Nonreflecting boundary conditions

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1、NONREFLECTINGBOUNDARYCONDITIONSadissertationsubmittedtotheprograminscientificcomputingandcomputationalmathematicsandthecommitteeongraduatestudiesofstanforduniversityinpartialfulfillmentoftherequirementsforthedegreeofdoctorofphilosophyByMarcusJ.GroteJune

2、1995cCopyright1995byMarcusJ.GroteAllRightsReservediiIcertifythatIhavereadthisdissertationandthatinmyopinionitisfullyadequate,inscopeandinquality,asadissertationforthedegreeofDoctorofPhilosophy.ProfessorJosephB.Keller(PrincipalAdviser)IcertifythatIhavere

3、adthisdissertationandthatinmyopinionitisfullyadequate,inscopeandinquality,asadissertationforthedegreeofDoctorofPhilosophy.ProfessorGeneH.GolubIcertifythatIhavereadthisdissertationandthatinmyopinionitisfullyadequate,inscopeandinquality,asadissertationfor

4、thedegreeofDoctorofPhilosophy.ProfessorJosephE.OligerApprovedfortheUniversityCommitteeonGraduateStudies:DeanofGraduateStudiesiiiMeinenEltern,undmeinemBruderJanivAbstractUnboundeddomainsoftenariseinengineeringapplications,suchasacousticorelec-tromagnetic

5、scatteringfromabodyofarbitraryshapeimmersedinaninnitemedium.Numericalmethodscanhandlecomplicatedgeometries,inhomogeneousmediaandnonlinearities.Yettheyrequireanarticialboundary,whichsurroundstheregionofinterest,totruncatetheunboundedexteriordomainandt

6、theinniteproblemonanitecomputer.Asaconsequence,nonre ectingboundaryconditionsmustbeimposedatthearticialboundary,toensurethatitappearstransparenttotheprop-agatingwavesanddoesnotgenerateanyspuriousre ections.Thisworkpresentsexactnonre ectingboundarycon

7、ditionsatarticialboundariesforthenumericalsolutionoftheHelmholtzequationandthetimedependentwaveequationinunboundeddomains.Theseboundaryconditionsensurethatthesolutioninsidetheboundeddomaincoincideswiththesolutionoftheoriginalunboundedproblem.Inthetimeh

8、armoniccase,themodiedDtNconditionisintroducedtoremovethedicultiesthatarisewhentheexactDtN(Dirichlet-to-Neumann)conditionistruncatedforuseincomputation.Thisensureswell-posednessandhigheraccuracyofthetruncatedboundarycondition.Th