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Chebyshev多项式在频域无限水深格林函数的高效数值逼近中的应用（英文）.docx

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Chebyshev多项式在频域无限水深格林函数的高效数值逼近中的应用（英文） Title:EfficientNumericalApproximationoftheGreen'sFunctionofanInfiniteDepthusingChebyshevPolynomialsinFrequencyDomain Abstract: TheGreen'sfunctionplaysacrucialroleinsolvingproblemsinvolvingwavepropagationininfinitedepthdomains.EfficientandaccuratenumericalapproximationmethodsfortheGreen'sfunctioncansignificantlyenhancethecomputationalefficiencyandfacilitatetheanalysisofwavephenomena.Chebyshevpolynomials,withtheirexcellentapproximationproperties,havebeenwidelyusedinthespectralmethodsforsolvingvariousmathematicalproblems.Inthispaper,weexploretheapplicationofChebyshevpolynomialsinfrequencydomaintoefficientlyapproximatetheGreen'sfunctionofaninfinitedepthdomain. Keywords:Chebyshevpolynomials,Green'sfunction,numericalapproximation,spectralmethod,wavepropagation 1.Introduction TheGreen'sfunctionrepresentsthefundamentalsolutiontoawaveequationinaninfinitedepthdomain,describingtheresponseofasystemtoanimpulseorpointsource.Accurateandefficientapproximationofthisfunctioniscrucialforvariousapplicationsinwavepropagation,suchasseismicanalysis,oceanacousticmodeling,andelectromagneticwavepropagation.Traditionalmethods,suchasthestationaryphasemethodandFouriertransformtechniques,sufferfromlimitationsincomputationalefficiencyandaccuracy.Thisnecessitatesthedevelopmentofalternativeapproaches,suchasthosebasedonspectralmethodsusingChebyshevpolynomials. 2.ChebyshevPolynomialsandtheirProperties Chebyshevpolynomialsareasetoforthogonalpolynomialsdefinedontheinterval[-1,1].Theypossessuniquepropertiesthatmakethemattractiveforapproximationpurposes.Thesepolynomialshaveaboundedrangeof-1to1,minimizingapproximationerrorsneartheendpointsofthedomain.Additionally,theyexhibitclusteringbehaviorneartheboundaries,whichisadvantageousforapproximatingsolutionsoverinfinitedomains. 3.SpectralMethodsinFrequencyDomain SpectralmethodsutilizethepropertiesofChebyshevpolynomialsforefficientapproximationoffunctionsinthefrequencydomain.Bymappingtheinfinitedepthdomaintoaboundeddomainu