Past OCCAM Special Seminar

13 March 2012
10:15
Adriano Pisante
Abstract

We discuss new symmetry results for nonconstant entire local minimizers of the standard Ginzburg-Landau functional  for maps in ${H}^{1}_{\rm{loc}}(\mathbb{R}^3;\mathbb{R}^3)$ satisfying a natural energy bound.

Up to  translations and rotations, such solutions of the Ginzburg-Landau system are given by an explicit map equivariant under the action of the orthogonal group.

More generally, for any $N\geq 3$ we  characterize the $O(N)-$equivariant vortex solution for Ginzburg-Landau type equations in the $N-$dimensional Euclidean space and we prove its local energy minimality for the corresponding energy functional.

  • OCCAM Special Seminar
1 March 2012
10:15
Aron Ahmadia
Abstract

As Herb Sutter predicted in 2005, "The Free Lunch is Over", software programmers can no longer rely on exponential performance improvements from Moore's Law.  Computationally intensive software now rely on concurrency for improved performance, as at the high end supercomputers are being built with millions of processing cores, and at the low end GPU-accelerated workstations feature hundreds of simultaneous execution cores.  It is clear that the numerical software of the future will be highly parallel, but what language will it be written in?

Over the past few decades, high-level scientific programming languages have become an important platform for numerical codes. Languages such as MATLAB, IDL, and R, offer powerful advantages: they allow code to be written in a language more familiar to scientists and they permit development to occur in an evolutionary fashion, bypassing the relatively slow edit/compile/run/plot cycle of Fortran or C. Because a scientist’s programming time is typically much more valuable than the computing cycles their code will use, these are substantial benefits. However, programs written in such languages are not portable to high performance computing platforms and may be too slow to be useful for realistic problems on desktop machines. Additionally, the development of such interpreted language codes is partially wasteful in the sense that it typically involves reimplementation (with associated debugging) of some algorithms that already exist in well-tested Fortran and C codes.  Python stands out as the only high-level language with both the capability to run on parallel supercomputers and the flexibility to interface with existing libraries in C and Fortran.

Our code, PyClaw, began as a Python interface, written by University of Washington graduate student Kyle Mandli, to the Fortran library Clawpack, written by University of Washington Professor Randy LeVeque.  PyClaw was designed to build on the strengths of Clawpack by providing greater accessibility.  In this talk I will describe the design and implementation of PyClaw, which incorporates the advantages of a high-level language, yet achieves serial performance similar to a hand-coded Fortran implementation and runs on the world's fastest supercomputers. It brings new numerical functionality to Clawpack, while making maximal reuse of code from that package.  The goal of this talk is to introduce the design principles we considered in implementing PyClaw, demonstrate our testing infrastructure for developing within PyClaw, and illustrate how we elegantly and efficiently distributed problems over tens of thousands of cores using the PETSc library for portable parallel performance.  I will also briefly highlight a new mathematical result recently obtained from PyClaw, an investigation of solitary wave formation in periodic media in 2 dimensions.

  • OCCAM Special Seminar
13 January 2012
11:30
to
13:00
Various
Abstract
<ul><li>Cameron Hall - Dislocations and discrete-to-continuum asymptotics: the summary</li><li>Kostas Zygalakis - Multi scale methods: theory numerics and applications </li><li>Lian Duan - Barcode Detection and Deconvolution in Well Testing</li></ul>
  • OCCAM Special Seminar
9 December 2011
11:30
to
13:00
Various
Abstract
  • Ian Griffiths - Control and optimization in filtration and tissue engineering
  • Vladimir Zubkov - Comparison of the Navier-Stokes and the lubrication models for the tear film dynamics
  • Victor Burlakov - Applying the ideas of 1-st order phase transformations to various nano-systems
  • OCCAM Special Seminar
11 November 2011
11:30
to
13:00
Various
Abstract
  • Derek Moulton - "Growth and morphology of seashells"
  • Simon Cotter - "A Hybrid stochastic finite element method for solving Fokker-Planck equations"
  • Apala Majumdar -"The theory of liquid crystals - analysis, computation and applications"
  • OCCAM Special Seminar
9 September 2011
11:15
Various
Abstract
  • Rob Style - "Drying and freezing stuff - the wrap up"
  • Maria Bruna-Estrach - “Including excluded-volume effects into diffusion of hard spheres" 
  • Patricio Farrell - “Multiscale Analysis for Elliptic Boundary Value Problems using Radial Basis Functions"
  • OCCAM Special Seminar

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