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二维单步交替方向隐式时域有限差分法吸收边界性能分析.docx

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二维单步交替方向隐式时域有限差分法吸收边界性能分析 Abstract: Thetwo-dimensionalsingle-stepsalternatingimplicittime-domainfinite-differencemethod(ADI-TDFDM)iswidelyusedinmodelingwavepropagationinthepresenceofcomplexgeologicalstructures.However,theperformanceofADI-TDFDMintermsofitsabilitytohandleabsorbingboundaryconditionsisstillunderinvestigation.Inthispaper,weexaminetheperformanceofADI-TDFDMwithdifferentabsorbingboundaryconditions,includingthePerfectlyMatchedLayer(PML)andConvolutionalPerfectlyMatchedLayer(CPML),throughnumericalsimulations.Ourresultsindicatethat,foragivensetofparametersandagivennumericalmodel,CPMLhasbetterperformancethanPMLinabsorbingthescatteredwaves. Introduction: TheADI-TDFDMisapowerfulandwidelyusednumericalsimulationmethodinthestudyofwavepropagation.TheADI-TDFDMisbasedonthefinite-differencemethod(FDM)andtheimplicittime-steppingalgorithm.TheADI-TDFDMcanaccuratelysimulatewavepropagationinthepresenceofcomplexgeologicalstructures. TheADI-TDFDMhassubstantialadvantagesoverothernumericalmethodsinmodelingwavepropagation,suchasitsstabilityandcomputationalefficiency.However,theperformanceofADI-TDFDMintermsofitsabilitytohandleabsorbingboundaryconditionsisstillunderinvestigation. Inthispaper,wewillexaminetheperformanceofADI-TDFDMwithdifferentabsorbingboundaryconditions.WefirstintroducetheADI-TDFDManditsimplementationintwo-dimensionalsimulations.Then,wewilldiscussthetheorybehinddifferentabsorbingboundaryconditionsandcomparetheirperformanceusingnumericalsimulation. ADI-TDFDM: TheADI-TDFDMisanumericalsimulationmethodusedtomodelwavepropagation.TheADI-TDFDMisbasedontheimplicittime-steppingalgorithm,whichismorestablethantheexplicittime-steppingalgorithm.TheADI-TDFDMisalsomorecomputationallyefficientthanothernumericalmethods. TheADI-TDFDMisbasedonthefollowingequation: (Eq.1)U^{n+1}=B_x^{-1}(A_yU^{(n+1/2)}+B_yU^{n}+C_yU^{(n-1/2)}) whereUisthewavefield,nisthetimestep,xandyarethespatialdirections,andA,B,andCarematrices. TheADI-TDFDMcanbeimplementedintwo-dimensionalsimulationsasfollows: (Eq.2)