A Special Session in Computational Mathematics at the
AMS Central Section Meeting
September 14-15, University of Texas, San Antonio, San Antonio 2024
AMS Central Section Meeting
September 14-15, University of Texas, San Antonio, San Antonio 2024
Session #SS25:
Advances in Mathematical and Numerical Analysis of Partial Differential Equations for Application-Oriented Computations
Organizers:
- Abdul Khaliq (Middle Tennessee State University, abdul.khaliq@mtsu.edu)
- Jaeun Ku (Oklahoma State University, jku@okstate.edu)
- Qin Sheng (Baylor University, Qin_Sheng@baylor.edu)
- Bruce Wade (University of Louisiana at Lafayette, bruce.wade@louisiana.edu)
- Xiang-Sheng Wang (University of Louisiana at Lafayette, xiangsheng.wang@louisiana.edu)
- Yangwen Zhang (University of Louisiana at Lafayette, yangwen.zhang@louisiana.edu)
Abstract:
The latest advances in computational analysis for partial differential equations with realistic applications are the focus in this mini-session. We bring together investigators from various backgrounds to present and discuss the cutting-edge theory and methods of application-oriented computations for PDE. The latest machine learning challenges in these fields will also be explored. This mini-session serves as a platform to exchange new ideas, extend academic networks, and incubate future cooperation. Graduate students are encouraged to participate in the special event.
SS25 Informational Flyer: AMS FALL 2024 Central Sectional Meeting: SS25.
Important Deadlines
Meeting & Hotel Reservations: August 23, 2024
- Abstract Submission for acceptance into this Special Session, SS25: May 31, 2024
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- Speakers must be registered in order to submit an abstract, and all speakers must submit abstracts by the deadline. Talks without abstracts submitted by the deadline cannot be scheduled. Talks are expected to be about 20-minutes with 10 minutes for questions and transitions between talks.
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- Abstract Submission to the AMS once accepted in SS25: July 23, 2024
- Website for AMS Registration
Instructions for Submission
- Please email your proposed title & abstract to any of the organizers by May 31, 2024. If accepted for this Special Session, you will then submit the talk to the AMS sectional organizers. Talks are 20 minutes in length. It is possible, if the schedule permits, to present two successive 20 minute blocks.
Special Session SS25 Confirmed Speakers (as of April 10, 2024)
This list has no particular order until a future date.- Time: Not specified
Title: Comparison of the Spectral Method and the Continuous Interior Penalty Finite Element Method for the Phase Field Crystal Equation
Presenter: Natasha Sharma
Affiliation: University of Texas at El Paso
Abstract: In this talk, we present two recently developed numerical schemes for the phase field crystal (PFC) equation and report on our findings based on a series of performance tests in terms of efficiency, accuracy, and ease of implementation. We focus our comparative study on formulations that originate from spectral methods and finite element methods. Numerical results will be presented and discussed. In addition, the dynamics of the physical processes captured by the PFC will be presented to illustrate the robustness of the proposed methods for modeling different applications such as crystal growth in a supercooled liquid and crack propagation in a ductile material.
- Time: Not specified
Title: Efficient Krylov-Based Exponential Time Differencing Method
Presenter: Bruce Wade
Affiliation: University of Louisiana at Lafayette
Abstract: We discuss a Krylov subspace approximation-based locally extrapolated exponential time differencing method for nonlinear advection-diffusion-reaction systems and compare its performance to established schemes.
- Time: Not specified
Title: An Exploration of a Nonconventional Way of Operator Splitting Methods for Solving Diffusion Equations
Presenter: Qin Sheng
Affiliation: Baylor University
Abstract: This talk concerns an application of an operator decomposition formula in Lagrangian optimizations for solving linear and semi-linear diffusion equations. It has revealed in our preliminary investigations that the nonconventional splitting configuration may not only provides an effective enhancement to conventional splitting methods, but also introduces a flexible way for constructing multi-parameter operator splitting strategies in many cutting-edge applications. Simulation experiments will be given.
- Time: Not specified
Title: Integral Equation Method for the 1D Steady State Poisson-Nernst-Planck Equations
Presenter: Robert Krasny
Affiliation: University of Michigan
Abstract: An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations describing charge transport through transmembrane ion channels. The differential equations are cast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by midpoint and trapezoid rules and the resulting algebraic equations are solved by Gummel iteration. Numerical tests demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. Results for a multi-domain Potassium ion channel model are in good agreement with published results. This is joint work with Zhen Chao (Western Washington University) and Weihua Geng (Southern Methodist University).
- Time: Not specified
Title: Modeling Analytical Ultracentrifugation Experiments with an Adaptive Space-Time Finite Volume Solution of the Lamm Equation for Non-Ideal Solute and Solvent Conditions.
Presenter: Weiming Cao
Affiliation: University of Texas at San Anotonio
Abstract: We present a solution of the Lamm equation based on the adaptive space-time finite volume method (ASTFVM) for modeling solutes displaying variable sedimentation and diffusion coefficients. Such conditions are observed when sedimenting molecules are measured at high concentration where they exhibit concentration-dependent nonideality or when co-sedimenting solutes create a density and viscosity gradient during the experiment. Variable sedimentation and diffusion coefficients are also observed in experiments performed in compressible solvents, where a density and viscosity gradient develops during rotor acceleration. The ASTFVM method provides a robust, accurate and efficient solution to these cases and has been integrated into the optimization methods in the UltraScan software for analytical ultracentrifugation analysis in biophysics and biochemistry.
- Time: Not specified
Title: A Fourth-Order Exponential Time Differencing Scheme with a Real and Distinct Poles Rational Approximation for Solving Nonlinear Systems of Reaction Diffusion Equations.
Presenter: Wisdom K. Attipoe
Affiliation: Clarkson University
Abstract: Reaction-diffusion systems are mathematical models that describe the spatiotemporal dynamics of chemical substances as they diffuse and react. Variety of time discretization schemes have been developed to solve the stiff ODE system resulting from the spatial-discretization of the PDE. The quest to develop more efficient and accurate schemes to handle very stiff and non-smooth problems is ever increasing. In this work, we develop a fourth-order, L-stable, parallelizable exponential time differencing scheme (ETD) by approximating the matrix exponentials in the class of ETD Runge-Kutta schemes with a fourth-order non- Padé rational function having real distinct poles (RDP). A variety of non-linear reaction-diffusion systems having Dirichlet, Neumann and periodic boundary conditions are used to empirically validate the order of convergence of the scheme and compare its performance with existing fourth order schemes.
- Time: Not specified
Title: Euler Maruyama Numerical Approximation of Stochastic Differential Equations with Continuously Distributed Delay.
Presenter: Roshini Samanthi Gallage
Affiliation: University of Oklahoma
Abstract: In this talk, processes with continuously distributed delay which depend on weighted averages of past states over the entire time lag interval are discussed. We give generalized Khasminskii-type conditions which along with local Lipschitz conditions are sufficient to guarantee the existence of a unique solution of certain n-dimensional nonlinear stochastic delay differential equations (SDDEs) with continuously distributed delay. We give conditions under which Euler-Maruyama numerical approximations of such nonlinear SDDEs converge in probability to their exact solutions. Further, the Euler Maruyama numerical approximation results of some SDDE models are discussed to analyze the numerical approximation error values and trajectory behaviors. Joint work with Dr. Harry Randolph Hughes
- Time: Not specified
Title: A Fourth-Order Exponential Time Differencing Scheme with Dimensional Splitting for Solving Semilinear Parabolic PDE.
Presenter: Emmanuel O. Asante-Asamani
Affiliation: Clarkson University
Abstract: A fourth-order exponential time differencing (ETD) Runge-Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction-diffusion equations (RDE). By approximating the matrix exponential in the scheme with the A-acceptable Padé (2,2) rational function, the resulting scheme (ETDRK4P22-IF) is verified empirically to be fourth-order accurate for several RDE. The scheme is shown to be more efficient than competing fourth-order ETD and IMEX schemes, achieving up to 20X speed-up in CPU time. Inclusion of up to three pre-smoothing steps of a lower order L-stable scheme facilitates efficient damping of spurious oscillations arising from problems with non-smooth initial/boundary conditions.
- Time: Not specified
Title: Numerical Experiments Using the Barycentric Lagrange Treecode to Compute Correlated Random Displacements for Brownian Dynamics Simulations
Presenter: Lei Wang
Affiliation: University of Wisconsin- Milwaukee
Abstract: To account for hydrodynamic interactions among solvated molecules, Brownian dynamics simulations require correlated random displacements ${\bf g} = D^{1/2}{\bf z}$, where $D$ is the $3N \times 3N$ Rotne-Prager-Yamakawa diffusion tensor for a system of $N$ particles and ${\bf z}$ is a standard normal random vector. The Spectral Lanczos Decomposition Method (SLDM) computes a sequence of Krylov subspace approximations ${\bf g}_k\,{\to}\,{\bf g}$, but each step requires a dense matrix-vector product $D{\bf q}$ with a Lanczos vector ${\bf q}$, and the $O(N^2)$ cost of computing the product by direct summation (DS) is an obstacle for large-scale simulations. This work employs the barycentric Lagrange treecode (BLTC) to reduce the cost of the matrix-vector product to $O(N\log N)$ while introducing a controllable approximation error. Numerical experiments compare the performance of SLDM-DS and SLDM-BLTC with particular attention on the effect of the BLTC approximation error.
- Time: Not specified
Title: TBA
Presenter: Harish Bhatt
Affiliation Utah Valley University
Abstract: TBA.
- Time: Not specified
Title: TBA
Presenter: Eduardo Servin Torres
Affiliation: Baylor University
Abstract: TBA.
- Time: Not specified
Title: TBA
Presenter: Julienne Kabre
Affiliation: Nova Southeastern University
Abstract: TBA.
- Time: Not specified
Title: TBA
Presenter: Lei Wang
Affiliation: University of Wisconsin- Milwaukee
Abstract: TBA.
- Time: Not specified
Title: TBA
Presenter: Rajan Adhikari
Affiliation: Oklahoma State University
Abstract: TBA.
- Time: Not specified
Title: TBA
Presenter: Jauen Ku
Affiliation: Oklahoma State University
Abstract: TBA.
Contact
Primary email address: bruce.wade@louisiana.edu
UL Lafayette main contact:
Dr. Bruce Wade, Professor & Department Head
215 Maxim Doucet Hall
337.482.5172 or 337.482.5173
bruce.wade@louisiana.edu
Mailing address:
Department of Mathematics
P.O. Box 43568
University of Louisiana at Lafayette
Lafayette, LA 70504-3568
