简介：Inmagneticresonanceelastography,oneseekstoreconstructtheshearmodulusfrommeasurementsofthedisplacementfieldinthewholebody.Inthispaper,wepresentanoptimizationapproachwhichsolvestheproblembysimplyminimizingadiscrepancyfunctional.Inordertorecoveracomplexanomalyinahomogenousmedium,wefirstobservethattheinformationcontainedinthewavefieldshouldbedecomposedintotwoparts,a'near-field'partintheregionaroundtheanomalyanda'far-field'partintheregionawayfromtheanomaly.Aswillbejustifiedboththeoreticallyandnumerically,separatingthesescalesprovidesalocalandprecisereconstruction.

简介：Asanimportantmodelinquantumsemiconductordevices,theSchrodinger-Poissonequationshavegeneratedwidespreadinterestsinbothanalysisandnumericalsimulationsinrecentyears.Inthispaper,wepresentGaussianbeammethodsforthenumericalsimulationoftheone-dimensionalSchrodinger-Poissonequations.TheGaussianbeammethodsforhighfrequencywavesoutperformthegeometricalopticsmethodinthattheformerareaccurateevenaroundcaustics.ThepurposesofthepaperarefirsttodeveloptheGaussianbeammethods,basedonourpreviousmethodsforthelinearSchrodingerequation,fortheSchrodinger-Poissonequations,andthenchecktheirvalidityforthisweakly-nonlinearsystem.

简介：Westudythenumericalbehavioursoftherelaxedasynchronousmultisplittingmethodsforthelinearcomplementarityproblemsbysolvingsometypicalproblemsfrompracticalapplicationsonarealmultiprocessorsystem.Numericalresultsshowthattheparallelmultisplittingrelaxationmethodsalwaysperformmuchbetterthanthecorrespondingsequentialalternatives,andthattheasynchronousmultisplittingrelaxationmethodsoftenoutperformtheircorrespondingsynchronouscounterparts.Moreover,thetwo-sweeprelaxedmultisplittingmethodshavebetterconvergencepropertiesthantheircorrespondingone-sweeprelaxedonesinthesensethattheyhavelargerconvergencedomainsandfasterconvergencespeeds.Hence,theasynchronousmultisplittingunsymmetricrelaxationiterationsshouldbethemethodsofchoiceforsolvingthelargesparselinearcomplementarityproblemsintheparallelcomputingenvironments.

简介：Inthispaper,weconsiderthelocaldiscontinuousGalerkinmethod(LDG)forsolv-ingsingularlyperturbedconvection-diffusionproblemsinone-andtwo-dimensionalset-tings.TheexistenceanduniquenessoftheLDGsolutionsareverified.Numericalex-perimentsdemonstratethatitseemsimpossibletoobtainuniformsuperconvergencefornumericalfluxesunderuniformmeshes.Thankstotheimplementationoftwo-typedif-ferentanisotropicmeshes,i.e.,theShishkinandanimprovedgrademeshes,theuniform2p+1-ordersuperconvergenceisobservednumericallyforbothone-dimensionalandtwo-dimensionalcases.