Search Research Symposium Abstracts

Fully implicit P0-based schemes for PDEs modeling phase change*

We present our recent results on numerical schemes for evolution PDE models involving multivalued maximal monotone graphs. The unifying scheme of our work is fully implicit treatment of the nonlinearity and the use of lowest order spatial discretizations appropriate for the low regularity of the solutions and free boundaries, typical for the solutions of, [Read More...]

Presenter: Malgorzata Peszynska, Oregon State University
Authors: Azhar Alhammali, Lisa Bigler, Choah Shin, and Naren Vohra
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 10:15 am

equilibrate flux recovery for cut finite element method

We aim to recover locally conservative and $H(div)$ conforming fluxes for the linear Cut Finite Element Solution with Nitsche's method for Poisson problems with Dirichlet boundary condition. The computation of the conservative flux in the Raviart-Thomas space is completely local and does not require to solve any mixed problem. The $L^2$-norm of the [Read More...]

Presenter: Cuiyu He, University of Texas Rio Grande Valley
Authors: Cuiyu He and Daniela Capatina
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 10:40 am

Optimized Schwarz waveform relaxation and mixed hybrid finite element methods for transport problems in porous media

This talk is concerned with numerical schemes for linear advection-diffusion problems, in which different time steps (with no CFL restrictions) can be used in different parts of the domain. A mixed formulation is considered where the flux variable represents the total flux (i.e., both diffusive and advective flux, instead of only diffusive flux as in [Read More...]

Presenter: T.T. Phuong Hoang, Auburn University
Authors: Thi-Thao-Phuong Hoang
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 11:05 am

On the Stochastic Approximation Method for a Parameter Identification Problem in a PDE

This work focuses on the inverse problem of identifying a stiffness parameter in a stochastic linear elasticity system that models displacements in human tissues under prescribed forces. An optimization approach for the problem is considered and we discuss a projected-gradient type stochastic approximation method used for the [Read More...]

Presenter: Baasansuren Jadamba, Rochester Institute of Technology
Authors: Rachel Hawks and Baasansuren Jadamba
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 11:30 am

Applications of K-Spectral Sets

The value of K from a K-spectral set is used to bound any analytic function of a matrix. We use results in [M. Crouzeix and A. Greenbaum, Spectral sets: numerical range and beyond, SIAM Jour. Matrix Anal. Appl., 40 (2019), pp. 1087-1101] to derive a variety of K-spectral sets and show how they can be used in some applications. We compare the K values derived [Read More...]

Presenter: Natalie Wellen, University of Washington
Authors: Anne Greenbaum and Natalie Wellen
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 3:30 pm

Computing Committors in Collective Variables Via Mahalanobis Diffusion Maps*

Many interesting problems concerned with rare event quantification arise in chemical physics. A typical problem is finding reaction channels and transition rates for conformal changes in a biomolecule. To reduce the dimensionality and make the description of transition processes more comprehensible, often a set of physically motivated collective variables [Read More...]

Presenter: Maria Cameron, University of Maryland, College Park
Authors: Luke Evans, Maria Cameron, Pratyush Tiwary
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 3:55 pm

Quantum algorithms for Hamiltonian simulation with unbounded operators

Recent years have witnessed tremendous progress in developing and analyzing quantum algorithms for quantum dynamics simulation of bounded operators (Hamiltonian simulation). However, many scientific and engineering problems require the efficient treatment of unbounded operators, which frequently arise due to the discretization of differential operators. Such [Read More...]

Presenter: Di Fang, University of California, Berkeley
Authors: Dong An, Di Fang, Lin Lin
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 4:20 pm

Numerical Optimal Transport on the Sphere

The problem of optimal transportation, which involves finding the most cost-efficient mapping between two measures, arises in many different applications. We consider the special case of optimal transport on the sphere, which is of particular importance in the design of optical systems and in mesh generation. This problem can be formulated as a fully [Read More...]

Presenter: Brittany Froese Hamfeldt, New Jersey Institute of Technology
Symposium Year: 2022
Session: Women in Numerical Analysis and Scientific Computing
Presentation Time: June 17, 2022; 4:45 pm