[Crib-list] 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]

 		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/