[Crib-list] TODAY: SPEAKER: Nathaniel Trask (Brown) Computational Research in Boston and Beyond Seminar (CRIBB) -- Friday, Feb, 5, 2016 --TIME: 12:00 Noon in Building 32, Room 124 (Stata)

[Shirley Entzminger]

 	T O D A Y . . .


 		COMPUTATIONAL RESEARCH in BOSTON and BEYOND Seminar



DATE:	      	Friday, February 5, 2016
TIME:		12:00 PM  1:00 PM
LOCATION:	Building 32, Room 124 (Stata) --  (32 Vassar Street)

 		http://whereis.mit.edu/?mapterms=32-124&mapsearch=go)

 	(Pizza will be provided at 11:45 AM outside Room 32-124.)


TITLE:		Compatible meshless discretization through
 		$\ell_2$-optimization


SPEAKER:	Nathaniel Trask (Brown University)


ABSTRACT:

Meshless methods provide an ideal framework for scalably simulating problems 
involving boundaries undergoing large deformation or interfaces between 
multiple materials. Discretization points may be moved in a Lagrangian fashion 
without the need for either costly mesh topology updates or diffuse Eulerian 
treatment of interfaces. Of the range of meshless discretizations available, 
there is a distinct lack of methods that maintain a sense of compatibility 
while simultaneously achieving high-order accuracy. In this talk, we present a 
new discretization that generalizes staggered primal/dual discretizations to 
unstructured point sets. Using only the epsilon-neighborhood graph of 
discretization points and solving inexpensive optimization problems, we 
construct divergence and gradient operators that mimic the algebraic structure 
of compatiblemesh-based discretizations. When applied to a model div-grad 
diffusion problem, we obtain high-order convergence for smooth solutions and 
observe monotone fluxes for problems with discontinuous material properties. We 
then present a new mixed meshless discretization for the Stokes equations, 
using a divergence-free moving least squares method for velocity and staggered 
moving least squares for the pressure. This approach achieves equal order 
convergence for both velocity and pressure, making it ideal for simulating 
problems in dense suspension flows dominated by lubrication forces. We finally 
assemble the Stokes solver, a Poisson-Boltzmann solver based on the staggered 
scheme, and a 6-DOF solver for colloid dynamics together into a monolithic, 
fully implicit scheme that we use to study electrophoretic suspensions. By 
using auxiliary space algebraic multigrid preconditioning to solve the 
resulting system, we obtain an efficient, robust, and highly accurate new tool 
for studying these problems in complex geometries.

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Massachusetts Institute of Technology
Cambridge, MA  02139


For information about the Computational Research in Boston and Beyond Seminar 
(CRIBB), please visit...


 			http://math.mit.edu/crib/