When a hurricane threatens North Carolina, researchers use computational models to predict how the ocean waters will rise, and what areas will be flooded. Emergency managers rely on fast and accurate storm surge predictions from these models to make decisions and estimate damages during storm events. These models use unstructured, finite-element meshes to describe the…
The the 14th Annual NC State University Graduate Student Research Symposium will be held in the Jane S. McKimmon Center on Wednesday, March 20, 2019. The poster session will be from 1:30pm to 4:00pm. This year, there will be over 200 poster presentations representing research being conducted in 70 graduate programs from all colleges. …
In the first part of this work, we consider the strategy of realizing the solution of the three-dimensional linear wave equation with radial Cauchy data as a limit of radial exterior solutions satisfying vanishing Neumann and Dirichlet conditions, on the exterior of vanishing balls centered at the origin. We insist on robust arguments based on energy methods and strong convergence. Our findings show that while one…
Fixed point theory studies the extent to which fixed points of a self map of a space are intrinsic. In many mathematical settings, the existence of a solution can be rephrased in terms of the existence of a fixed point for an appropriate map, leading to applications across mathematics. Variations of fixed point problems have…
“I have traversed this bottomless night, which extinguished all light and joy of my life. I entreat you, leave the science of parallel alone”, wrote a Hungarian mathematician Farkas Bolyai to his son János, horrified at the thought that his son is attracted by the problem of parallels. János was not deterred, however, and discovered,…
Convex optimization problems appear naturally across the sciences in fields such as compressed sensing, statistics, machine learning, image processing, and inverse problems. This talk will discuss the theory, applications, and methods of proximal minimization: a wide-reaching subset of convex optimization. Advantages: you do not need your optimization problem to be differentiable (e.g. minimization problems with l-1…
(Brief Note: In this talk, we utilize Jupyter notebooks to re-create some of our published results in real-time and also build a "computational intuition" for the ideas presented. In this way, we are (mostly) transparent about all the computations involved in our work. I will email these materials to anyone interested after the presentation.) Models are useful for…
We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other)…
A Floer homology is an invariant of a closed, oriented 3-manifold Y that arises as the homology of a chain complex whose generators are either the set of solutions to a differential equation or the intersection points between Lagrangian manifold, and its differential arises as the count of solutions of a differential equation on Y…
Time-dependent hyperbolic partial differential equations can be efficiently solved using adaptive mesh refinement, with a hierarchy of finer grid patches in regions where the solution is discontinuous or rapidly varying. These patches can be adjusted every few time steps to follow propagating waves. For many problems the primary interest is in tracking waves that reach…