Commit bf79d994 authored by Conor McCoid's avatar Conor McCoid
Browse files

Homepage: updated files, incl. tetra, triangles, and dd26

parent 2b826e58
......@@ -67,9 +67,9 @@ dd {
<div class="main-content">
<dl>
<dt><a href="ongoing/Intersection_of_tetrahedra.pdf">Tetrahedral intersections</a></dt>
<dd>This is the follow-up to my paper "A provably robust algorithm for 2D triangle-triangle intersections in floating point arithmetic" (see Publications).
It discusses in detail the 3D version of the algorithm found there.</dd>
<dt><a href="ongoing/mccoid2020tetrahedra.pdf">Tetrahedral intersections</a></dt>
<dd>This is the follow-up to my paper "A provably robust algorithm for 2D triangle-triangle intersections in floating-point arithmetic" (see Publications).
It discusses in detail the 3D version of the algorithm found there as well as how to extend the algorithm to arbitrary dimensions.</dd>
<dt><a href="ongoing/IOM.pdf">IOMcc</a></dt>
<dd>The continuation of my masters thesis.
This looks at extending the results of my paper "Preconditioning of spectral methods via Birkhoff interpolation" to general linear operators, with a focus on constant coefficient linear operators.</dd>
......
......@@ -68,6 +68,11 @@ dd {
<div class="main-content">
<h3>Talks</h3>
<dl>
<dt><a href="presentations/TALK_DD26_2020_cycles.pdf">Cycles in Newton-Raphson-accelerated Alternating Schwarz</a>,
with Martin J. Gander, DD26 2020</dt>
<dd>DDM is a conference devoted to domain decomposition methods. DD26 was originally meant to be held in Hong Kong in December 2019
but was postponed one year when it was held online.
In this talk I examine cycling behaviour in 1D Schwarz methods that have been accelerated by Newton's method.</dd>
<dt><a href="presentations/TALK_algoritmy_2020_provably.pdf">A provably robust algorithm for triangle intersections</a>,
with Martin J. Gander, ALGORITMY 2020</dt>
<dd>ALGORITMY is held every three to four years at the Grand Hotel Permon in Podbansk&eacute;, Slovakia.
......
......@@ -102,16 +102,20 @@ dd {
<h3>Submitted for review</h3>
<dl>
<dt><a href="pubs/PRE_mccoid2020provably.pdf">A provably robust algorithm for triangle-triangle intersections in floating point arithmetic</a>,
with Martin J. Gander, preprint (2020)</dt>
<dd>Motivated by the unexpected failure of the triangle intersection component of the
Projection Algorithm for Nonmatching Grids (PANG), this article provides a robust version
with proof of backward stability. The new triangle intersection algorithm ensures consistency
across three types of vertex calculations. The proof of stability draws an exhaustive list
of graphs representing the intersections and codifies possible errors as graph rewrites.
These rewrites are shown to either map between the listed graphs or be impermissible by the
algorithm. The article concludes with a comparison between the old and new intersection
algorithms for PANG using an example found to reliably generate failures in the former.</dd>
<dt><a href="pubs/PRE_mccoid2021provably.pdf">A provably robust algorithm for triangle-triangle intersections in floating point arithmetic</a>,
with Martin J. Gander, preprint, submitted to TOMS (2021)</dt>
<dd>Motivated by the unexpected failure of the triangle intersection component of the Projection Algorithm for
Nonmatching Grids (PANG), this article provides a robust version with proof of backward stability. The new
triangle intersection algorithm ensures consistency and parsimony across three types of calculations. The set
of intersections produced by the algorithm, called representations, is shown to match the set of geometric
intersections, called models. The article concludes with a comparison between the old and new intersection
algorithms for PANG using an example found to reliably generate failures in the former.</dd>
<dt><a href="pubs/mccoid2021cycles.pdf">Cycles in Newton-Raphson preconditioned by Schwarz (ASPIN and its cousins)</a>
with Martin J. Gander, preprint, submitted to DD26 proceedings (2021)</dt>
<dd>Newton-Raphson preconditioned by Schwarz methods does not have sufficient convergence criteria.
We explore an alternating Schwarz method accelerated by Newton-Raphson to find an example where the underlying Schwarz method converges but the Newton-Raphson acceleration fails.
Alternating Schwarz is posed as a fixed point iteration to make use of theory for generic root-finding methods.
An algorithm is proposed combining several aspects of this theory and others to guarantee convergence.</dd>
</dl>
<h3>Other</h3>
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment