48 citations · 252 across the 96 of their papers we have counts for
6 papers · 1 filter
External optimal control of nonlocal PDEs
Harbir Antil, Ratna Khatri, Mahamadi Warma
Very recently M. Warma has shown that for nonlocal PDEs associated with the fractional Laplacian, the classical notion of controllability from the boundary does not make sense and…
A class of parabolic systems associated with optimal controls of grain boundary motions
Harbir Antil, Ken Shirakawa, Noriaki Yamazaki
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain b…
Certified reduced basis methods for fractional Laplace equations via extension
Harbir Antil, Yanlai Chen, Akil Narayan
Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorith…
A Note on QR-Based Model Reduction: Algorithm, Software, and Gravitational Wave Applications
Harbir Antil, Dangxing Chen, Scott E. Field
While the proper orthogonal decomposition (POD) is optimal under certain norms it's also expensive to compute. For large matrix sizes, it is well known that the QR decomposition pr…
Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications
Harbir Antil, Carlos N. Rautenberg
We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muc…
A problem in control of elastodynamics with piezoelectric effects
Harbir Antil, Thomas S. Brown, Francisco-Javier Sayas
We consider an optimal control problem where the state equations are a coupled hyperbolic-elliptic system. This system arises in elastodynamics with piezoelectric effects -- the el…