Related papers: An adaptive finite element/finite difference domai…
We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell's…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
The aim of this paper is to propose an optimal control optimization algorithm for reconstructing admittivity distributions (i.e., both conductivity and permittivity) from multi-frequency micro-electrical impedance tomography. A convergent…
This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
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 new method for the numerical reconstruction of the variable refractive index of multi-layered circular weakly guiding dielectric waveguides using the measurements of the propagation constants of their eigenwaves. Our numerical…
This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-based a posteriori error estimator is both an upper and lower…
We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…
We introduce a new domain decomposition strategy for time harmonic Maxwell's equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is…
We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error…
Model-based reconstruction approaches for the medical imaging modality Magnetic Particle Imaging (MPI) are typically based on the Langevin model, which assumes instantaneous alignment of the particles magnetic momenta with the applied…
A deep learning model is proposed for reconstructing 2D dielectric breast images from time-domain signals. Unlike existing learning models that employ a fixed antenna array, where input data consists solely of measurements, the proposed…
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions…
This paper deals with the reconstruction of small-amplitude perturbations in the electric properties (permittivity and conductivity) of a medium from boundary measurements of the electric field at a fixed frequency. The underlying model is…
We calculate the effective electromagnetic Lagrangian up to the lowest-order corrections in the derivatives for two fermionic systems of interest in condensed matter physics in the linearized approximation of the tight-binding Hamiltonian…
Breast lesion localization using tactile imaging is a new and developing direction in medical science. To achieve the goal, proper image reconstruction and image registration can be a valuable asset. In this paper, a new approach of the…
We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) =…
We investigate numerically the homogenized permittivities of composites made of low index dielectric inclusions in a ferroelectric matrix under a static electric field. A refined model is used to take into account the coupling between the…