Computational and Applied Mathematics Seminar
Fall 2021
Mondays at 4:10 p.m. (ZOOM or in-person (Room to be announced) talks)
The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.
- October 18
Title: Stable numerical scheme for Maxwell-Stefan diffusion systems
Xiaokai Huo
TU Wien
Abstract: Developing stable numerical schemes for cross diffusion systems is a challenging task. In this talk, we present a stable numerical scheme for Maxwell-Stefan diffusion systems. The scheme is conservative, energy stable and positivity-preserving. These nice properties stem from a variational structure and are proved by reformulating the finite difference scheme into an equivalent optimization problem. The solution to the scheme emerges as the minimizer of the optimization problem, and as a consequence energy stability and positivity-preserving properties are obtained. The work is done jointly with Hailiang Liu, Athanasios Tzavaras and Shuaikung Wang.
ZOOM Link:
Time: Oct 18, 2021 04:00 PM Central Time (US and Canada)
Join from a PC, Mac, iPad, iPhone or Android device:
Please click this URL to start or join. https://iastate.zoom.us/j/95892565381
Or, go to https://iastate.zoom.us/join and enter meeting ID: 958 9256 5381
Join from dial-in phone line:
Dial: +1 646 876 9923 or +1 301 715 8592
Meeting ID: 958 9256 5381
Participant ID: Shown after joining the meeting
International numbers available: https://iastate.zoom.us/u/ael0LyKQhA
- October 25
Title:
Abstract:
ZOOM Link:
- November 01
Title: A reinterpreted discrete fracture model for fracture and barrier networks
Yang Yang
Michigan Technological University
Abstract: In this talk, we construct the reinterpreted discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional Darcy’s law into the hybrid-dimensional Darcy’s law where fractures and barriers are represented as Dirac-delta functions contained in the permeability tensor and resistance tensor, respectively. This model is able to account for the influence of both highly conductive fractures and blocking barriers accurately on non-conforming meshes. The local discontinuous Galerkin (LDG) method is employed to accommodate the form of the hybrid-dimensional Darcy’s law and the nature of the pressure/flux discontinuity. The performance of the model is demonstrated by several numerical tests.
ZOOM Link:
- November 08
Title:
University
Abstract:
ZOOM Link:
- November 15
Title:
Stefan Schnake
Oak Ridge National Laboratory
Abstract:
ZOOM Link:
- November 29
Title:
University
Abstract:
ZOOM Link:
- December 06
Title:
University
Abstract:
ZOOM Link:
- September 06
Title:
University
Abstract:
- September 13
Title:
University
Abstract:
ZOOM Link:
- September 20
Time: 11am-12pm (In-Person)
Title: Weak Solutions in Nonlinear Poroelasticity withIncompressible Constituents
Boris Muha
University of Zagreb, Croatia
Abstract: We consider quasi-static poroelastic systems with incompressible con-stituents, nonlinear permeability dependent on solid dilation, and physi-cal types of boundary conditions (Dirichlet, Neumann, and mixed) for thefluid pressure, motivated by applications in biomechanics and in particulartissue perfusion. These systems fall in the category of implicit, degeneratenonlinear evolution problems. We provide a straightforward fixed pointmap strategy for proving existence of weak solutions, made possible dueto a novel result on uniqueness of weak solution to the associated linearporoelasticity system with given permeability as a function of space andtime. The uniqueness proof is based on obtaining energy estimates for allweak solutions, rather than just the constructed (as limits of approxima-tions) solutions. The results of this work provide a foundation to addressstrong solutions and uniqueness of weak solutions for the nonlinear porousmedia system.This is joint work with L. Bociu and J. Webster.
ROOM: 401 Carver
Time: 4:10pm-5pm (ZOOM)
Title: Numerical study of non-uniqueness for 2D compressible isentropic Euler equations
Yi Jiang
Southern Illinois University Edwardsville
Abstract: In this talk, I will present our recent numerical study on a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the designed initial data has an algebraic singularity in vorticity at the origin. These are different from the multi-dimensional Riemann problems widely studied in the literature. Our computations provide numerical evidence of the existence of initial value problems with multiple solutions, thus revealing a fundamental obstruction toward the well-posedness of the governing equations. The compressible Euler equations are solved using the positivity-preserving discontinuous Galerkin method.
ZOOM Link:
Join from a PC, Mac, iPad, iPhone or Android device:
Please click this URL to start or join. https://iastate.zoom.us/j/94078306977
Or, go to https://iastate.zoom.us/join and enter meeting ID: 940 7830 6977
Join from dial-in phone line:
Dial: +1 301 715 8592 or +1 312 626 6799
Meeting ID: 940 7830 6977
Participant ID: Shown after joining the meeting
International numbers available: https://iastate.zoom.us/u/avcRgRiiS
- September 27
Title: Applications of Anderson acceleration to algorithms for Newtonian and non-Newtonian fluid simulation
Leo Rebholz
Clemson University
Abstract: After reviewing recent theoretical results for Anderson acceleration (AA), we consider its application to solving incompressible Navier-Stokes equations and regularized Bingham equations. For NS, the classical penalty method is considered, which typically will only work with very small penalty (but very small penalty causes issues with iterative solvers, making it not practical for large scale use). For regularized Bingham, we consider a Picard type iteration that has trouble converging for small regularization parameter. We show that both of these methods can be cast as a fixed point iterations that fall into the AA theory framework, which allows for improved convergence rates to be proven. Moreover, numerical results reveal that with AA, the classical penalty method is very effective even with O(1) penalty parameter and regularized Bingham Picard iteration is dramatically improved and nearly robust with respect to the regularization parameter.
ROOM: 008 Carver Hall
- October 04
Title:
University
Abstract:
ZOOM Link:
- October 11
Title: Bayesian Method for Inverse Scattering Problems
Jiguang Sun
Michigan Technological University
Abstract: Inverse scattering problems arise from many important applications. In this talk, we propose a new method combining the non-iterative method and the Bayesian approach. The problem is formulated as a statistical model using the Bayes' formula. The well-posedness is proved in the sense of the Hellinger metric. The direct method is used to obtain information to construct priors, which is critical to the convergence of the MCMC algorithm. In particular, we study some inverse scattering problems with non-unique solutions and demonstrate the performance of the proposed method.
ZOOM Link: Time: Oct 11, 2021 04:00 PM Central Time (US and Canada)
Join from a PC, Mac, iPad, iPhone or Android device:
Please click this URL to start or join. https://iastate.zoom.us/j/99350375576
Or, go to https://iastate.zoom.us/join and enter meeting ID: 993 5037 5576
Join from dial-in phone line:
Dial: +1 312 626 6799 or +1 646 876 9923
Meeting ID: 993 5037 5576
Participant ID: Shown after joining the meeting
International numbers available: https://iastate.zoom.us/u/abthSiL7nw