Wavelets on Intervals Derived from Arbitrary Compact Supported Biorthogonal Multiwavelets.

The Canadian Applied and Industrial Mathematics (CAIMS) Annual Meeting, Jun 12-16, 2022, online. Talk: Sharp Stability Results and Sixth Order Compact Finite Difference Scheme for the 2D Helmholtz Equation.

Applied Mathematics Institute (AMI) Seminar Series, Apr 1, 2022, Edmonton, AB. Talk: Wavelet Galerkin Method for an Electromagnetic Scattering from a Large Cavity Problem.

Applied Mathematics Institute (AMI) Seminar Series, Nov 19, 2021, Edmonton, AB. Talk: Dirac Assisted Tree Method for Helmholtz Equations with Large Wavenumbers.

Online International Conference on Computational Harmonic Analysis, Sept 13-17, 2021, online. Talk: Wavelets on Intervals Derived from Arbitrary Compact Supported Biorthogonal Multiwavelets.

PIMS-AMI Workshop on Applied Harmonic Analysis and Statistical Learning, Aug 2-3, 2018, Edmonton, AB. Talk: On a Generalized Construction of Biorthogonal Wavelets on a Bounded Interval.

Calgary Applied and Industrial Mathematical Sciences Conference, May 21-22, 2017, Calgary, AB. Talk: Boundary handling technique in wavelet-based finite element method.

ICERM Modern Applied and Computational Analysis, Jun 26-30, 2023. Providence, RI. Poster: Wavelet Galerkin Method for an Electromagnetic Scattering Problem.

Foundations of Computational Mathematics, Jun 12-21, 2023. Paris, France. Poster:  Wavelet Galerkin Method for an Electromagnetic Scattering Problem.

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