yiannis/spring_2013

Spring 2013 research plans


Primary goals

  1. Finalize research proposal, form committee and arrange oral examination.
  2. Submit revised version of ESSPRK paper.
  3. Investigate strong stability preservation of additive multistep methods (including numerical tests).
  4. Work on high order explicit/implicit RK methods with downwinding.

Pending papers

  1. ESSPRK paper (with David, Colin Macdonald and Jim Verner)
    (submit by end of January 2013)

Working papers

  1. Internal error propagation (with David, Lajos and Matteo)
    (Work on SSP section: 2nd/3rd order methods, convergence of SSPRK for linear PDEs)

Potential conferences

  1. SciCADE 2013: September 16-20, 2013, Valladolid, Spain
    (info for contributed talk announced by 31/01/13)
  2. AMMCS 2013: August 26-30, 2013, Waterloo, Ontario, Canada
    (deadline for submitting abstract: March 15, 2013)

Workshops

  1. Positivity Workshop: 2-5 June



Week-by-week schedule

January 26 - 30:

  • Finalize research proposal.
  • Submit revised version of ESSPRK paper.

February 2 - 6:

  • Submit research proposal.
  • Prepare presentation for research proposal defence.
  • Contact committee and arrange date for examination (2nd March)
  • Prepare for AMCS 252 (TA)
  • Work on internal error propagation paper.

February 9 - 13:

  • Prepare for research proposal defence (further reading)
  • Numerical tests for additive multistep methods.
  • TA duties.

  • Work on internal error propagation paper (cont.)

    Present methods with downwinding and relevant research in group meeting?

February 16 - 20:

  • Prepare for research proposal defence (further reading)
  • Search for possible implicit DWSSPRK(2,2) and DWSSPRK(s,3) with arbitary large SSP coeffcient.
  • TA duties.

February 23 - 27:

  • Prepare for research proposal defence.
  • Answer questions posed in “Step Sizes for Strong Stability Preservation with Downwind-Biased Operators” and relative David’s wiki comments.
    Ideas:
    1. Fix a number of parameters and plot the polynomial as a function of the remaining parameters. Examine the behavior of the polynomial for various values of a.m.r.
    2. Work on the stability function of DW methods. Examine the relation of the order conditions of the stability function and SSP conditions.
  • TA duties.

March 2 - 6:

  • Research proposal defence.
  • Further reading about DW methods.
  • TA duties.

March - May:

  • Complete at least one research topic.




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