Research

Broadly speaking, my research interests are in numerical methods and the application of high performance computing to mathematical and physical problems. In particular, I am interested in the numerical simulation of wave propagation problems with an emphasis on development and implementation of efficient and accurate methods for the truncation of unbounded domains. Additionally I am interested in investigating questions arising in mathematical biology, where my primary focus has been on micro-scale behavior of both passive objects and active swimmers in low Renyolds number flows.

Publications

(Preprint) Elastohydrodynamics of swimming helices: effects of flexibility and confinement .
LaGrone, J., Cortez, R., and Fauci, L. Submitted to Phys. Rev. Fluids.

Double Absorbing Boundaries for Finite-Difference Time-Domain Electromagnetics.
LaGrone, J. and Hagstrom, T., 2016. Journal of Computational Physics, 326, pp.650-665.

Radiation Boundary Condition Pack Library --- rbcpack.org (2015)
Responsible for all code related to FDTD/Yee and second order finite difference interfaces along with the corresponding documentation and examples. This work was done in collaboration with HyPerComp, Inc.

Selected Presentations

Microdynamics in Regularized Brinkman Flow.
SIAM Texas-Louisiana Section Meeting, October 2018, Baton Rouge, Louisiana.

Chemotaxis Modeling for Sperm Motility.
Society for Mathematical Biology Annual Meeting, July 2018, Sydney, Austrailia.

Simulating Bacterial Motility in Confined Environments.
IUTAM Symposium on Motile Cells in Complex Environments, May 2018, Udine, Italy.

Applications of Complete Radiation Boundary Conditions to Electromagnetic and Elastic Problems
Undergraduate Math Seminar, March 2017, Xavier University of New Orleans.

High Order Radiation Boundary Conditions for Elastic Waves.
ICOSAHOM 2016, July 2016, Rio de Janeiro, Brazil.

Applications of Complete Radiation Boundary Conditions,
RTG Seminar, January 2016, Rensselaer Polytechnic Institute

Double Absorbing Boundaries for Finite-Difference Time-Domain Electromagnetics,
Applied Math Seminar, November 2015, University of New Mexico