4:00 pm – 5:30 pm on every other Fridays in G5 Rolla Building, coffee and cookies are served around 3:30 in 202 Rolla Building. This seminar/colloquium series focus on a broad question in the field or discusses a specific question in a general way to facilitate a conversation between researchers (including graduate students) with different areas of expertise. The talk is 50 minutes long plus about 40 minutes for questions and discussions. If you are interested to present your work at this seminar/colloquium series, please contact Dr. Qingguo Hong via email: qingguohong@mst.edu.
Up coming speakers of Spring 2024 are as follows:
- Date: 04/19/2024, Havener Distinguished Lecture;
- Speaker: Edriss Titi, University of Cambridge;
- Title: Rigorous Analysis and Numerical Implementation of Nudging Data Assimilation Algorithms;
- Abstract: In this talk, we will introduce downscaling data assimilation algorithms for weather and climate prediction based on discrete coarse spatial scale measurements of the state variables (or only part of them, depending on the underlying model). The algorithm is based on linear nudging of the coarse spatial scales in the algorithm’s solution toward the observed measurements of the coarse spatial scales of the unknown reference solution. The algorithm’s solution can be initialized arbitrary and is shown to converge at an exponential rate toward the exact unknown reference solution. This indicates that the dynamics of the algorithm is globally stable (not chaotic) unlike the dynamics of the model that governs the unknown reference solution. Capitalizing on this fact, we will also demonstrate uniform in time error estimates of the numerical discretization of these algorithms, which makes them reliable upon implementation computationally. Furthermore, we will also present a recent improvement of this algorithm by employing nonlinear nudging, which yields super exponential convergence rate toward the unknown exact reference solution.
- Date: 05/03/2024;
- Speaker: Xiaosong Du, Missouri University of Science and Technology;
- Title: TBA;
- Abstract: TBA.
Past talks:
- Date: 02/09/2024;
- Speaker: Lijun Jiang, Missouri University of Science and Technology;
- Title: Computational Electromagnetics (CEM) for Electromagnetic Compatibility (EMC) – A Mathematical Physics in Electromagnetics;
- Abstract: Rising frequencies in both baseband and carrier signals have made IC and electronic designs a complex mixed-signal EMC/EMI (Electromagnetic Compatibility and Electromagnetic Immunity), SI/PI (Signal Integrity and Power Integrity) challenge. It has become essential for a new design to go through exclusive simulation optimizations and verifications before being taped out. Because CEM technologies generate fundamental physical insights for electromagnetic environments, CEM has become an indispensable part of today’s IC and RF EDA systems to boost the integration density in both 2D and 3D. This talk will focus on our CEM progresses for EMC/EMI/SI/PI. To solve large multiscale problems, several divide and conquer strategies have been developed based on the most efficient mathematical representations of our physical insights, such as fast multiple algorithms, equivalent principle algorithm, etc. The connection between physics and mathematics played a critical role guiding us to solve bottleneck issues such as bandwidth, efficiency, and inhomogeneity. Meanwhile, the multi-physics evaluations have to be introduced to solve practical complex designs, especially for novel 3D IC integration and material engineering. It is exciting to see that CEM has become one of the enabling technologies for today’s IC and high-speed link systems.
- Date: 02/23/2024;
- Speaker: Hongqiu Chen, University of Memphis;
- Title: How to approximate infinity;
- Abstract: It has been common practice for decades to approximate localized solutions of evolution equations set on unbounded spatial domains by solutions of associated periodic initial-value problems or Dirichlet problems. We mention especially the work of Zabusky and Kruskal in the early 1960’s, but we don’t doubt that this practice goes back further, though not much further as computers of large enough scale to handle even one-space and one-time dimensional problems were not available much earlier. Despite this method’s long history, rigorous theory with error estimates is sparse. It is our purpose to sketch theory with error estimates for such methodology here. This is done in the context of long-crested, surface water wave models. The two models we analyze are both unidirectional, long-wave models. While the theory is concretely attached to these models, one could formulate a more general theory if so desired.
- Date: 03/08/2024;
- Speaker: Shuang Wang, Shandong Jianzhu University;
- Title: Lattice Boltzmann Method from Microscopic to Macroscopic Level;
- Abstract: The Lattice Boltzmann Method (LBM) has become as a significant research area in recent years, since it grew out of the Lattice Gas Method in the late 1980s.The derivation and inherent structure of the lattice Boltzmann equation make it a powerful solver for Partial Differential Equations (PDEs). The nature of its discrete scheme lends itself to scalability on parallel computing architectures and adaptability to complex geometries boundary. This presentation will introduce the fundamentals of the Lattice Boltzmann Method, the relationship between mesoscopic distribution functions and macroscopic variables, and practical implementation techniques. We will focus on the Chapman-Enskog analysis to understand why the LBM can yield different macroscopic equations compared to standard methods. Additionally, we will introduce two applications from our research: the application in the Navier-Stokes-Darcy equation and the application in the diffusion equation with a discontinuous coefficient. These examples will demonstrate how LBM can be tailored to interface problems through basic analysis and finite different techniques.
- Date: 03/22/2024;
- Speaker: Daoru Han, Missouri University of Science and Technology;
- Title: Progresses on using Immersed Finite Element (IFE) in problems related to space exploration;
- Abstract: In this “Age of Artemis”, we are excited to work on some challenging and interesting projects related to the theme of lunar exploration and space electric propulsion. Particularly, I will present two ongoing projects: 1) a project looking into plasma charging of conducting and dielectric materials (funded by NSF); and 2) a project developing multi-scale high fidelity modeling for electrospray propulsion (funded by AFOSR). Both projects have roots dated back to early development of the novel immersed finite element (IFE) method as field solvers for problems arising from space science and engineering.
- Date: 04/05/2024;
- Speaker: Qingguo Hong, Missouri University of Science and Technology;
- Title: A New Practical Framework for the Stability Analysis of Perturbed Saddle-point Problems and Applications；
- Abstract: This talk provides a new abstract stability result for perturbed saddle-point problems which is based on a proper norm fitting. We derive the stability condition according to Bauska’s theory from a small inf-sup condition, similar to the famous Ladyzhenskaya-Bauska-Brezzi (LBB) condition, and the other standard assumptions in Brezzi’s theory under the resulting combined norm. The proposed framework allows to split the norms into proper seminorms and not only results in simpler (shorter) proofs of many stability results but also guides the construction of parameter robust norm-equivalent preconditioners. These benefits are demonstrated with several examples arising from vector Laplacian equation and different formulations of Biot’s model of consolidation.
- Date: 04/09/2024;
- Speaker: Jason Murphy, University of Oregon;
- Title: Some inverse problems for nonlinear Schrödinger equations；
- Abstract: We discuss the problem of recovering an unknown nonlinearity from the scattering behavior of solutions in the setting of nonlinear Schrödinger equations. After discussing some approaches to address the case of gauge-invariant nonlinearities, we discuss some new difficulties arising in the case of non-gauge-invariant nonlinearities. This talk will discuss some joint work with R. Killip, M. Visan, and G. Chen.