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Department of Mathematics

Upcoming Seminars

Memorial Union on sunny day

Join us for an upcoming seminar featuring mathematics faculty and invited speakers on one of our seven research topics. You may also see upcoming seminars by topic:

Numerical analysis of coupled free-flow and porous media flow problems

STAG 111
Applied Mathematics and Computation Seminar

Speaker: Aycil Cesmelioglu

ABSTRACT: In this talk, I will focus on the numerical analysis of several coupled problems involving both free-flow and porous media flow. These problems are commonly encountered in applications such as groundwater contamination, where contaminants spread through both surface and subsurface flows. I will present numerical discretizations based on strongly conservative hybridizable discontinuous Galerkin (HDG) methods, emphasizing well-posedness and error estimates. Finally, I will present results from various computational experiments. BIO:Dr. Cesmelioglu is a Professor in the Department of Mathematics and Statistics at Oakland University, where she has been a faculty member since 2012. She holds a Ph.D. in Computational and Applied Mathematics from Rice University (2010) and held a postdoctoral position at the Institute for Mathematics and its Applications (2010-2012). Her research focuses on numerical methods for partial differential equations with specific interest in fluid flow… Read more.

Hecke continued fractions and connection points on Veech surfaces

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Algebra and Number Theory Seminar

Speaker: Julian Boulanger

Given a billiard trajectory on a regular polygon starting from thecenter of the polygon and eventually ending at a vertex, is it true thatthe trajectory starting from the center but in the opposite direction also ends eventually at a vertex ? By symmetry, this is certainly true if the number of sides is even. In the odd case, we will see that the answer is 'yes' for the equilateral triangle and the regular pentagon, but 'no' if the polygon has 7 sides or more! The question is closely related to determining the real numbers (in some algebraic field) having a finite Hecke continued fraction expansion, or equivalently cusp representative of the Hecke modular surface. We will also encounter so-called translation surfaces and their Veech groups, and we will discuss the notion of connection points on such surfaces. Read more.

High-order time integration for nonlinearly partitioned multiphysics

STAG 111
Applied Mathematics and Computation Seminar

Speaker: Benjamin Southworth

In multiscale and multiphysics simulation, a predominant challenge is the accurate coupling of physics of different scales, stiffnesses, and dimensionalities. The underlying problems are usually time dependent, making the time integration scheme a fundamental component of the accuracy. Remarkably, most large-scale multiscale or multiphysics codes use a first-order operator split or (semi-)implicit integration scheme. Such approaches often yield poor accuracy, and can also have poor computational efficiency. There are technical reasons that more advanced and higher order time integration schemes have not been adopted however. One major challenge in realistic multiphysics is the nonlinear coupling of different scales or stiffnesses. Here I present a new class of nonlinearly partitioned Runge-Kutta (NPRK) methods that facilitate high-order integration of arbitrary nonlinear partitions of ODEs. Order conditions for an arbitrary number of partitions are derived via a novel edge-colored… Read more.

Sink or Soar: the interplay between buoyant bubbles and sinking sediments inenergizing turbulence near the ice-ocean boundary

STAG 111
Applied Mathematics and Computation Seminar

Speaker: Megan Wengrove

ABSTRACT: At the terminus of tidewater glaciers an interplay of connected processes result in the melt of ice. From both field and laboratory observations, it has been suggested that both bubbles and sediments could be important yet neglected contributors to ice melt at the submarine tidewater glacier terminus. In the laboratory it has been shown that as glacier ice melts, air trapped in pores inside of the ice is released creating flow transpiration at the boundary and buoyant bubble rise at the ice-ocean interface, leading to increased melt (Wengrove et al.,2023). Additionally, during separate laboratory experiments, sediments entrained in the subglacial discharge plume are shown to increase the entrainment of warm ocean water toward the ice leading to higher melt rates (McConnochie andCenedese, 2023). In July 2024, we made the first ever video observations of both bubbles rising and sediments mixing and falling from a stationary-bolted platform to an Alaskan tidewater glacier… Read more.

The role of boundary constraints in simulating biological systems with nonlocal dispersal

STAG 111
Applied Mathematics and Computation Seminar

Speaker: Gabriela Jaramillo

ABSTRACT:Population and vegetation models often use nonlocal forms of dispersal to describe the spread of individuals and plants. When these long-range effects are modeled by spatially extended convolution kernels, the mathematical analysis of solutions can be simplified by posing the relevant equations on unbounded domains. However, in order to numerically validate these results, these same equations then need to be restricted to bounded sets. Thus, it becomes important to understand what effects, if any, do the different boundary constraints have on the solution. To address this question we present a quadrature method valid for convolution kernels with finite second moments. This scheme is designed to approximate at the same time the convolution operator together with the prescribed nonlocal boundary constraints, which can be Dirichlet, Neumann, or what we refer to as free boundary constraints. We then apply this scheme to study pulse solutions of an abstract 1-d nonlocal Gray-Scott… Read more.

The effect of Anderson acceleration on the convergence order of superlinear and sublinear nonlinear solvers

TBA
Applied Mathematics and Computation Seminar

Speaker: Leo Rebholz

We consider the effect of Anderson acceleration (AA) on the convergence order of nonlinear solvers in fixed point form $x_{k+1}=g(x_k)$, that are looking for a fixed point of g. While recent work has answered the fundamental question of how AA affects the convergence rate of linearly converging fixed point iterations (at a single step), no analytical results exist (until now) for how AA affects the convergence order of solvers that do not converge linearly. We first consider AA applied to general methods with convergence order r, and show that AA changes the convergence order to (at least) (r+1)/2 for depth m=1; a more complicated expression for the order is found for the case of larger m. This result is valid for superlinearly converging methods and also locally for sublinearly converging methods where r<1 locally but r$\rightarrow$1 as the iteration converges, revealing that AA asymptotically slows convergence for superlinearly converging methods but (locally) accelerates it for… Read more.