[1] He is known for his contributions to numerical analysis of Partial Differential equations particularly in the fields of computational fluid dynamics, computational electromagnetics, acoustics, elasticity and image processing with applications to first Temple ostraca and recently deep earning for forward and inverse problems in PDEs, His research interests include algorithms solving partial differential equations (PDEs) including scattering and inverse scattering, image processing, and crack propagation.
Another main contribution includes fast algorithms for the Navier-Stokes equations based on preconditioning techniques, radiation boundary conditions and high order accuracy for wave propagation in general shaped domains using difference potentials.
Algorithmic handwriting analysis of Judah’s military correspondence sheds light on the composition of biblical texts, which appeared in PNAS was quoted by numerous sources including the front page of the NY Times.
Other research uses deep learning to detect sources and obstacles underwater using the acoustic wave equation and data at a few noisy sensors.
Recent applications of deep learning include using large time steps and improving the accuracy of finite differences for high frequencies on coarse grids.