scholarly journals Galerkin methods for a Schrödinger-type equation with a dynamical boundary condition in two dimensions

2015 ◽  
Vol 49 (4) ◽  
pp. 1127-1156 ◽  
Author(s):  
D. C. Antonopoulou
Keyword(s):  
Boundary Condition ◽  
Type Equation ◽  
Two Dimensions ◽  
Galerkin Methods ◽  
Dynamical Boundary Condition

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.

The Effect of Spatial Distance and Domain Knowledge Distinctiveness on Auditor Reliance on IT Specialists

2019 ◽  
Vol 34 (1) ◽  
pp. 81-103 ◽  
Author(s):  
Rina M. Hirsch
Keyword(s):  
Boundary Condition ◽  
Social Identity ◽  
Social Identity Theory ◽  
Domain Knowledge ◽  
Identity Theory ◽  
Two Dimensions ◽  
Spatial Distance ◽  
Social Biases ◽  
Office Location

ABSTRACT Due to limitations in IT expertise, auditors frequently rely upon IT specialists during audit engagements. Does social similarity between the auditor and an IT specialist induce social biases that affect the auditor's reliance on the specialist? Using an experiment with 60 auditors, I examine how financial auditors' reliance on IT specialists is affected by two dimensions of social similarity: the IT specialist's spatial distance (in-house office location versus sourcing from another office) and domain knowledge distinctiveness (distinct versus overlapping) relative to financial auditors. My findings provide evidence of a possible boundary condition to the widely accepted social identity theory by documenting the interaction of two dimensions of social similarity on auditor behavior. Specifically, when IT specialists possess distinct (overlapping) domain knowledge, auditors place greater (similar) reliance on out-of-office specialists relative to in-house specialists.

scholarly journals Numerical Solution of Acoustic Scattering by an Adaptive DtN Finite Element Method

2013 ◽  
Vol 13 (5) ◽  
pp. 1277-1244 ◽  
Author(s):  
Xue Jiang ◽  
Peijun Li ◽  
Weiying Zheng
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Adaptive Method ◽  
Two Dimensions ◽  
Adaptive Finite Element ◽  
Acoustic Wave Scattering

AbstractConsider the acoustic wave scattering by an impenetrable obstacle in two dimensions, where the wave propagation is governed by the Helmholtz equation. The scattering problem is modeled as a boundary value problem over a bounded domain. Based on the Dirichlet-to-Neumann (DtN) operator, a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle. An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition. Numerical experiments are included to compare with the perfectly matched layer (PML) method to illustrate the competitive behavior of the proposed adaptive method.

scholarly journals 2nd Order Parallel Splitting Methods for Heat Equation

2017 ◽  
Vol 1 (1) ◽  
pp. 01-10
Author(s):  
M. Aziz ◽  
M. A. Rehman
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Two Dimensions ◽  
Splitting Technique ◽  
Local Boundary ◽  
Local Boundary Condition ◽  
Non Local ◽  
Parallel Splitting ◽  
Matrix Exponential Function ◽  
Order Parallel

In this paper, heat equation in two dimensions with non local boundary condition is solved numerically by 2nd order parallel splitting technique. This technique used to approximate spatial derivative and a matrix exponential function is replaced by a rational approximation. Simpson’s 1/3 rule is also used to approximate the non local boundary condition. The results of numerical experiments are checked and compared with the exact solution, as well as with the results already existed in the literature and found to be highly accurate.

scholarly journals The large diffusion limit for the heat equation with a dynamical boundary condition

2020 ◽  
Vol 23 (01) ◽  
pp. 2050003
Author(s):  
Marek Fila ◽  
Kazuhiro Ishige ◽  
Tatsuki Kawakami
Keyword(s):  
Boundary Condition ◽  
Diffusion Coefficient ◽  
Heat Equation ◽  
Half Space ◽  
Laplace Equation ◽  
Diffusion Limit ◽  
Dynamical Boundary Condition ◽  
Suitable Sense ◽  
Large Diffusion

We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the Laplace equation with the same dynamical boundary condition.

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