求解Helmholtz問(wèn)題的最優(yōu)Schwarz算法.pdf

1、學(xué)校代號(hào)：學(xué)號(hào)；密級(jí)：10532S03062003湖南大學(xué)碩士學(xué)位論文求解Helmholtz問(wèn)題的最優(yōu)Schwarz算法Y892753生僮皇逭厶熊名；壺亡直昱垣蛙名叢塑攙：萱壘壬教援靖差皇位；鏨堂皇吐量絲盜堂院童些名整；鹽簋數(shù)堂迨室提童旦塑；2Q逝芏Q旦!旦迨塞鳘避旦鱧；2QQ生鱧且22旦笞整重雖盒圭廑!奎冀蛭塑握碩士學(xué)位論文AbstractHelmholtzequation(一△一u。)釷=，hasbeenwidelyappliedi

2、nphysics，engineeringandscientificcomputationIt’ssignificanttesearchefficientnumericalmethodsforsolvingHelmholtzequationindealingwithmanyphysicalquestionsinsomefields，such82electromagnetics，acousticsandSOonDomaindecomposi

3、tionmethods，developedfromSchwarzalternatingmethod(1870)，havebeenwidelystudiedrecentlyduetotheadvantagesofreducingthelargescaleproblemintosmallerones，reducingthecomplexproblemsintosimplerOllesandturningserialcomputinginto

4、parallelcomputingAfterseveraldozensyearsofdevelopment，especiallywiththerap_iddevelopmentofparallelmachineandparallelcomputingtechnique，correspondingtheoreticresearchesofdomaindecompositionmethodshavemadegreatprogressItsa

5、pphcationshavegraduallyextendedtomanyfieldsInthelastdecent，oneofdomaindecompositionmethods，SchwarzwaveformrelaxationmethodlhasobtainedwidespreadpromotionandapplicationInthispaperwemainlystudyclassicalSchwarzmethodsandits

6、waveformrelaxationvariantforHelmholtzequation，F(xiàn)irstlyweanalyzetheconvergenceofclassicalSchwarzmethodforHeknhottzequationItshowsthattheclassicalSchwarzalgorithmisnoteffectiveforHelmholtzequationEspeciallythealgorithmdiver

7、geswhenthesubdomainshavenooverlapNevertheless，thealgorithmCanbeappliedtoHelmholtzequationbychangingthetransmissionconditionfromDirichletconditionfortheclassicalSchwarzcasetogeneralRobinconditionInthepaper，thecontinuousan

8、ddiscreteoptimaltransmissionconditionsfortheSchwarzalgorithmwithoutoverlapfortheHelmholtzequationarestudiedTheseconditionare，however，nonlocalinnatureInthispaper，weintroducelocalapproximationsforbothcontinuousanddiscreteC

9、ases，whichmayoptimizetheperformanceoftheSchwarzmethodWeconcludeSUchalgorithmintheclassofoptimizedSchwarzmethods，whichbelongtowaveformrelaxationSchwarzalgorithmMoreover，severaikindsofpromotionsofoptim／zedSchwarzmethodarep