Talks at Computational and Applied Mathematics Seminar are regularly scheduled on Wednesday, 2:00 - 3:00 pm in Snow Hall Room 306.
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 (KU)
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:
Wednesday, September 30, 2026:
Wednesday, Octorber 7, 2026:
Speaker: Weishi Liu (KU)
Shear flow of nematics: multiplicity, bifurcation and stability of stationary solutions
Abstract:
In this talk, we will discuss three topics on shear flows of nematic liquid crystals via the Ericksen-Leslie models, aiming at presenting more or less a (semi-)global picture of dynamical behavior of the physical problem.
Wednesday, Octorber 14, 2026:
Speaker: Sumit Kumar (Institute for Information Sciences, KU)
An image-based, high-order finite element framework for computational simulation of cardiac ablation
Abstract:
Atrial fibrillation (AFib) is an irregular heart rhythm (i.e., an arrhythmia) that currently affects approximately 33 to 59 people worldwide. This is a serious heart rhythm disorder that often causes the heart to beat very rapidly. AFib may lead to blood clots in the heart, as well as an increased risk of stroke and heart failure. It is caused by abnormal electrical signals in the heart. Treatments for AFib focus on resetting and controlling the heartbeat and preventing blood clots and may include medication, electrical cardioversion, catheter ablation, pacemaker implantation, and maze surgery.
In this talk, I will present our image-based, high-order finite element framework for computational simulation of electro-thermal cardiac ablation. High-order calculations are used to accurately predict the electrical energy deposition and the resulting transient thermal response, thereby allowing determination of the thermal dose for the ablation procedure. There are two main components of our high-order finite element framework. The first component is the reconstruction of the cardiac myocardium anatomy from segmented MRI voxel data. This involves the extraction of a smooth reference surface using the marching cubes method. An initial low-order hexahedral mesh is generated directly on the voxels, and a pillow layer of elements is added to conform the elements to the exterior boundary. The low-order mesh is enriched with midpoints, which are then projected onto the reference surface and smoothed. This straight-sided high-order mesh is then curved, resulting in a highly accurate representation of the cardiac anatomy.
The second component is a high-order finite element solver used to simulate electrothermal cardiac ablation. The electrical field is governed by quasi-static current conservation, and the resulting Joule heating is coupled to the transient Pennes bioheat equation, which incorporates thermal conduction, blood perfusion, and convective cooling. Temperature-dependent electrical and thermal properties are also considered. The results produced by the PDE solver are in good agreement with those obtained using COMSOL. The proposed framework, therefore, provides an accurate basis for high-fidelity radiofrequency cardiac ablation simulation and may be used in patient-specific treatment planning for individuals diagnosed with atrial fibrillation.
Wednesday, Octorber 21, 2026:
Speaker: Jiajie Chen (University of Chicago)
Smooth imploding singularities in compressible Euler and related equations
Abstract:
In this talk, we will discuss recent developments in constructing smooth self-similar imploding singularities in the compressible Euler equations and establishing their nonlinear stability. We will also explain how certain Euler imploding singularities can be lifted or perturbed to construct vorticity blowup in compressible Euler, as well as singularities in kinetic equations and the complex-valued defocusing nonlinear wave equation.
Wednesday, Octorber 28, 2026:
Wednesday, November 4, 2026:
Speaker: Jeremiah Buenger (KU)
Wednesday, November 11, 2026:
Speaker: Jon Tremblay (KU)
Wednesday, November 18, 2026:
Speaker: Xuemin Tu (KU)
Wednesday, November 25, 2026:
Thanksgiving Break
Wednesday, December 2, 2026:
Wednesday, December 9, 2026: