- Boundary integral equations, especially retarded potentials and Time Domain BIE
- Discontinuous Galerkin methods, with a focus on the Hybridizable DG scheme
- Scattering and wave propagation, with an emphasis on transient acoustic and elastic waves
- Coupling of different numerical methods, especially BEM with FEM/DG
- Stokes and Stokes-Darcy flow
Current members (spring 2019)
F.J. Sayas (adviser), Allan Hungria, Shukai Du, Hasan
Eruslu, and Hugo Diaz (graduate students)
- Our new book Variational Techniques for Elliptic Partial Differential Equations: Theoretical Tools and Advanced Applications, the brick is being published by CRC press. It will be available on February 5, 2019.
- NSF Grant. 2018-2021. NSF-DMS 1818867. Simulation
and numerical analysis in elastodynamics.
Not so new, but still interesting
- Recent NSF Grant. 2012-2016. NSF-DMS 1216356. Numerical simulation and analysis of transient waves in unbounded domains.
- The deltaBEM code is available in this new site. All the code is ready to be downloaded.
- The monograph Retarded Potentials and Time Domain Integral Equations, a road map, has been published by Springer Verlag as Volume 50 of their series in Computational Mathematics
- SIAM Review republished the paper The validity of
Johnson-Nedelec's BEM-FEM coupling on polygonal
interfaces in their SIGEST section.
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University of Delaware.