# 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. Submitted to the Journal of Non-Newtonian Fluid Mechanics.

### 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¶

### 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.