- Software development
- Tsunami modeling
- Volcano modeling
- Extracorporeal shock wave therapy and lithotripsy
- Solving hyperbolic problems on curved manifolds
- Cartesian grid (cut cell) method for hyperbolic problem
The LeVeque research group’s research interests span many areas, including numerical analysis, computational fluid dynamics, nonlinear partial differential equations, mathematical theory of conservation laws, and software development, including the CLAWPACK software for solving conservation laws and other hyperbolic systems modeling wave propagation. It is also involved in research in many applications areas, including astrophysics, geophysics, and biophysics.
- Logically Rectangular Finite Volume Methods with Adaptive Refinement on the Sphere
by M. J. Berger and D. A. Calhoun, and C. Helzel, and R. J. LeVeque Phil. Trans. R. Soc. A 2009 367, 4483-4496.
- CSE 2009: Python for Scientific Computing at CSE 2009
by F. Perez, H. P. Langtangen, and R. LeVeque SIAM News 42, Number 5, June 15, 2009.
- Python Tools for Reproducible Research on Hyperbolic Problems
by R. J. LeVeque. Computing in Science and Engineering (CiSE) 11(2009), pp. 19-27. (Special issue on reproducible research.)
- Correction to the article A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources by Vaughan et al.
by J. T. Beale, D. L. Chopp, R. J. LeVeque, and Zhilin Li Comm. Appl. Math. Comput. Sci. 3 (2008), pp. 95-100.