Picture of Me at Yarmouth Lighthouse

Aaryn Tonita, B.Sc.

Department of physics and Astronomy

6224 Agricultural Rd.

Vancouver BC

V6T 1Z1



Office phone: 1-604-822-2095


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This is the current state of my research and intentions as of the date selected.

Current State:

  1. Working program:
    • adaptively polygonizes a parametric curve to minimize open angle between two consecutive line segments, takes the midpoint between two current points to make comparison of angle..
    • using a galerkin finite element method, computes general relativistic initial data for axisymmetric spacetime using the above curve as a generator for a marginally trapped surface of revolution.
    • uses bisection method to find point on the actual parametric curve that is closest to a given boundary point on the approximating polygon
  2. Parameters:
    • theta0 = opening angle criteria, the closer this is to pi or 180 degrees, the more accurate the approximating polygon will be.
    • hmax = "maximum size" of a given finite element, problems occur if this is taken too small
    • grade = maximum ratio of the areas of two adjacent elements
    • rmax = radius at which the discretization truncates spacetime.
  3. Interface:
    • program is called either from the command line (usage statement is included) or from a perl script which reads a config file and reads the above parameters.
  4. Specification of curve:
    • Curve is written as a parametric curve and a shell script is called to compile a binary file which has a variable maximal radius and discretication.
  5. Available curves:
    • So far, superellipses, squares with rounded corners, and rippled circles have been tested.

To do:

  1. On the program
    • clean up source code and add comments
  2. Physics:
    • Implement an apparent horizon finder.
    • use the apparent horizon to place a lower limit on the mass, compute the ADM mass for an upper limit.
    • run a large number of various shaped apparent horizons.
  3. Writing:
    • Finish introduction section of thesis.
  4. Testing
    • Irregular meshes have terrible trouble with numerical differentiation. I have implemented a bicubic interpolation and need to extensively test for vanishing residuals.
    • Develop program to test for long thin elements which cause spurious solutions.
My work is funded by NSERC/CRSNG.