Christina Frederick


Assistant Professor

Department of Mathematical Sciences

New Jersey Institute of Technology


office: CULM 518

email: christin [at] njit [dot] edu

phone: 9735965328




Multiscale Modeling and Inverse Problems

My research focuses on inverse problems for multiscale partial differential equations (PDEs) in which solution data is used to determine coefficients in the equation. PDE-constrained inverse problems can pose a huge computational challenge, in particular when the coefficients are of multiscale form. The mathematical analysis is based on homogenization theory for PDEs and applied harmonic analysis in the form of information theory. The numerical analysis involves the design of algorithms that incorporate techniques from multiscale computation to forward modeling. This research can be applied to microstructure recovery problems arising in exploration seismology, medical imaging, and underwater acoustics.



Sampling Theory and Riesz bases of exponentials

These studies establish the close relation between computational grids in multiscale modeling and sampling strategies developed in information theory. We consider multiscale functions of the type that are studied in averaging and homogenization theory and in multiscale modeling. Using results regarding inverse Vandermonde matrices, we prove that under certain band limiting conditions these multiscale functions can be uniquely and stably recovered from non-uniform samples of optimal rate. It is also interesting to extend this study to multivariate bandlimited functions and higher dimensional sampling lattices.



Applications in Engineering and Science