Upcoming Seminars

Pressure Robust Scheme for Incompressible Flow

Speaker: Lin Mu

In this talk, we shall introduce the recent development regarding the pressure robust finite element method (FEM) for solving incompressible flow. We shall take the weak Galerkin (WG) scheme as the example to demonstrate the proposed enhancement technique in designing the robust numerical schemes and then illustrate the extension to other finite element methods. Weak Galerkin (WG) Method is a natural extension of the classical Galerkin finite element method with advantages in many aspects. For example, due to its high structural flexibility, the weak Galerkin finite element method is well suited to most partial differential equations on the general meshing by providing the needed stability and accuracy. Due to the viscosity and pressure independence in the velocity approximation, our scheme is robust with small viscosity and/or large permeability, which tackles the crucial computational challenges in fluid simulation. Then this method will be applied to solve several other… Read more.

Using Symbolic Regression to Learn the Deterministic Dynamics of Giant Kelp Populations in a Persistent Kelp Forest

Speaker: Cheyenne Jarman

For over a century, ecologists have pursued the task of characterizing species’ population dynamics via mathematical equations derived from first principles. This pursuit has yielded foundational models, such as Verhulst’s logistic growth and the Lotka-Volterra predator-prey equations, as well as untold numbers of more detailed models that vary widely across the spectrum of mechanistic to phenomenological. But what if ecologists could look to data and machine learning for assistance? Would these same equations come to light, or would novel equation forms to describe the population and community dynamics emerge? Here, we applied a form of machine learning known as symbolic regression to the 30+ year, biannually monitored time series of kelp and urchin abundances of San Nicolas Island, CA. We thereby infer the Pareto front of human interpretable single-species equations that best describe kelp dynamics over increasing levels of equation complexity. Comparing the mathematical forms and… Read more.

"Towards Optimal Design with Maxwell's Equations and HMM" by Wei Xi Boo and "A mixed finite element approach to a flow vegetation root-soil model" by Nachuan Zhang

Speaker: Wei Xi Boo and Nachuan Zhang

Abstract for Wei Xi Boo presentation We are interested in designing materials that have unique electromagnetic properties, for example, a material that does not absorb 5G signals. Electromagnetic waves like 5G signals are governed by a set of partial differential equations called Maxwell's equations. To describe the interaction of electromagnetic waves with materials, we couple Maxwell's equations with constitutive laws like the Lorentz model and Landau–Lifshitz model. However, materials with such unique electromagnetic properties often have nano-scale structures. It poses a challenge to solve the particular solutions for Maxwell's equations numerically due to the computational cost. A numerical method for simulating Maxwell’s equations coupled with Heterogeneous Multiscale Methods for the constitutive laws will be presented. Abstract for Nachuan Zhang presentation We consider a vegetation root-soil model which couples a Richards PDE in the soil domain and saturated flow in the… Read more.

"Improving CT Reconstructions Through Regularization" by Peter Cowal and "Flash X-Ray Systems" by Gregory Detweiler

Speaker: Peter Cowal and Gregory Detweiler

Abstract of talk by Peter Cowal The problem of computed tomographic (CT) reconstruction is ill-posed and benefits from regularization, especially when scan data is noisy or incomplete. This talk will discuss historical and current regularization schemes applied to CT reconstruction, as well as their numerical implementation via the alternating direction method of multipliers (ADMM). Abstract of talk by Gregory Detweiler Conventional x-ray computed tomography (CT) attempts to image a snapshot of a static object in one instance of time. In fact, any movement of the object during the x-ray projection collection process degrades the quality of the CT reconstruction, and so attempts may be made to suppress object motion during the projection collection process, or methods for correcting for motion may be used after data collection. In contrast, in some cases one may actually desire to create a time series of CT reconstructions of an object undergoing some dynamic process. One method of… Read more.

Reduced Basis Methods for Radiative Transfer Equation

Speaker: Fengyan Li

Radiative transfer equations (RTEs), as a class of kinetic equations, are fundamental models to describe the physical phenomena of energy or particle transport through mediums that are affected by absorption, emission, and scattering processes. Deterministic simulation can provide an accurate description of the solutions, however they face many computational challenges, most prominently the need to compute the angular flux which is defined in the high dimensional phase space. Leveraging the existence of a low-rank structure in the solution manifold induced by the angular variable in the scattering dominating regime, in this work, we design and test reduced order models (ROMs) for the linear RTE model based on reduced basis methods (RBMs). As an established ROM for parametric models, RBM features a greedy algorithm in the offline (i.e. training) stage. It selects a number of representative parameter values via a greedy procedure. During the online stage, a reduced solution for a given… Read more.

"Modeling Hypothermia and Hyperthermia with an Enhanced Bioheat Equation" by Tyler Fara and "A Discrete Curvature Approach to the Drill String Bending Problem" by Arthur Mills

Speaker: Tyler Fara and Arthur Mills

Abstract of talk by Arthur Mills In the drilling of a well, the drill string may come into contact with the well bore. The curvature of the well bore determines where these contact points arise. As the drill bit turns, potential contact points are created along the wall of the well. These candidates then become realized as contact points once the bit passes threshold distances related to the surface features of these points. Beyond a certain distance these contact points become permanent in the sense that the drill string will remain in contact with these points for the entirety of the drilling operation. We will use standard techniques from the differential geometry of curves and surfaces to determine these points of contact and compute them in a MATLAB implementation. Read more.

Using Chemical Potential and Gibbs Potential to Model Vapor Transport Through Partially Saturated Porous Media and As Boundary Conditions for Nanopores or Swelling Porous Media

Speaker: Lynn Schreyer

The concept of a potential (e.g. chemical potential, Gibbs potential) in regards to modeling transport in porous media is not intuitive. Yet understanding it helps provide physical intuition and using it as a primary unknown can, in some cases, simplify the model. We will consider two examples: It is well known that water vapor transport in porous media is enhanced when the porous media is partially saturated with liquid water. Modeling vapor transport at the pore scale is traditionally done by considering pressures as the primary dependent variables, which then involves capturing contact angles and curvature. Here we show that by changing the dependent variable to relative humidity (or more generally chemical potential), a much simpler model can be developed and is conceptually easier to understand. Comparing analytical results with experimental data show that indeed, it is a reasonable model. When bulk fluid is in contact with a swelling porous media, membranes, or nanopores, it… Read more.

Applied Mathematics and Computation Seminar

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Applied Mathematics and Computation Seminar

Speaker: Madison Phelps

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Applied Mathematics and Computation Seminar

Speaker: Naren Vohra

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Applied Mathematics and Computation Seminar

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