Events
Department of Mathematics and Statistics
Texas Tech University
 | Monday
Oct. 30
|
| Algebra and Number Theory
No Seminar
|
Sequential (quickest) change-point detection is the branch of statistics concerned with the design and analysis of methods for rapid but reliable anomaly detection in "live" monitored processes. The subject's areas of application are virtually unlimited, and include quality and process control, anomaly and failure detection, surveillance and security, finance, seismology, navigation, intrusion detection, boundary tracking---to name a few. We provide a brief overview of the state-of-the-art in quickest change-point detection with particular emphasis placed on the recently proposed Generalized Shiryaev--Roberts (GSR) detection procedure (it was proposed in 2008, but the paper came out only in 2011). Notwithstanding its relatively "young age", the GSR procedure has already been shown to have strong optimality properties, not exhibited by such mainstream detection methods as the Cumulative Sum (CUSUM) "inspection scheme" and the Exponentially Weighted Moving Average (EWMA) chart. Hence the interest in the GSR procedure.
Please attend this week's Statistics seminar at 4 PM (UT-5) Monday via this Zoom link.
Meeting ID: 936 8405 5788
Passcode: 473062
We will discuss current status and progress in several challenging problems, which remain open for a long time. Also, I will suggest some new problems and conjectures, which sound appropriate for PhD projects of our graduate students.
Abstract pdf
Abstract. The discretization of the Euler equations of gas dynamics ("compressible hydrodynamics") in a moving material frame is at the heart of many multi-physics simulation codes. The Arbitrary Lagrangian-Eulerian (ALE) framework is frequently applied in these settings in the form of a Lagrange phase, where the hydrodynamics equations are solved on a moving mesh, followed by a three-part "advection phase" involving mesh optimization, field remap and multi-material zone treatment.
This talk presents a general Lagrangian framework [1] for discretization of compressible shock hydrodynamics using high-order finite elements. The use of high-order polynomial spaces to define both the mapping and the reference basis functions in the Lagrange phase leads to improved robustness and symmetry preservation properties, better representation of the mesh curvature that naturally develops with the material motion and significant reduction in mesh imprinting. We will discuss the application of the curvilinear technology to the “advection phase” of ALE, including a DG-advection approach for conservative and monotonic high-order finite element interpolation (remap), as well as to coupled physics, such as electromagnetic diffusion. We will also review progress in robust and efficient algorithms for high-order mesh optimization, matrix-free preconditioning, high-order time integration and matrix-free monotonicity, which are critical components for the successful use of high-order methods in the compressible ALE settings.
In addition to their mathematical benefits, high-order finite element discretizations are a natural fit for modern HPC hardware, because their order can be used to tune the performance, by increasing the FLOPs/bytes ratio, or to adjust the algorithm for different hardware. In this direction, we will present some of our work on scalable high-order finite element software that combines the modular finite element library MFEM [2], the high-order shock hydrodynamics code BLAST [3] and its miniapp Laghos [4], where we will demonstrate the benefits of our approach with respect to strong scaling and GPU acceleration. Finally, we will give a brief update on related efforts in the co-design Center for Efficient Exascale Discretizations (CEED) in the Exascale Computing Project (ECP) of the DOE [5].
[1] "High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics", V. Dobrev and Tz. Kolev and R. Rieben, SIAM Journal on Scientific Computing, (34) 2012, pp.B606-B641.
[2] MFEM: Modular finite element library, http://mfem.org.
[3] BLAST: High-order shock hydrodynamics, http://llnl.gov/casc/blast.
[4] Laghos: Lagrangian high-order solver, https://github.com/CEED/Laghos.
[5] Center for Efficient Exascale Discretizations, http://ceed.exascaleproject.org.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room MATH 011 (basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 968 6501 7586
* Passcode: Applied
 | Wednesday
Nov. 1
7 PM
MA 108
|
| Mathematics Education
Math Circle
Aaron Tyrrell
Department of Mathematics and Statistics, Texas Tech University
|
Math Circle Fall Poster
abstract 2 PM CDT (UT-5)