Convergence of an Explicit Iterative Leap-frog Discontinuous Galerkin Method for Time-domain Maxwell's Equations in Anisotropic Materials

We propose an explicit iterative leap-frog discontinuous Galerkin method for time-domain Maxwell's equations in anisotropic materials and derive its convergence properties. The a priori error estimates are illustrated by numerical means in some experiments. Motivated by a real application which encompasses modeling electromagnetic wave's propagation through the eye's structures, we simulate our model in a 2D domain aiming to represent a simple example of light scattering in the outer nuclear layer of the retina.Comment: 14 pages, 6 figure

A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability

In this paper we consider the numerical solution of a coupled geomechanics and a stress-sensitive porous media reservoir flow model.We combine mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. This work focuses on deriving convergence results for the numerical solution of this nonlinear partial differential system. We establish convergence with respect to the L2-norm for the pressure and for the average fluid velocity and with respect to the H1-norm for the deformation. Estimates respect to the L2-norm for mean stress, which is of special importance since it is used in the computation of permeability for poroelasticity, can be derived using the estimates in the H1-norm for the deformation. We start by deriving error estimates in a continuous-in-time setting. A cut-off operator is introduced in the numerical scheme in order to derive convergence. The spatial grids for the discrete approximations of the pressure and deformation do not need be the same. Theoretical convergence error estimates in a discrete-in-time setting are also derived in the scope of this investigation. A numerical example supports the convergence results

Stability of finite difference schemes for complex diffusion processes

In this paper we present a rigorous proof for the stability of a class of finite difference schemes applied to nonlinear complex diffusion equations. Complex diffusion is a common and broadly used denoising procedure in image processing. To illustrate the theoretical results we present some numerical examples based on an explicit scheme applied to a nonlinear equation in the context of image denoising.FCT PTDC/SAU-ENB/111139/200

Improved adaptive complex diffusion despeckling filter

Despeckling optical coherence tomograms from the human retina is a fundamental step to a better diagnosis or as a preprocessing stage for retinal layer segmentation. Both of these applications are particularly important in monitoring the progression of retinal disorders. In this study we propose a new formulation for a well-known nonlinear complex diffusion filter. A regularization factor is now made to be dependent on data, and the process itself is now an adaptive one. Experimental results making use of synthetic data show the good performance of the proposed formulation by achieving better quantitative results and increasing computation speed.Fundação para a Ciência e TecnologiaFEDERPrograma COMPET

Ocular fundus Imaging: from structure to function

Imaging the ocular fundus, namely the retina, to detect and/or monitor changes over time from the healthy condition is of fundamental importance to assess onset and disease progression and is a valuable tool to understand the basic mechanisms of ocular diseases. Current trends point to the need for less or non-invasive approaches, to the need for detailed (higher spatial and temporal resolution) imaging systems and to the quantification as opposed to qualitative classification of any findings. In this work we present a snapshot of our research by presenting two examples of technical development aiming to obtain structural and function information from the human retina, in vivo, using non-invasive techniques, namely optical coherence tomography imaging. Based on our experience and developed work, we are now starting to bridge the gap to brain imaging as the eye is only the starting point of vision.FCTFEDERProgram COMPET

Numerical solution of time-dependent Maxwell’s equations for modeling scattered electromagnetic wave’s propagation

We present the discontinuous Galerkin method combined with a low-storage Runge-Kutta method as an accurate and efficient way to numerically solve the time-dependent Maxwell’s equations. We investigate the numerical scheme in the context of modeling scattered electromagnetic wave’s propagation through human eye’s structures

Cuidados de enfermagem de reabilitação à pessoa com lesão medular metastática: relato de caso

Introdução: A Lesão Medular Metastática (LMM) apresenta-se como uma emergência oncológica, para prevenir lesões neurológicas irreversíveis, tratar a dor, manter a mobilidade e a funcionalidade dos doentes. O foco na alta precoce para casa exige uma rápida adaptação à nova condição, tornando o tempo de internamento complexo e desafiante. Objetivo: Descrever as necessidades de cuidados de enfermagem de reabilitação de uma pessoa com LMM no internamento hospitalar. Métodos: Relato de caso baseado nas guidelines CARE. Resultados: Verificaram-se constantes adaptações ao programa de reabilitação, que exigiram a articulação da equipa multidisciplinar. A intervenção dos enfermeiros de reabilitação na identificação de necessidades, na prevenção de complicações, na capacitação da pessoa e cuidador, foi determinante para um célere e seguro regresso a casa. Conclusão: Identificaram-se necessidades e repostas providenciadas ao doente com LMM em fase aguda. A enfermagem de reabilitação contribuiu para a prevenção de complicações, preparação para a alta e para um regresso a casa seguro.info:eu-repo/semantics/publishedVersio

Stability of finite difference schemes for complex diffusion processes

Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of complex diffusion finite difference scheme