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Department of Mathematics

Upcoming Events

Branwen Purdy at her stall during OMSI meet-a-scientist day.

Branwen Purdy prepares hands-on activities for kids at the OMSI Meet-A-Scientist Day in Portland, to share hands-on learning experiences about her research in topological data analysis.

Join us for these events hosted by the Department of Mathematics, including colloquia, seminars, graduate student defenses and outreach, or of interest to Mathematicians hosted by other groups on campus.

Access our archive of events

One-ended halfspaces in group splittings

Kidder Hall 237
Geometry and Topology Seminar

Speaker: Samuel Shepherd

I will introduce the notion of halfspaces in group splittings and discuss the problem of when these halfspaces are one-ended. I will also discuss connections to JSJ splittings of groups, and to determining whether groups are simply connected at infinity. This is joint work with Michael Mihalik. Read more.

Autonomous Finite Elements and Deep Learning to Assist Orthopedists and Endocrinologists

STAG 113
Applied Mathematics and Computation Seminar

Speaker: Zohar Yosibash

ABSTRACT: Finite element analysis requires a qualified analyst to generate the necessary input data, verify the output and post process the analysis results for a meaningful conclusion. The required expertise and labor efforts precluded the use of FEA in daily medical practice for example. Recent scientific advancements such as low dose CT scans, machine learning, and high order FEA which allows an inherent verification methodology of the numerical accuracy, make it possible to provide a fully autonomous process for assessing bone strength and fracture risk. This autonomous process, named autonomous finite element (AFE) analysis, introduces a paradigm shift in the use of FEA. This talk addresses a novel AFE for patient-specific analysis of human femurs used nowadays in clinical practice: it involves an automatic segmentation of femurs from CT-scans by U-Net, an automatic mesh generation and application of boundary conditions based on anatomical points, a high-order FE analysis with… Read more.

Improving the accuracy of coupled physics packages in Earth system models

STAG 113
Applied Mathematics and Computation Seminar

Speaker: Sean Santos

ABSTRACT: Earth system models solve exceedingly complicated multiphysics problems by breaking down the Earth system hierarchically into smaller sub-models (e.g. atmosphere, ocean, land, and sea ice), which are composed of smaller components themselves. This decomposition of an Earth system model (which may require millions of lines of code in its software implementation) into many small modules is a vital part of model development. However, naïve coupling of modular physics packages using first-order methods can significantly reduce model accuracy, or even produce numerical instability. This talk covers two examples from the Energy Exascale Earth System Model (E3SM). First, we will see that “sequential” (Lie-Trotter) splitting is a major source of error for E3SM’s cloud and precipitation physics. We will discuss our evaluation of several proposed alternatives, including Strang splitting and multirate methods. Second, we will see that E3SM is prone to spurious “oscillations” in winds… Read more.

Model order reduction for seismic applications

STAG 113
Applied Mathematics and Computation Seminar

Speaker: Kathrin Smetana

ABSTRACT: Full waveform inversion to monitor changes in seismicity is a computationally expensive and challenging task. The latter is due to the fact that the discretization of the seismic wave equation can have millions of degrees of freedom. Moreover, aiming at estimating, for instance, the elastic structure at every grid point results in a large parameter space within the inverse problem. Model order reduction (MOR) techniques can help to speed up the computations, using low-dimensional models that capture the original system's important features. However, for large-scale wave propagation problems, constructing efficient reduced models is challenging as MOR methods can suffer from a slow decay of the Kolmogorov n-width for such problems, thus, requiring a large number of basis functions to reach the desired accuracy. In our work, we address the mentioned challenge as follows: We transform the problem to the Laplace domain, where we can exploit that the output of interest – the… Read more.

The numerical solution of time-fractional initial-boundary value problems

STAG 113
Applied Mathematics and Computation Seminar

Speaker: Martin Stynes

ABSTRACT: An introduction to fractional derivatives and some of their properties will be presented. The regularity of solutions to Caputo fractional initial-value problems is then discussed; it is shown that typical solutions have a weak singularity at the initial time $t=0$. This singularity has to be taken into account when designing and analysing numerical methods for the solution of such problems. To address this difficulty we use graded meshes, which cluster mesh points near $t=0$, and answer the question: how exactly should the mesh grading be chosen? Finally, initial-boundary value problems are considered, where the time derivative is a Caputo fractional derivative. (This is a fractional-derivative generalisation of the classical parabolic heat equation.) Once again a weak singularity appears at $t=0$, and the mesh in the time coordinate should be graded to compute satisfactory numerical solutions. This problem is the most widely studied fractional-derivative problem in the… Read more.

Some theoretical results on finite convergence property and temporary stalling behavior of Anderson acceleration on linear systems

STAG 113
Applied Mathematics and Computation Seminar

Speaker: Yunhui He

ABSTRACT: In this talk, we consider Anderson acceleration with window size $m$ (AA(m)) applied to fixed-point iteration for linear systems. We explore some conditions on the $m+1$ initial guesses of AA(m), aiming for the residuals $r_{m+1}=0$. We propose the sufficient and necessary conditions on the $m+1$ initial guesses for $r_{m+1}=0$. These findings can help us better understand the performance between original fixed-point iteration and Anderson acceleration. Meanwhile, it may give us some guidance on the choice of good initial guesses. Moreover, we give examples to show the temporary stalling behavior of Anderson acceleration applied to solving linear systems. BIO: Yunhui He is currently an Assistant Professor in the Department of Mathematics at the University of Houston. During 2021-2023 she was a Postdoctoral Research Fellow in the Department of Computer Science at the University of British Columbia. In 2018, She obtained her PhD after three years' study from Memorial… Read more.

Math For All Conference

TBD
Conference

Math for all in Corvallis has the purpose of fostering inclusivity in mathematics by holding talks and discussions in both research and education. This conference will be targeted to undergraduate and graduate students, post-docs, and faculty members from all institutions in Oregon and provide a friendly, open environment to learn and discuss mathematics. Read more.