scholarly journals TIME ACCURATE FAST THREE-STEP WAVELET-GALERKIN METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 04 (01) ◽  
pp. 65-79 ◽  
Author(s):  
MANI MEHRA ◽  
B. V. RATHISH KUMAR
Keyword(s):  
Galerkin Method ◽  
Numerical Experiments ◽  
Nonlinear Problems ◽  
Taylor Series Expansion ◽  
Two Dimensions ◽  
One Dimension ◽  
Advection Equation ◽  
Galerkin Methods ◽  
Present Scheme ◽  
Wavelet Galerkin Method

We introduce the concept of three-step wavelet-Galerkin method based on the Taylor series expansion in time. Unlike the Taylor–Galerkin methods, the present scheme does not contain any new higher-order derivatives which makes it suitable for solving nonlinear problems. Numerical schemes taking advantage of the wavelet bases capabilities to compress the operators and sparse representation of functions which are smooth, except for localized regions, up to any given accuracy are presented. Here numerical experiments deal with advection equation with the spiky solution in one dimension, two dimensions and nonlinear equation with a shock in solution in two dimensions. Numerical results indicate the versatility and effectiveness of the proposed scheme.

scholarly journals Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems with Rough Data

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Konrad Simon ◽  
Jörn Behrens
Keyword(s):  
Nonlinear Problems ◽  
Higher Dimensions ◽  
Two Dimensions ◽  
Multiscale Methods ◽  
Galerkin Methods ◽  
Standard Methods ◽  
Multiscale Problems ◽  
Eulerian Method ◽  
Lower Order Terms ◽  
New Framework

AbstractWe introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when the model involves dominant lower order terms. Our idea to overcome the associated difficulties is a semi-Lagrangian based reconstruction of subgrid variability into a multiscale basis by solving many local inverse problems. Globally the method looks like a Eulerian method with multiscale stabilized basis. We show example runs in one and two dimensions and a comparison to standard methods to support our ideas and discuss possible extensions to other types of Galerkin methods, higher dimensions and nonlinear problems.

A Note on the Convergence Analysis of a Diffuse-domain Approach

2012 ◽  
Vol 12 (2) ◽  
pp. 153-167 ◽  
Author(s):  
Sebastian Franz ◽  
Hans-Görg Roos ◽  
Roland Gärtner ◽  
Axel Voigt
Keyword(s):  
Differential Equation ◽  
Convergence Analysis ◽  
Plane Problem ◽  
Half Plane ◽  
Numerical Experiments ◽  
Two Dimensions ◽  
Elliptic Differential Equation ◽  
One Dimension ◽  
Approximation Quality

Abstract We analyse the error behaviour of a diffuse-domain approximation of an elliptic differential equation. In one dimension and for a half-plane problem in two dimensions an approximation quality of order one in the interface parameter is shown. Some supporting numerical experiments are also presented.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

scholarly journals COUNTRY MATTERS: WELL-BEING AND EMIGRATION PLANS AMONG UNIVERSITY STUDENTS IN SLOVAKIA AND BULGARIA: THE MEDIATION EFFECT OF ROOTEDNESS

2020 ◽  
pp. 107-119
Author(s):  
Frederika Lučanská ◽  
◽  
Oľga Orosová ◽  
Vihra Naydenova ◽  
Jozef Benka ◽  
...  
Keyword(s):  
University Students ◽  
Exploratory Study ◽  
Online Survey ◽  
Well Being ◽  
Two Dimensions ◽  
Mediation Effect ◽  
One Dimension ◽  
Psychological Mechanisms ◽  
The Relationship

The objective of this exploratory study was to examine the relationship between well-being, rootedness and emigration plans (EP) among university students in Slovakia and Bulgaria. It also explored the mediation effect of rootedness in the relationship between well-being and EP. The data were collected throughan online survey (SLiCE 2016). The research sample consisted of 361 university students (M=22.4 years, SD=3.8) from Slovakia (141, 86.5% female) and Bulgaria (220, 69.1% female). Based on their emigration plans, the respondentswere dividedinto two groups;those who do not plan to leave (n=218, 60.4%) and those who plan to leave in the long term (n=143, 39.6%) after they finish university. ForSlovakia, all factors were significantly related toEP. Furthermore, the association between well-being and EP was fully mediated by two dimensions of rootedness with different psychological mechanisms. For Bulgaria, only well-being and onedimension of rootedness,desire for change,were significantly related to EP. It was also found that the association between well-being and EP was partially mediated by only one dimension of rootedness –desire for change. This study highlightsthat rootedness hasa different relationship with other examined factorsin different countries and also that it is necessary to respect the cultural and socio-economic featuresof acountry.

Sign in / Sign up

Export Citation Format

Share Document