My research interests lie broadly in the fields of applied mathematics and data science, including numerical analysis, scientific computing and statistical learning. Some of the research projects I've worked on, and continue to be interested in, are:
Statistical learning, variable selection and penalized regression, including LASSO, elastic net, SCAD, MCP, etc;
Exploring low-rank structures, compressed sensing techniques and randomized algorithms in kinetic theory;
Fast structured spectral methods, including fast structured Galerkin methods, fast structured collocation methods and fast structured Jacobi transforms;
Efficient spectral sparse grid methods for high dimensional problems, with applications in electronic Schrödinger equations;
Extended spectral methods, including Müntz-Galerkin Methods and enriched spectral methods, for the problems with low regularity and corner singularities;
Two-level spectral methods for nonlinear elliptic equations with multiple solutions;
Rational spectral collocation methods for singularly perturbed problems with thin boundary layers.
Introducing Folded Concave Penalized Regression: New Variable Selection Methods in the REGSELECT Procedure in SAS Viya, SAS Technical Papers.
A Survey of Methods in Variable Selection and Penalized Regression, Proceedings of the SAS Global Forum 2020 Conference. [Talk Video]
Jingwei Hu, Jie Shen and Yingwi Wang, A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions, Kinetic and Related Models, 2020, 13(4), pp 677-702.
Wenting Shao, Shi Sun and Yingwei Wang, An economical cascadic multigrid method for the weak Galerkin finite element approximation of second order elliptic problems, Journal of Computational and Applied Mathematics, 2019, 362, pp 341-353.
Jie Shen, Yingwei Wang, Jianlin Xia, Fast structured Jacobi-Jacobi transforms, Mathematics of Computation, 2019, 88(318), pp 1743-1772.
Yingwei Wang, Wenrui Hao, Guang Lin, Two-level spectral methods for nonlinear differential equations with multiple solutions, SIAM Journal on Scientific Computing, 2018, 40(4), pp B1180–B1205, CORRECTION.
Jie Shen, Yingwei Wang, Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems, SIAM Journal on Scientific Computing, 2016, 38(4), pp A2357–A2381.
Jie Shen, Yingwei Wang, Jianlin Xia, Fast structured direct spectral methods for differential equations with variable coefficients, I. The one-dimensional case, SIAM Journal on Scientific Computing, 2016, 38(1), pp A28–A54. CORRECTION
Suqin Chen, Yingwei Wang, A rational spectral collocation method for third-order singularly perturbed problems, Journal of Computational and Applied Mathematics, 2016, 307, pp 93-105.
Jie Shen, Yingwei Wang, Haijun Yu, Efficient spectral-element methods for the electronic Schrödinger equation, Sparse Grids and Applications - Stuttgart 2014 (Volume 109 of the series Lecture Notes in Computational Science and Engineering), 2016, pp 265-289.
Suqin Chen, Yingwei Wang, Xionghua Wu, Rational spectral collocation method for a coupled system of singularly perturbed boundary value problems, Journal of Computational Mathematics, 2011, 29(4), pp 458-473.
Yingwei Wang, Suqin Chen, Xionghua Wu, A rational spectral collocation method for solving a class of parameterized singular perturbation problems, Journal of Computational and Applied Mathematics, 2010, 233(10), pp 2652-2660.
Yingwei Wang, Suqin Chen, Xionghua Wu, The exponential time differencing and rational spectral collocation method for the singularly perturbed Burgers-Huxley problem, Mathematica Numerica Sinica, 2010, 32(2), pp 171-182, (in Chinese).
Suqin Chen, Xionghua Wu, Yingwei Wang, Weibin Kong, The Laplace transform method for Burgers' equation, International Journal for Numerical Methods in Fluids, 2010, 63(9), pp 1060-1076.
Yu Huang, Chenglong Xu, Yingwei Wang, Spectral method using Hermite functions for semilinear wave equations with strong damping, The International Conference on Information Science and Engineering, 2009, pp 401-403.
Suqin Chen, Xionghua Wu, Yingwei Wang, Weibin Kong, High accuracy time and space transform method for advection-diffusion equation in an unbounded domain, International Journal for Numerical Methods in Fluids, 2008, 58(11), pp 1287-1298.
Fast Structured Spectral Methods, my Ph.D. Dissertation, 2017.
Estimation of bathymetry in environmental flows, Technical report of the Twenty-first Mathematical and Statistical Modeling Workshop for Graduate Students, pages 40-63 in the pdf file, 2015.
Rational Spectral Collocation Methods for Singularly Perturbed Problems, my Masters’ Thesis (in Chinese), 2010.
Spline Trefftz Method for Convection-Diffusion Equation, the technical report based on my undergraduate dissertation, 2007.
Introduction to Muntz Polynomial Approximation,
--- Numerical Analysis Seminar, NCSU, March 27, 2018.
Introduction to Muntz Polynomial Approximation,
--- Analysis and Applied Mathematics Seminar, University of Illinois at Chicago, March 5, 2018.
Introduction to Muntz Polynomial Approximation,
--- Applied and Computational Mathematics Seminar, University of Wisconsin-Madison, Oct. 13, 2017.
Efficient Spectral Methods for Electronic Schrodinger Equation,
--- SIAM Conference on Computational Science and Engineering, Hilton Atlanta, GA, Feb 27- March 3, 2017.
--- Joint Mathematics Meetings, Hyatt Regency Atlanta, GA, Jan 4-7, 2017.
Two-level spectral methods for nonlinear differential equations with multiple solutions, at AMS Special Sessions on Nonlinear Systems and Applications.
Müntz-Galerkin methods and applications to mixed Dirichlet-Neumann boundary value problems, at AMS Special Sessions on Advances in Numerical Analysis for Partial Differential Equations.
Math Graduate Research Day, Purdue University, November 19, 2016.
Fast Structured Spectral Methods [slides],
--- Workshop on Fast Direct Solvers , Purdue University, November 12-13, 2016.
Müntz-Galerkin Methods And Applications To Mixed Dirichlet-Neumann Boundary Value Problems,
--- The 2nd Annual Meeting of SIAM Central States Section, University of Arkansas at Little Rock, September 30 - October 2, 2016.
Introduction to Müntz polynomials and their application to numerical solutions of differential equations,
--- Student Colloquium, REC 307, Purdue University, September 28, 2016.
Fast Structured Spectral Methods,
--- SIAM Great Lakes Spring Meeting, University of Michigan at Dearborn, MI, April 30, 2016.
Fast Structured Jacobi-Jacobi Transform,
--- Fourteenth Copper Mountain Conference on Iterative Methods, Copper Mountain, CO, March 20-25, 2016.
Fast Structured Spectral Methods,
--- CS&E/CLS Seminar, Feb. 17, 2016, LWSN 3102, Purdue Univeristy.
Fast Structured Spectral Methods,
--- AMS Special Session on The Mathematics of Computation, Joint Mathematics Meetings, Washington State Convention Center, Seattle, WA, January 6-9, 2016.
Fast Structured Spectral Methods,
--- Special Session on Frontiers in Computational Mathematics, AMS Central Fall Sectional Meeting, Loyola University Chicago, IL, October 2-4, 2015.
Fast Structured Spectral Methods,
--- Midwest Numerical Analysis Day, Wright State University, Dayton, OH, April 25, 2015.
Fast Structured Spectral Methods,
---The 1st Annual Meeting of SIAM Central States Section, Missouri University of Science and Technology, Rolla, MO, April 11-12, 2015.
Efficient spectral methods for electronic structure calculations,
--- 3rd Workshop on Sparse Grids and Applications, University of Stuttgart, Stuttgart, Germany, September 1-5, 2014.
Fast Structured Direct Spectral Methods for Differential Equations with Variable Coefficients,
---2014 SIAM Annual Meeting ( Section: Numerical Methods in PDE III ), The Palmer House, Chicago, IL, July 7-11, 2014.
Fast structured spectral methods,
--- International Conference on Spectral and High-order Method, Salt Lake City, UT, June 23-27,2014.
Fast structured spectral methods,
--- Department of Mathematics, Tongji University, Shanghai, China, May 20, 2014.
Sparse grid methods for high-dimensional problems,
--- Graduate Research Day 2014, LILY 3118, Purdue University, April 12, 2014.
Introduction to Electronic Schrödinger Equation,
--- Student Colloquium, REC 309, Purdue University, April 3, 2014.
Efficient spectral Galerkin methods for electronic structure calculations,
--- Mathematical and Numerical Methods for Complex Quantum Systems, University of Illinois at Chicago, IL, March 26-30, 2014.
The Müntz-Gelerkin method for the mixed Dirichlet-Neumann boundary value problem,
--- Graduate Research Day 2013, Purdue University, April 13, 2013.
Spectral-Galerkin Method based on Müntz Polynomials,
--- 5th Computational Science and Engineering Student Conference (CSESC 2013), Purdue University, April 5, 2013.
Hypocoercivity and Sensitivity Analysis in Kinetic Equations and Uncertainty Quantification, University of Wisconsin-Madison, October 2 — 5, 2017.
The 3rd Annual Meeting of SIAM Central States Section, Colorado State University, Fort Collins, CO, September 29 — October 1, 2017.
79/80th Midwest PDE Seminar, University of Illinois at Chicago, September 14-17, 2017.
International Conference on Current Trends and Challenges in Numerical Solution of Partial Differential Equations, Purdue University, July 7-8, 2017.
SIAM Great Lakes Section 2017 Spring Meeting, Oakland University, Rochester, MI, April 29, 2017.
Midwest Algebraic Geometry Graduate Conference, University of Illinois at Chicago, April 21-23, 2017.
AMS Spring Central Sectional Meeting, Indiana University, Bloomington, IN, April 1-2, 2017.
New Trends in Quantum and Classical Kinetic Equations and Related PDEs, University of Wisconsin-Madison, Oct 6 - 8, 2016.
MSRI-LBNL Summer School on Electronic Structure Theory, UC Berkeley, CA, July 18 - 29, 2016.
Summer School on Quantum and Kinetic Theory for Complex Systems, UC Santa Barbara, CA, June 13 - 17, 2016.
The 35th Southeastern Atlantic Regional Conference on Differential Equations, The University of North Carolina at Greensboro, NC, Oct 10-11, 2015.
Industrial Math/Stat Modeling Workshop for Graduate Students, North Carolina State University, Raleigh, NC, July 12-22, 2015.
PETSc: Tutorial and Workshop, Theory and Computing Sciences Conference Center, Argonne National Laboratory, IL, June 15-18, 2015.
International Conference on Numerical Partial Differential Equations and Their Applications, Wuhan University, Wuhan, China, May 25-29, 2015.
Advanced Numerical Methods in the Mathematical Sciences, Texas A&M University, College Station, TX, May 4–7, 2015.
7th Computational Science and Engineering Student Conference (CSESC 2015), Purdue University, March 27, 2015.
ICERM Semester Program: High-Dimensional Approximation, Brown University, Providence, Rhode Island, September 8 - December 5, 2014.
International Workshop on the Finite Element/Spectral Methods, Shanghai Normal University, Shanghai, China, May 16-18, 2014.
Forum on Scientific and Engineering Computing, Institute of Computational Mathematics Chinese Academy of Sciences, Beijing, China, June 3-4, 2013.
68th Midwest Partial Differential Equations Seminar, University of Notre Dame, IN, November 4-6, 2011.
Midwest Numerical Analysis Day, Purdue University, May 7-8, 2011.
International Conference on Advances in Partial Differential Equations and Their Applications , Fudan University, Shanghai, China, May 31-June 4, 2010.
International Summer School on Discontinuous Galerkin Finite Element Methods and Spectral Methods for Scientific Computing, Institute of Computational Mathematics Chinese Academy of Sciences, Beijing, China, August 3-15, 2009.