david/Summer 2012 Travel and Research

Travel

  • June 4-5: @Simula
  • June 6-17: Vacation
  • June 18-August 31: @OCCAM (Oxford)
  • June 27-July 1: @TUM (Munich)
  • July 9-13 @Graz, Austria (Euro. Solid Mech.)
  • August 14-17: Vacation

Papers nearing completion (to be submitted in summer)

  1. 2D cylindrical stegotons with Manuel (to J. Nonlin. Sci.)
    • Interactions (long thin domains)
    • Finish writing
    • This is now ready to be submitted. We also discovered a new interesting phenomenon that merits investigation.

  2. Effective order SSP Runge-Kutta methods, with Yiannis and Colin Macdonald (to SINUM) (submitted)

  3. Optimal RK stability polynomials with Aron (to CAMCOS) (submitted)

  4. Many-stage integrators for spectral difference methods with Matteo and Willem Deconinck (submitted to SISC)
    • Complete numerical experiments and conclusions
    • Finish writing
  5. PeanoClaw (Kristof Unterweger, Tobias Wienzierl, and Aron) (to SISC)
    • Complete implementation of AMR capability (Kristof)
    • Numerical examples
    • Writing
    • We’re in the process of debugging the code.

Developing research projects

Direct development:

  • Runge-Kutta accuracy optimization
    • Develop and test toy examples
    • Discuss more with Trefethen

I didn’t make any progress on this.

  • Multi-time integrators (w/Colin Macdonald, Steve Ruuth)

Colin and I got a lot of interesting results and have a draft paper. We still need some interesting examples.

  • New results on the radius of absolute monotonicity (with Tihi Kocsis, Adrian Nemeth, Lajos Loczi)

We decided to split these results up among different papers. Writing is ongoing.

Advisory support:

  • Software development for the closest point method:
    • A parallel CPM implementation in Python (Xin Zhao)
    • Github repository, documentation, testing, integration (Oxford student?)

Xin has produced a working code. Next we hope to get it running on Shaheen.

  • Theoretical and software development for the closest point method:
    • Convergence proof(s) (Tom Maerz)

One new convergence proof. We plan to write this up in the fall.

  • SSP explicit multistep Runge-Kutta methods (with Sigal Gottlieb and Zach Grant)
    • Incorporate Zach’s code into RK-Opt
    • Determine what remains to be done and scope of project

We have a draft paper that is slowly progressing.

Ideas

Some ideas that I’m exploring which might become full-fledged projects later in the summer are:

- Accuracy of downwind RK methods (with Zoltan Horvath)
- Internal stability of explicit Runge-Kutta methods with many stages (With Matteo)
- Implicit SSP methods, including multistep multistage, high order downwind, and some good example problems (with Sigal Gottlieb)

Stuff I’m neglecting: - Combinatorial approach to waves in layered media (with Bojan Popov) - Methods for seismic imaging (with Tariq al-Khalifah) - CUDAClaw - Wrap for Python - Work on writing (after George Turkiyyah provides draft)

Week-by-week outline

  • May 19-24:
    • Carefully formulate and write up bisection convergence proof for convex region case
    • Resubmit SharpClaw paper
    • Downwind RK convergence analysis
    • Draft absolute monotonicity paper
  • May 26-30:
    • Plan closest point method parallelization with Aron and Xin
    • Final polishing and submission of stability optimization paper
    • Writing for SD/RK optimization paper

  • June 2-18: Vacation

  • June 18-24:
    • Discuss stability polynomial optimization with Trefethen
    • Discuss numerical methods for magma flow with Katz
    • Plan CPM parallelization
    • Plan CPM convergence work
    • Improve CPM software development practices (write tests!)
    • Writing for cylindrical stegoton paper
  • June 25 - July 1: Travel – speak at ISPDC and work on PeanoClaw @TUM
    • Writing and numerical experiments for PeanoClaw paper
  • July 2-6:
    • Finish and submit cylindrical stegoton paper
    • CPM convergence work
    • Multi-time integrators – develop convection-diffusion example
  • July 9-13: Euro. Travel – speak at Solid Mech. @Graz, Austria

  • July 16-20:

  • July 23-27:
    • Multi-time integrators
    • Radius of absolute monotonicity
  • July 30-Aug. 3:
  • Aug. 6-10:
  • Aug. 13-17: Vacation (Hungary)
  • Aug. 20-24: CPM convergence and mix-time

  • Aug. 27-31: CPM convergence and mix-time