Talks at Computational and Applied Mathematics Seminar are regularly scheduled on Wednesday, 2:00 - 3:00 pm in Snow Hall Room 306.

Fall 2026 - Spring 2027

Wednesday, September 2, 2026:

Organizational meeting

Wednesday, September 9, 2026:

Wednesday, September 16, 2026:

Speaker: Weizhang Huang 

Regularization and preconditioning for efficient iterative solution of singular Neumann problems

Abstract:

Finite element discretizations of boundary value problems with nontrivial null spaces lead to singular linear systems, posing challenges for efficient and robust iterative solvers. This talk presents the development of a unified rank-one regularization framework for such problems, with applications to the pure Neumann Poisson equation and pure traction linear elasticity. The framework encompasses common regularization strategies, including pinning and mean-zero enforcement, and eliminates the kernel without altering the original solution. A general rank-one regularization is developed for the Poisson problem, while multiple rank-one regularizations address the multidimensional rigid-body-motion null space in elasticity. A rigorous spectral theory is established for the regularized and preconditioned systems, including explicit characterization of the lifted zero eigenvalues and sharp bounds for the perturbed nonzero spectrum. The resulting preconditioned conjugate gradient method for Poisson problems exhibits mesh-independent convergence, while the preconditioned generalized minimal residual method for elasticity is robust with respect to both mesh size and the locking parameter. Numerical experiments in two and three dimensions confirm the theoretical results and demonstrate the effectiveness of the proposed methods, including for elasticity problems with strongly heterogeneous and discontinuous material coefficients.

Wednesday, September 23, 2026:

Speaker: Jeremiah Buenger

Wednesday, September 30, 2026:

Wednesday, Octorber 7, 2026:

Speaker: Weishi Liu

Wednesday, Octorber 14, 2026:

Speaker: Sumit Kumar

Wednesday, Octorber 21, 2026:

Speaker: Jiajie Chen (University of Chicago)

Wednesday, Octorber 28, 2026:

Speaker: Jake Weaver

Wednesday, November 4, 2026:

Wednesday, November 11, 2026:

Speaker: Jon Tremblay

Wednesday, November 18, 2026:

Speaker: Xuemin Tu

Wednesday, November 25, 2026:  

Thanksgiving Break

Wednesday, December 2, 2026:

Wednesday, December 9, 2026: