I am a developer of the open source code IBAMR, which is a MPI parallelized implementation of the immersed boundary method with adaptive mesh refinement. Most of my work, in some way or another, is directly related to using or developing this software. More information can be found at ibamr.github.io.

Relevant publications:

• https://doi.org/10.48550/arXiv.2309.00548

Github project:

• https://ibamr.github.io/

Blood clotting is a complicated phenomenon with many interesting mathematical questions. At the microscale are dozens of complex chemical reactions to activate and bind platelets. While at the macroscale there are complex tissues and fluid motion. One question that we focus on is how the internal mechanics of the blood clots affect the hemodynamics in different tissues.

Relevant publications:

• https://doi.org/10.1002/cnm.3700

Github project:

• https://github.com/abarret/AV2D

Many biological systems involve concentration fields that advect with a fluid and diffuse over a complex, moving domain, for example leaflet thrombosis, particulate transport in the lungs, and drug absorption in the gut. We develop scalable and efficient methods to solve advection diffusion problems with general boundary conditions on complex surfaces.

Relevant publications:

• https://doi.org/10.1016/j.jcp.2021.110805

Github project:

• https://github.com/abarret/AdvDiffSolvers

My dissertation work at UNC-CH was related to developing and implementing numerical methods for viscoelastic fluids based on Oldroyd-B models. We used these methods to develop models of bacterial locomotion in viscoelastic fluids.

Relevant publications:

• https://doi.org/10.17615/znd0-ye14

• https://doi.org/10.1017/jfm.2016.99

• https://doi.org/10.48550/arXiv.2310.08787