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 & Preprints

Complex dynamics of long, flexible fibers in shear.

[arXiv Preprint]. LaGrone, J., Cortez, R. Yan, W., and Fauci, L. Journal of Non-Newtonian Fluid Mechanics. In Press.

Elastohydrodynamics of swimming helices: effects of flexibility and confinement.

[arXiv Preprint]. LaGrone, J., Cortez, R., and Fauci, L. Phys. Rev. Fluids 4, 033102. 2019.

Double Absorbing Boundaries for Finite-Difference Time-Domain Electromagnetics.

[Preprint]. LaGrone, J. and Hagstrom, T., 2016. Journal of Computational Physics, 326, pp.650-665.

Radiation Boundary Condition Pack Library — rbcpack.org

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

Numerical methods for (a) Absorbing boundaries in wave propagation and (b) Elastohydrodynamics in flagellar swimming.

Sandia National Lab, Albuquerque, New Mexico

Numerical Simulation of Viscoelastic Fibers.

Math Colloquium, April 2019, University of New Orleans.

Helical Buckling of Elastic Fibers in Straining Flows.

GFS follow on: Mathematics of form in active and inactive media, March 2019, Isaac Newton Institute for Mathematical Sciences, Cambridge, United Kingdom.

Numerical Simulation of Viscoelastic Fibers.

Oakridge National Lab, February 2019, Oak Ridge, Tennessee.

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.