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Dynamic optimization is currently limited by sensitivity computations that require information from full forward and adjoint wave fields. Since the forward and adjoint solutions are computed in opposing time directions, the forward solution…
Diffractive optical elements with a large diffraction angle require feature sizes down to sub-wavelength dimensions, which require a rigorous electromagnetic computational model for calculation. However, the computational optimization of…
Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern…
Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…
We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To…
This paper introduces the application of the asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, which asynchronous convergence is established under…
In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge amount of frames are generated, and thus it poses a great demand of parallel computing in order to solve this large-scale…
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…
Inverse design techniques in the context of nanophotonics have helped in discovery of compact and counter-intuitive structures/shapes. We introduce the concept of spectral domain inverse design to search through the optical trade-space…
Complementation, the inverse of the reduced product operation, is a technique for systematically finding minimal decompositions of abstract domains. File' and Ranzato advanced the state of the art by introducing a simple method for…
Many optimization problems in electrical engineering consider a large number of design parameters. A sensitivity analysis identifies the design parameters with the strongest influence on the problem of interest. This paper introduces the…
This paper presents a novel backtracking strategy for additive Schwarz methods for general convex optimization problems as an acceleration scheme. The proposed backtracking strategy is independent of local solvers, so that it can be applied…
This work focuses on numerically solving a shape identification problem related to advection-diffusion processes with space-dependent coefficients using shape optimization techniques. Two boundary-type cost functionals are considered, and…
In this paper, we develop a dual alternating direction method of multipliers (ADMM) for an image decomposition model. In this model, an image is divided into two meaningful components, i.e., a cartoon part and a texture part. The…
The design of RFIC often involves exploring a large number of design variations in an invariant background composed of the processing stack and unchanged circuit blocks. Conventional electromagnetic solvers require a full-domain simulation…
We present sharp estimates for the extremal eigenvalues of the Schur complements arising in saddle point problems. These estimates are derived using the auxiliary space theory, in which a given iterative method is interpreted as an…
For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from…
Rapid advances in deep learning have brought not only myriad powerful neural networks, but also breakthroughs that benefit established scientific research. In particular, automatic differentiation (AD) tools and computational accelerators…
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…
Full-wave simulations are indispensable for nanophotonics and electromagnetics but are severely constrained on large systems, especially multi-channel ones such as disordered media, aperiodic metasurfaces, and densely packed photonic…