Michael Singer
Lawrence Livermore National Laboratory
Large blood clots that migrate to the heart or lungs can be
fatal. Patients who are at high risk of pulmonary embolism
have a handful of therapeutic options, including the endovascular
insertion of a metallic filter designed to trap clots before
they become fatal. But, once a filter has trapped clots,
physicians must decide what to do; if left unattended, the
accumulation of additional clots in the filter may lead to
vessel occlusion. Our work uses the method of overlapping
grids, as implemented in the Overture software framework,
to examine flow through a filter that is designed to trap
blood clots. In particular, we identify regions of stagnant
and recirculating flow that may facilitate the formation of
additional clots. We also identify regions of high wall
shear stress. Flow through a partially occluded filter is
also modeled, and the impact of different sizes, shapes,
and orientations of clots is examined. Our results characterize
the hemodynamics of clinically relevant flows and may be used by
clinicians to make informed medical decisions.
Yuan Yao
Stanford University
Modern ranking data is often incomplete, unbalanced, and arises from a complex network. We will propose a method to analyze such data using combinatorial Hodge theory, which may be regarded as an additive decomposition of a skew-symmetric matrix into three matrices with special properties. In this framework, ranking data is represented as a skew-symmetric matrix and Hodge-decomposed into three mutually orthogonal components corresponding to globally consistent, locally consistent, and locally inconsistent parts of the ranking data. Rank aggregation then naturally emerges as projections onto a suitable subspace and an inconsistency measure of the ranking data arises as the triangular trace distribution. A geometric interpretation of this technique applied to the Netflix dataset may be obtained via SVD and some of its nonlinear extensions. One surprising revelation is that Netflix movies, despite being from a high-dimensional dataset, are distributed around a horseshoe-shaped 1-dimensional submanifold of the 4-dimensional sphere. The skew-symmetric matrix in this setting approximates gradient flows of rank aggregation functions on the 1-dimensional manifold.
This is joint work with Lek-Heng Lim, University of California, Berkeley.
Mohamed Ebeida
University of California at Davis
A new adaptive hybrid mesh generation method is presented in this paper to deal with
planar domains of arbitrary shapes. The tree decomposition is governed by a size function
in 2D. Our main goal is to efficiently produce an adequate mesh for the Reynolds-averaged
Navier-Stokes numerical simulations of turbulent viscous flow. The result is an adaptive
quad-dominant hybrid mesh ready for the application of agglomeration multigrid methods.
Several application examples are provided to show the strength of this approach. A simple
optimization step is required and enables the extension of this method to 3D in a straight
forward manner.
Tamar Shinar
Stanford University
We propose a novel solid/fluid coupling method that treats the coupled
system in a fully implicit manner making it stable for arbitrary time steps,
large density ratios, etc. We show that our method exactly conserves
momentum of the coupled system. Notably, our method uses the standard
Cartesian fluid discretization and does not require (moving) conforming
tetrahedral meshes or ALE frameworks. Furthermore, we use a standard
Lagrangian framework for the solid, thus supporting arbitrary solid
constitutive models, both implicit and explicit time integration, etc. The
method is quite general, working for smoke, water, and multiphase fluids as
well as both rigid and deformable solids, and both volumes and thin shells.
Unlike previous methods, rigid shells and cloth are handled automatically
with no special treatment, and we support fully one-sided discretizations
without leaking. Our equations are fully symmetric, which is a natural
result of properly conserving momentum.
A set of movies can be viewed at
http://physbam.stanford.edu/~shinar/minggu/movies/.
Chris Rycroft
University of California at Berkeley
Despite being common in everyday experience, flowing dense
granular materials exhibit surprisingly complex behavior, that has
prompted renewed scientific interest over the past decade. A number of
continuum models have been proposed with some success, although a
complete description is still lacking, due in part to the complexities
of capturing stochastic effects at the particle level. Discrete
atomistic modeling has also been a useful tool, but it is
computationally intensive, and the particle-by-particle description it
provides can occlude the relevant collective physics. This talk will
present the results of several different simulation studies, that
combine continuum and discrete ideas to gain a better physical
understanding. These results will be used to formulate a simulation
coupling a continuum PDE model with a stochastic particle description,
that runs rapidly and captures a wide variety of features of granular
flows.
Andy Aspden
Lawrence Berkeley National Laboratory
Abstract in pdf format
Damian Rouson
Sandia National Laboratory
This talk will present software design patterns using the new
object-oriented features of Fortran 2003 and will compare those
features with their C++ counterparts where possible. The objective of
the presented work is to facilitate natural language expression of
coupled partial differential equations (PDEs) in source code. Two new
patterns will be presented along with the application of one pattern
from Gamma et al. [1994] in the context of solving PDEs. The new
semi-discrete pattern embodies the discretization of evolution
equations in situations where those equations can be encapsulated in a
single physical abstraction. The new puppeteer pattern expresses a
method for coupling these individual abstractions into a multiphysics
package. The puppeteer mediates all inter-abstraction communication
and allows for fully implicit integration even when nonlinear
couplings exist between otherwise separate abstract data types. The
puppeteer also allows for swapping physical models at runtime, while
scalar field and grid templates allow for swapping spatial
discretizations at compile-time. After code demonstrations that use
the Lorenz dynamical system as a proxy for nonlinear, coupled,
semi-discrete systems, the talk will provide architectural
descriptions of how we have employed the design patterns to extend the
Navier-Stokes solver of Rouson et al. [2008] to simulate more
complicated phenomena, including quantum hydrodynamics,
magnetohydrodynamics, and planetary boundary layers.
Gamma, E., R. Helm, R. Johnson, and J. Vlissides. Design Patterns: Elements of Reusable Object-Oriented Software, Addison-Wesley, 1994.
Rouson, D.W.I., R. Rosenberg, X. Xu, I. Moulitsas, and
S.C. Kassinos. "A grid-free abstraction of the Navier-Stokes equations
in Fortran 95/2003," ACM Trans. Math. Soft., 34:1, Article 2,
2008.
Michael Mahoney
Yahoo Research
Given an m x n matrix A and a rank parameter k, define the leverage of the
i-th row of A to be the i-th diagonal element of the projection matrix onto
the span of the top k left singular vectors of A. Historically, this
statistical concept (and generalizations of it) has found extensive
applications in, e.g, diagnostic regression analysis. Very recently, this
concept has been central in the development of improved algorithms for
several fundamental matrix problems. Two examples of this will be
described. The first problem is the least squares approximation problem,
in which there are n constraints and d variables. Classical algorithms,
dating back to Gauss and Legendre, use O(nd^2) time. We describe a
randomized algorithm that uses only roughly O(n d log d) time to compute a
relative-error, i.e., 1+/-epsilon, approximation. The second problem is
the problem of selecting a ``good'' set of exactly k columns from an m x n
matrix, and the algorithm of Gu and Eisenstat provides the best previously
existing result. We describe a two-stage algorithm that improves on their
result (assuming that k is not extremely large). Recent application of
these ideas in modern statistical data analysis will be briefly described.
James Lambers
Stanford University
This talk presents a reformulation of Krylov Subspace Spectral
(KSS) Methods, which build on the many contributions of Gene Golub, et al.
pertaining to moments and Gaussian quadrature in the spectral domain in
order to produce high-order accurate approximate solutions to
variable-coefficient time-dependent PDE. This reformulation serves two
useful purposes. First, it reveals that KSS methods are actually high-order
operator splittings that are defined implicitly, in terms of derivatives of
the nodes and weights of Gaussian quadrature rules with respect to a
parameter. Second, it improves the numerical stability of these methods by
removing cancellation arising from the approximation of these derivatives by
finite differences, instead computing these derivatives analytically.
Efficient algorithms for computing these derivatives are provided, as well
as the first application of KSS methods to systems of coupled PDE.
George Pau
Lawrence Berkeley National Laboratory
High-fidelity simulations of subsurface flow play an important role in
evaluating scenarios for carbon sequestration, assessing the long-term
fate of contaminants, and designing effective petroleum recovery
strategies. Here we consider a new adaptive multigrid refinement (AMR)
method for multiphase, incompressible flows in porous media. Our basic
time-stepping algorithm is based on a total velocity splitting that
decouples the
system into an elliptic PDE and a system of nonlinear hyperbolic
conservation laws. In this talk, I will describe some of the issues
involved in developing the AMR solver, focusing on how data at different
levels of grids are synchronized. I will also present some numerical
results that demonstrate the algorithm's accuracy and convergence
properties, as well as the scaling properties of the parallelized code.
Cleve Moler
The MathWorks
I've known Beresford and Velvel since the early '60s, when I was a grad
student and before either was at Berkeley. I'll try to remember some
stories from these early days.
Horst Simon
Lawrence Berkeley National Laboratory
In this talk I will try to summarize developments in
solving large sparse eigenvalue problems over the last thirty years.
In the mid 1970s Beresford made fundamental contributions to the
understanding of the Lanczos algorithm that he summarized in his
landmark book "The Symmetric Eigenvalue Problem" (SEP) in 1980.
Further developments of the Lanczos algorithm in the 1980s and 1990s
by Beresford, his students, and others inspired by SEP, led to our
ability today of solving extremely large systems on the current
generation of multicore parallel systems.
David Hough
Sun Microsystems
In 1977 I finally graduated from UCB and, a few months later, what became the IEEE
754 standardization effort began to coalesce.
IEEE 754 was my principal technical preoccupation from about 1978-1982.
Its successor effort 754R has kept me even busier sinnce 2001 - seven years
and counting. In between, I implemented parts of 754
and found out what hadn't been done very well.
I studied the right balance between hardware and software implementation,
I studied how to test hardware and software implementations,
I studied extending its principles to additional functions,
I studied getting language standards interested in supporting it,
and I wrote down some of what I had learned.
Today I'll outline the progress that happened and the progress
that didn't happen in the last 30 years.
Ann Greenbaum
University of Washington
Abstract in pdf format
Ren-Cang Li
University of Texas at Arlington
Abstract in pdf format
Inderjit Dhillon
University of Texas at Austin
The main focus of Beresford's research during the last 10-15 years
has been on delivering the last word on the numerical solution of
the symmetric tridiagonal eigenproblem. In this talk, I will review
some of the reasons why Beresford and Berkeley were ideally
positioned to make remarkable progress on the problem.
Alexandre Chorin
University of California at Berkeley
One often has to make predictions on the basis of unreliable models, underresolved computations, and/or incomplete data. The usual approach is to do some averaging. I will show, with simple examples, that this can be a bad idea. The Mori-Zwanzig model of irreversible statistical mechanics offers an alternative which in principle is optimal, but it is hard to use. I will exhibit some approximate ways to tame its complexity, and also explain what irreversible statistical mechanics has to do with prediction. (joint work with Kupferman, Hald, and Stinis).
Robert Taylor
University of California at Berkeley
The presentation will summarize some of the developments in computational
mechanics that have evolved from studies in the structural engineering and
mechanics group at UCB. Many have been strongly influenced by interactions
between faculty in the structures group and those in mathematics and computer
science. Some milestones that have been achieved will be described.
Beresford Parlett
University of California at Berkeley
William Kahan
University of California at Berkeley
When I began to program an electronic computer in 1953, von Neumann
was still disparaging floating-point computation, which was generally
deemed impervious to error-analysis. Occassional anomalous results
were expected. Often they were attributed wrongly to
"Ill-Condition". Putting one's data through several numerical methods
some of whose results might agree was a prudent policy. Those days are
back. Their challenges will be illustrated by a program like some used
by structural engineers for forty years. To cope, we need debugging
aids like those in Section 14 of my web page's
Mindless.pdf . Help
can come only from the designers of harware, compilers and software
development systems after they are persuaded that the demand for such
aids is commercially significant.
This document will be posed at
http://www.eecs.berkeley.edu/~wkahan/BASCD08K.pdf .