Research
My general research area is algorithm development for numerically solving time-dependent partial differential equations, with a particular emphasis on plasma physics applications. Areas of interest: low-rank tensor decompositions, structure preserving discretizations, Fokker-Planck equations, Eulerian-Lagrangian/semi-Lagrangian methods, WENO methods. I have also started looking into the data science applications of low-rank tensor decompositions.
I have also written articles on promoting diversity in the LGBTQ+ mathematics community.
J. Nakao, G. Ceruti, and L. Einkemmer, "A Reduced Augmentation Implicit Low-rank (RAIL) integrator for solving three-dimensional diffusion and advection-diffusion equations in the Tucker tensor format." In preparation.
J. Nakao, J.-M. Qiu, and L. Einkemmer, "Reduced Augmentation Implicit Low-rank (RAIL) integrators for advection-diffusion and Fokker-Planck models." Accepted in SIAM Journal on Scientific Computing, (2024).
J. Chen, J. Nakao, J.-M. Qiu, and Y. Yang, "A high-order Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for scalar nonlinear conservation laws." Journal of Scientific Computing, 102:12 (2025).
J. Nakao, "Speeding up high-order algorithms in computational fluid and kinetic dynamics: based on characteristics tracing and low-rank structures." University of Delaware, (2023).
J. Nakao, J. Chen, and J.-M. Qiu, "An Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for solving convection and convection-diffusion equations." Journal of Computational Physics, 470 (2022), pp. 111589.
J. Nakao and Y.L. Han, "Preliminary simulated results modeling a dynamic heating cancer ablation probe." Proceedings of the ASME 2018 IMECE, Pittsburgh, PA, 2018.
Diversity Articles
C. Goff, M. Hill, and J. Nakao, "A Word From...Spectra on the Recent Efforts Supporting LGBTQ+ Mathematicians." Notices of the American Mathematical Society, 71:6 (2024), pp. 705-707.
J. Nakao, "Recent activities and progress by Spectra and the LGBTQ+ mathematics community." MAA FOCUS, 43:6 (2023/2024), pp. 10-13.
R. Buckmire, A. Folsom, C. Goff, A. Hoover, J. Nakao, and K.A. Sather-Wagstaff, "On best practices for the recruitment, retention, and flourishing of LGBTQ+ mathematicians." Notices of the American Mathematical Society, 70:6 (2023), pp. 979-985.
J. Nakao, "The pot of gold at the end of the rainbow -- how mathematics departments can increase LGBTQ+ inclusivity." MAA Math Values Blog, (2021).
Research Presentations
- A Brief Introduction to Low-Rank Tensor Decompositions (slides)
- A structure-preserving, conservative, low-rank tensor decomposition algorithm for the 1D2V Vlasov-Fokker-Planck equation