Applied/ACMS/Spring2025: Difference between revisions

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== Abstracts ==
== Abstracts ==


==== Chris Rycroft (UW–Madison) ====
==== Bernardo Cockburn (Minnesota) ====
Title: The reference map technique for simulating complex materials and multi-body interactions
Title: Transforming stabilization into spaces


Conventional computational methods often create a dilemma for fluid–structure interaction problems. Typically, solids are simulated using a Lagrangian approach with grid that moves with the material, whereas fluids are simulated using an Eulerian approach with a fixed spatial grid, requiring some type of interfacial coupling between the two different perspectives. Here, a fully Eulerian method for simulating structures immersed in a fluid will be presented [1]. By introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid, the interfacial coupling problem is highly simplified. The method is particularly well suited for simulating soft, highly-deformable materials and many-body contact problems [2], and several examples in two and three dimensions [3] will be presented.
In the framework of finite element methods for ordinary differential
equations, we consider the continuous Galerkin method  (introduced in 72) and
the discontinuous Galerkin method (introduced in 73/74). We uncover the fact
that both methods discretize the time derivative in exactly the same form, and
discuss a few of its consequences. We end by briefly describing our ongoing
work on the extension of this result to some Galerkin methods for partial
differential equations.

Revision as of 14:39, 6 June 2024

Spring 2025

date speaker title host(s)
Feb 2 Chris Rycroft (UW) The reference map technique for simulating complex materials and multi-body interactions
Feb 9 Scott Weady (Flatiron Institute) Entropy methods in active suspensions Saverio and Laurel
Mar 28 Spring break

Abstracts

Bernardo Cockburn (Minnesota)

Title: Transforming stabilization into spaces

In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.

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