<dd>This is the follow-up to my paper "A provably robust algorithm for 2D triangle-triangle intersections in floatingpoint arithmetic" (see Publications).

It discusses in detail the 3D version of the algorithm found there.</dd>

<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><ahref="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>

<dt><ahref="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><ahref="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><ahref="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>