相場(chǎng)模型Allen-Cahn方程的若干數(shù)值方法及應(yīng)用.pdf

1、碩士研究生學(xué)位論文新新新疆疆疆大大大學(xué)學(xué)學(xué)論文題目(中文)：相場(chǎng)模型AllenCahn方程的若干數(shù)值方法及應(yīng)用論文題目(英文)：SomenumericalmethodsapplicationsoftheAllenCahnequationofphasefieldmodel研究生姓名：?jiǎn)踢h(yuǎn)陽(yáng)學(xué)科專(zhuān)業(yè)：數(shù)學(xué)學(xué)位類(lèi)別：理學(xué)碩士研究方向：計(jì)算數(shù)學(xué)導(dǎo)師姓名職稱(chēng)：馮新龍教授論文答辯日期2016年05月27日學(xué)位授予日期年月日AbstractAbstr

2、actAllenCahn(AC)equationistheprimarymodelsimulatingphasefieldinmaterialssciencewhichdescribestheprocessofabinaryalloyatacertaintemperaturephaseseparation.Theanalyticalsolutionisgenerallydifficulttoobtain.Therefeitisneces

3、sarytoexplenewnumericalmethods.InthispaperwemainlystudythreenumericalmethodsofACequationtheyareWeightedEssentiallyNonOscillaty(WENO)methodoperatsplittingmethodradialbasisfunction(RBF)method.FirstlyusingsixderWENOschemein

4、spaceusingthirdderTVDRungeKuttamethodfdiscretizationintimewegivethestabilityproofofthefmat.Numericalexperimentsaretoobtainthehighdernumericalsolution.SecondlywedivideACequationintothreesubproblemstosolvetheproblembasedon

5、thesecondderoperatsplittingmethodsalsoprovethestabilityofthefmat.WeuseNonoscillationacteristicofthisfmatonACequationfimagerestationapplicationspresentnumericalexperimentstoshowtheaccuracyefficiencyofthemethod.Finallyusin

6、gRBFapproachestosolveACequationitsapplicationindiscontinuousdetectionthentheaccuracyefficiencyofthemethodareverifiedbysomenumericalexperiments.Keywds:AllenCahnequationWeightedessentiallynonoscillatymethodOperatsplittingm