Accurate Computation of Mathieu Functions

135 Pages·2013·6.66 MB·English

by  Malcolm M. Bibby, Andrew F. Peterson

Accurate Computation of
Mathieu Functions
Synthesis Lectures on
Computational
Electromagnetics
Editor
ConstatineA.Balanis,ArizonaStateUniversity
SynthesisLecturesonComputationalElectromagneticswillpublish50-to100-pagepublicationson
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AccurateComputationofMathieuFunctions
MalcolmM.BibbyandAndrewF.Peterson
www.morganclaypool.com
ISBN:9781627050852 paperback
ISBN:9781627050869 ebook
DOI10.2200/S00526ED1V01Y201307CEM032
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONCOMPUTATIONALELECTROMAGNETICS
Lecture#32
SeriesEditor:ConstatineA.Balanis,ArizonaStateUniversity
SeriesISSN
SynthesisLecturesonComputationalElectromagnetics
Print1932-1252 Electronic1932-1716
Accurate Computation of
Mathieu Functions
Malcolm M. Bibby and Andrew F. Peterson
GeorgiaInstituteofTechnology
SYNTHESISLECTURESONCOMPUTATIONALELECTROMAGNETICS
#32
M
&C Morgan &cLaypool publishers
ABSTRACT
islecturepresentsamodernapproachforthecomputationofMathieufunctions.esefunc-
tionsfindapplicationinboundaryvalueanalysissuchaselectromagneticscatteringfromelliptic
cylindersandflatstrips,aswellastheanalogousacousticandopticalproblems,andmanyother
applicationsinscienceandengineering.eauthorsreviewthetraditionalapproachusedforthese
functions, show its limitations, and provide an alternative “tuned” approach enabling improved
accuracy and convergence. e performance of this approach is investigated for a wide range of
parameters and machine precision. Examples from electromagnetic scattering are provided for
illustrationandtoshowtheconvergenceofthetypicalseriesthatemployMathieufunctionsfor
boundaryvalueanalysis.
KEYWORDS
ellipticcylinder,electromagneticscattering,boundaryvalueproblems