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A new homogenization-free boundary condition is introduced for the design of metasurfaces. The boundary condition, linking the tangential electric field to the induced surface current density within a unit cell, is described as a matrix…
Scattering of electromagnetic (EM) waves by many small particles, embedded in a given medium, is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for the effective…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
Integration of metasurfaces with guided mode sources like waveguides have opened new frontiers for on-chip optical integration. However, the state-of-the-art in the field has targeted applications where long focal distances over thousands…
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…
We introduce a new Large Eddy Simulation model in a channel, based on the projection on finite element spaces as filtering operation in its variational form, for a given triangulation $\{{\cal T}_h \}_{h>0}$. The eddy viscosity is expressed…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
Wavefront shaping is a technique for directing light through turbid media. The theoretical aspects of wavefront shaping are well understood, and under near-ideal experimental conditions, accurate predictions for the expected signal…
This paper proposes a novel real-time algorithm for controlling wave energy converters (WECs). We begin with the economic model predictive control (MPC) problem formulation and apply a novel, first-order optimization algorithm inspired by…
Within the MNPBEM toolbox, developed for the simulation of plasmonic nanoparticles using a boundary element method approach, we show how to include substrate and layer structure effects. We develop the methodology for solving Maxwell's…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
Credibility building activities in computational research include verification and validation, reproducibility and replication, and uncertainty quantification. Though orthogonal to each other, they are related. This paper presents…
We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal…
A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both…
Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…
The paper is an attempt to generalize a methodology, which is similar to the bounded-input bounded-output method currently widely used for the system stability studies. The presented earlier methodology allows decomposition of input space…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…