AfastadaptivesymplecticalgorithmnamedMultiresolutionSymplecticScheme(MSS)wasfirstpresentedtosolvetheproblemofthewavepropagation(WP)incomplexmedia,usingthesymplecticschemeandDaubechies'compactlysupportedorthogonalwavelettransformtorespectivelydiscretisethetimeandspacedimensionofwaveequation.TheproblemwassolvedinmultiresolutionsymplecticgeometryspaceundertheconservativeHamiltoniansystemratherthanthetraditionalLagrangesystem.Duetothefascinatingpropertiesofthewaveletsandsymplecticscheme,MSSisapromisingmethodbecauseoflittlecomputationalburden,robustnessandrealityoflong-timesimulation.
