32 documents found, page 1 of 4

Very high-order accurate discontinuous Galerkin method for curved boundaries wi...

Preserving the optimal convergence order of discontinuous Galerkin (DG) discretisations in curved domains is a critical and well-known issue. The proposed approach relies on the reconstruction for off-site data (ROD) method developed originally within the finite volume framework. The main advantages are simplicity, since the PDE solver only considers polyg- onal domains, and versatility, since any type of bound...

A mathematical model for the corneal transparency problem

Understanding the physical basis of corneal transparency has been a subject of interest amongst physicists, basic scientists and ophthalmologists. Impairment of corneal clarity is a significant cause of visual morbidity worldwide. Thus, it is essential to understand the mechanisms behind corneal transparency and how the alterations due to corneal pathologies affect vision. We use Maxwell’s equations to model li...

Mathematical models of the spread and consequences of the SARS-CoV-2 pandemics:...

Convergence of an explicit iterative leap-frog discontinuous Galerkin method fo...

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 do...

Convergence of an explicit iterative leap-frog discontinuous Galerkin method fo...

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 do...

Cross-Diffusion Systems for Image Processing: II. The Nonlinear Case

In this paper we study the application of 2×2 nonlinear cross-diffusion systems as mathematical models of image filtering. These are systems of two nonlinear, coupled partial differential equations of parabolic type. The nonlinearity and cross-diffusion character are provided by a nondiagonal matrix of diffusion coefficients that depends on the variables of the system. We prove the well-posedness of an initial-...

Stability of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell'...

In this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a fully explicit leap-frog type discontinuous Galerkin method. We present a sufficient condition for the stability and error estimates, for cases of typical boundary conditions, either perfect electric, perfect magnetic or first order Silver-Müller. The bounds of the stability region point out the influence of n...

Cross-Diffusion Systems for Image Processing: I. The Linear Case

The use of cross-diffusion problems as mathematical models of different image processes is investigated. Here the image is represented by two real-valued functions which evolve in a coupled way, generalizing the approaches based on real and complex diffusion. The present paper is concerned with linear filtering. First, based on principles of scale invariance, a scale-space axiomatic is built. Then, some propert...

Physical model of MDF boards

Aims to provide a physical model of MDF boards used in the manufacture of kitchen furniture doors. The existence of a board physical model and handling process (smoothing, drilling, and painting/lacquering) will allow computing (numerically) the board behavior when subject to the multiple physical phenomena taking place. The ability to numerically simulate the occurrence of defects would allow the determination...

Physical model of MDF boards

IKEA Industry is one of the biggest furniture manufacturers worldwide, due to high quality standards and strong cost consciousness, that made IKEA brand the leader in life at home. Part of IKEA supply chain, IKEA Industry in Paços de Ferreira stands for a ordable solutions for better living, by caring IKEAs values with humbleness and wield power, in striving to meet reality with constant desire for renewal, and...