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In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…
Fundamental bounds on quadratic electromagnetic metrics are formulated and solved via convex optimization. Both dual formulation and method-of-moments formulation of the electric field integral equation are used as key ingredients. The…
We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…
We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a…
Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is…
We present a new method for computing the transverse transfer matrix through superimposed axisymmetric RF and solenoid field maps. The algorithm constructs the transfer matrix directly from one dimensional RF and solenoid field maps without…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Seismic traveltime tomography represents a popular and useful tool for unravelling the structure of the subsurface across the scales. In this work we address the case where the forward model is represented by the eikonal equation and derive…
A fundamental challenge in the design of photonic devices, and electromagnetic structures more generally, is the optimization of their overall architecture to achieve a desired response. To this end, topology or shape optimizers based on…
We present here a brief overview of our work in developing a convolutionless quantum master equation approach suitable for mesoscopic sized systems. Our final equation can be used in the regimes where the golden rule approach is not…
In this work, we propose an adjoint-based optimization procedure to control the onset of the Rayleigh-B\'enard instability with a melting front. A novel cut cell method is used to solve the Navier-Stokes equations in the Boussinesq…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
We develop a sensitivity function for the design of electron optics using an adjoint approach based on a form of reciprocity implicit in Hamilton's equations of motion. The sensitivity function, which is computed with a small number of…
The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off--lattice model featuring spherocylinders with continuous…
This paper considers the optimal control problem for realizing logical gates in a closed quantum system. The quantum state is governed by Schrodinger's equation, which we formulate as a time-dependent Hamiltonian system in terms of the real…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
This paper presents an adjoint-assisted, topology-optimization-inspired approach for analyzing topological sensitivities in fluid domains based on porous media formulations -- without directly utilizing the porosity field as a design…
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…