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Finite Element Methods for Maxwell's Equations

Peter Monk

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.001.0001
Subject:
Mathematics, Numerical Analysis

Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell’s equations is now an increasingly important tool in science and ... More


Local Error Estimate and Variable Stepsize

Alfredo Bellen and Marino Zennaro

in Numerical Methods for Delay Differential Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506546
eISBN:
9780191709609
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506546.003.0007
Subject:
Mathematics, Numerical Analysis

This chapter focuses on the stepsize control mechanism, which plays a central role in the production of efficient numerical codes for DDEs. In particular, the importance of the choice of the ... More


Finite Elements Methods for the Cavity Problem

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0007
Subject:
Mathematics, Numerical Analysis

This chapter concerns the use of edge finite element methods to approximate the cavity problem with mixed boundary data. It provides two proofs of convergence of the discrete solution. First under ... More


Finite Elements on Tetrahedra

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0005
Subject:
Mathematics, Numerical Analysis

The finite element method is based on a geometric decomposition of the domain of Maxwell’s equations into simple elements. This chapter is devoted to tetrahedral elements, which are very common in ... More


FUNDAMENTAL CONCEPTS IN ONE DIMENSION

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0002
Subject:
Mathematics, Numerical Analysis

This chapter discusses the fundamental concepts that are further developed in the remainder of the book, in the context of a one-dimensional formulation. In doing so, the principles and underlying ... More


Scattering by a Bounded Inhomogeneity

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0011
Subject:
Mathematics, Numerical Analysis

This chapter continues the approximation of the field scattered by a bounded object. In this case, a penetrable scatterer (i.e., not a perfect conductor) is considered and the analysis of the ... More


The Scattering Problem Using Calderon Maps

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0010
Subject:
Mathematics, Numerical Analysis

This chapter presents a finite element method for scattering by a bounded scatterer in an infinite homogeneous background. The first task is to reduce the problem to a bounded domain, and in this ... More


Finite Elements on Hexahedra

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0006
Subject:
Mathematics, Numerical Analysis

An alternative to the tetrahedral elements discussed in the previous chapter is to use finite elements based on cubes, or more generally, hexahedra. Hexahedral elements have been used in several ... More


Measuring Uncertainty and Error Directly from End Estimates

Andrea Volkens, Judith Bara, Ian Budge, Michael D. McDonald, Robin Best, and Simon Franzmann

in Mapping Policy Preferences From Texts: Statistical Solutions for Manifesto Analysts

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199640041
eISBN:
9780191757181
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199640041.003.0007
Subject:
Political Science, Comparative Politics

This chapter starts by re-emphasising the importance of context in assessing estimate uncertainty and error. This not only means bringing general validity and reliability to the assessment but also ... More


Business Forecasting and Credit Decisions

Hrishikes Bhattacharya

in Banking Strategy, Credit Appraisal, and Lending Decisions: A Risk–Return Framework

Published in print:
2011
Published Online:
September 2012
ISBN:
9780198074106
eISBN:
9780199080861
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198074106.003.0013
Subject:
Economics and Finance, Financial Economics

This chapter discusses one of the most reliable and commonly used techniques of business forecasting, and develops an appraisal methodology by applying this technique. Of the various statistical ... More


Advantages of Cognitive Limitations

Yaakov Kareev

in Evolution and the Mechanisms of Decision Making

Published in print:
2012
Published Online:
May 2016
ISBN:
9780262018081
eISBN:
9780262306027
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262018081.003.0010
Subject:
Psychology, Social Psychology

Being a product of evolutionary pressures, it would not be surprising to find that what seems to be a limitation of the cognitive system is actually a fine-tuned compromise between a set of competing ... More


Metric-Based Approaches for Semi-Supervised Regression and Classification

Schuurmans Dale, Southey Finnegan, Wilkinson Dana, and Guo Yuhong

in Semi-Supervised Learning

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262033589
eISBN:
9780262255899
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033589.003.0023
Subject:
Computer Science, Machine Learning

This chapter discusses the explicit relationship that must be asserted between labeled and unlabeled data, which is a requirement of semi-supervised learning methods. Semi-supervised model selection ... More


Explicit Error Bounds via Total Variation

Lutz Dümbgen and Christoph Leuenberger

in Benford's Law: Theory and Applications

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691147611
eISBN:
9781400866595
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147611.003.0005
Subject:
Mathematics, Probability / Statistics

This chapter concerns the obtaining of explicit error estimates for convergence to Benford's law, with an analysis done through the total variation of the densities. This method yields reasonable ... More


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