Date Speaker Topic
M Sep 10 Everyone Organizational Meeting
Abstract: Discuss plans for the semester.
M Sep 17  Ana Budiša Domain decomposition preconditioner for mixed-dimensional flow problems in fractured porous media
Abstract: We are interested in the mixed-dimensional approach to modelling fractured porous media, where fractures and their intersections are represented as lower-dimensional structures and the mortar method is used for flow coupling between the matrix and fractures. The advantages of the model are immediate in handling complex geometries and large aspect ratios. However, the model has set new numerical challenges and developing a robust linear solver is still necessary. Our goal is to efficiently solve the single-phase flow problem by integrating into the numerical methods the critical role that fractures play in the system behaviour – global exchange of information through fracture flow. We exploit the natural domain decomposition setting imposed by the fracture networks, where fracture are taken as interfaces between subdomains. This approach provides a solver that combines the useful features of the model, such as high performance in case of fracture-dominant flow, but also shows robustness with regards to the system parameters (e.g. permeability, fracture aperture). The convergence and stability of the method is verified on several examples of fracture network configurations, and notable results in reduction of condition and iteration numbers are obtained for both cases of high and low fracture permeability.
M Sep 24
Abstract:
M Oct 1  Tim Atherton Morpho—A system for solving shape optimization problems.

Abstract:

We consider a class of free-boundary problems where both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces and elastomers. This class extends more familiar problems such as soap films for which the solutions are minimal surfaces. We developed a finite element algorithm to solve such problems incorporating dynamic mesh control and present test results for flexible capacitors and liquid crystal tactoids. The algorithm is embedded within a new programmable environment, Morpho, intended to solve this class of problems; the benefits and challenges of such an approach will also be discussed.
M Oct 8 Indigenous People’s Day No Seminar
M Oct 15 Guosheng Fu Explicit divergence-free DG methods for incompressible flow
Abstract:

We present an explicit divergence-free DG method for incompressible Euler and Navier-Stokes equations based

on velocity formulation only. A globally divergence-free finite element space is used for the velocity field, and the pressure field is eliminated from the equations by design. The resulting ODE system is discretized by the explicit third order strong-stability preserving Runge-Kutta method of Shu and Osher. Our spatial discretization produces the identical velocity field as the divergence-conforming DG method of [Cockburn et al., JSC 31(2007), pp 61-73 ] based on a velocity-pressure formulation, when the same DG operators are used for the convective and viscous parts.

Due to the global nature of the divergence-free constraint, there exist no local bases for our finite element space. We present a key result on the efficient implementation of the scheme by identifying the equivalence of the (dense) mass matrix inversion of the globally divergence-free finite element space to a standard (hybrid-)mixed Poisson solver. Hence, in each time step, a (hybrid-)mixed Poisson solver is used, which reflects the global nature of the incompressibility condition.  Since we treat viscosity explicitly for the Navier-Stokes equation, our method shall be best suited for unsteady high-Reynolds number flows so that the CFL constraint is not too restrictive.

The extension to incompressible MHD will also be discussed.

M Oct 22  Jeff Hokanson Exploiting Ridge Structure in Chance Constrained Design Under Uncertainty
Abstract:

In engineering applications it is important to create a design that is robust in the face of uncertainty of operating conditions, material properties, and realizations of the design. As a design which is robust to all possible uncertainties may be too conservative, an alternative is to allow the failure criteria to be violated with a small probability; this converts deterministic constraints on the design into chance constraints. These chance constraints pose a significant challenge for optimization. Here we discover low-dimensional ridge structure in the constraint functions for a multiphysics model of a jet nozzle: each constraint is well-approximated by a low-order polynomial of one or two linear combinations of the input variables. By exploiting this ridge structure, we are able to convert these chance constraints into an easier robust constraints over a low-dimensional set. Moreover this optimization problem can be converted into a simple linear program if the objective and constraint functions are approximated by one-dimensional ridges. Although approximations have been in made in this simplification, most can be made conservative such that the resulting solution satisfies the original constraints. This approach provides a compelling methodology for chance constrained optimization problems where constraints are expensive to evaluate and derivatives are unavailable.

M Oct 29

Fleurianne Bertrand

TBA
Abstract: TBA
M Nov 5  Howard Elman TBA
Abstract: TBA
M Nov 12 Veteran’s Day No Seminar
M Nov 19 Helen Suh
Abstract:
M Nov 26 James Murphy
Abstract:
M Dec 3  Sohom Ray
Abstract:
M Dec 10 John Germaine
Abstract:

 

Spring 2019

Date Speaker Topic
M Jan 21 Martin Luther King Jr. Day No Seminar
M Jan 28 Everyone Organizational Meeting
Abstract: Discuss plans for the semester.
M Feb 4  Daniel Sussman TBA
Abstract: TBA
M Feb 11  Maurice Fabien TBA
Abstract: TBA
M Feb 18  Patriot’s Day  No Seminar
M Feb 25
Abstract:
M Mar 4
Abstract:
M Mar 11 TBA
Abstract: TBA
M Mar 18 Spring Break No Seminar
M Mar 25 TBA
Abstract: TBA
M Apr 1
Abstract:
M Apr 8
Abstract:
M Apr 15
Abstract:
M Apr 22
Abstract:
M Apr 29
Abstract: