Related papers: Goal Oriented Adaptive Finite Element Method for t…
Diffraction limited resolution adaptive optics (AO) correction in visible wavelengths requires a high performance control. In this paper we investigate infinite impulse response filters that optimize the wavefront correction: we tested…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…
In finite-volume-based flow simulations, absorbing layers are widely used to reduce pressure wave reflections at boundaries of the computational domain. A disadvantage of absorbing layers is that they contain case-dependent parameters; thus…
For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These…
This paper is concerned with the numerical approximation of quantities of interest associated with solutions to parametric elliptic partial differential equations (PDEs). The key novelty of this work is in its focus on the quantities of…
With the goal of accurately extracting the optical field losses in a three-dimensional (3D), circularly coiled waveguide (e.g., bent optical fiber), this effort presents the numerical methodologies that are implemented for an envelope…
In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is ``exact'' in that given the approximation inherent in the…
High-Q optical resonances in photonic microcavities are investigated numerically using a time-harmonic finite-element method.
This work is motivated by the need of efficient numerical simulations of gas flows in the serpentine channels used in proton-exchange membrane fuel cells. In particular, we consider the Poisson problem in a 2D domain composed of several…
Adaptive optics can focus light through opaque media by compensating the random phase delay acquired while crossing a scattering curtain. The technique is commonly exploited in many fields, including astrophysics, microscopy, biomedicine…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…
We present a novel parametric finite element approach for simulating the surface diffusion of curves and surfaces. Our core strategy incorporates a predictor-corrector time-stepping method, which enhances the classical first-order temporal…
Geometrical optics (GO) is widely used in studies of electromagnetic materials because of its ease of use compared to full-wave numerical simulations. Exact solutions for waves can, however, differ significantly from the GO approximation.…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
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…