Search results for "Discontinuities"

Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques

2008

Abstract This paper introduces and analyzes new approximation procedures for bivariate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one-dimensional setting by Harten and Osher. Edge-adapted reconstructions are tailored to piecewise smooth functions with geometrically smooth edge discontinuities, and are therefore attractive for applications such as image compression and shock computations. The local approximation order is investigated both in L p and in the Hausdorff distance between graphs. In particular, i…

On a new centered strategy to control the accuracy of weighted essentially non oscillatory algorithm for conservation laws close to discontinuities

2020

Efficient boundary integral-resonant mode expansion method implementation for full-wave analysis of passive devices based on circular waveguides with…

2013

In this study, the efficient full-wave analysis of passive devices composed of circular and arbitrarily-shaped waveguides is considered. For this purpose, the well-known boundary integral-resonant mode expansion (BI RME) method has been properly extended. Circular waveguides are used for resonant mode expansion, whereas the arbitrary contour is defined by any combination of straight, circular and elliptical segments, thus allowing the exact representation of the most widely used geometries. The proposed algorithm extends previous implementations of the BI RME method based on circular waveguides by considering circular and elliptical arcs for defining arbitrary geometries. Similarly, it allo…

Fake Nodes approximation for Magnetic Particle Imaging

2020

Accurately reconstructing functions with discontinuities is the key tool in many bio-imaging applications as, for instance, in Magnetic Particle Imaging (MPI). In this paper, we apply a method for scattered data interpolation, named mapped bases or Fake Nodes approach, which incorporates discontinuities via a suitable mapping function. This technique naturally mitigates the Gibbs phenomenon, as numerical evidence for reconstructing MPI images confirms.

On the application of the generalized means to construct multiresolution schemes satisfying certain inequalities proving stability

2021

Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence o…

Fine-Mesh Numerical Simulations for 2D Riemann Problems with a Multilevel Scheme

2001

The numerical simulation of physical problems modeled by systems of conservation laws can be difficult due to the occurrence of discontinuities and other non-smooth features in the solution.

Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density

2014

Abstract We study the large time behavior of solutions to the Cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density | x | − 2 ∂ t u = Δ u m , in R N × ( 0 , ∞ ) , where m > 1 and N ≥ 3 , with nonnegative initial condition u ( x , 0 ) = u 0 ( x ) ≥ 0 . The asymptotic behavior proves to have some interesting and striking properties. We show that there are different asymptotic profiles for the solutions, depending on whether the continuous initial data u 0 vanishes at x = 0 or not. Moreover, when u 0 ( 0 ) = 0 , we show the convergence towards a peak-type profile presenting a jump discontinuity, coming from an interesting asymptotic simplification…

A Space-Time Meshless Method for Heat Transfer Problems With High Discontinuities

2013

The aim of this research is the development of a space-time driscretization method based on Diffuse Approximation Meshless method. This method, devoted to transient heat transfer problems presenting high temporal discontinuities, avoids any Finite-Difference time stepping procedure. The space-time discretization proposed here seems to be convenient for continuous transient heat transfer. Nevertheless, for problems including temporal discontinuities, some spurious oscillations, whose amplitudes depend on source power, appear. A new weight function respecting the principle of causality, based on a modification of the involved node’s selection and a normalisation of the distances, is developed…

Multi-level coupled cluster theory

2014

We present a general formalism where different levels of coupled cluster theory can be applied to different parts of the molecular system. The system is partitioned into subsystems by Cholesky decomposition of the one-electron Hartree-Fock density matrix. In this way the system can be divided across chemical bonds without discontinuities arising. The coupled cluster wave function is defined in terms of cluster operators for each part and these are determined from a set of coupled equations. The total wave function fulfills the Pauli-principle across all borders and levels of electron correlation. We develop the associated response theory for this multi-level coupled cluster theory and prese…

An interface model for analysis of deformation behaviour of discontinuities

1996

An interface constitutive model is presented accounting for slip and sliding effects and also for dilatancy phenomena. The microslip effects are described by considering spherical asperity interaction with variation of contact area and generation of progressive or reverse slip zones. The incremental constitutive equations are derived with proper memory rules accounting for generation and annihilation of particular slip zones during the process of variable loading. It is further assumed that sliding of spherical contacts occurs along large asperities whose slope varies due to the wear process. The predicted shear and dilatancy curves are shown to provide close quantitative simulation of avai…