Triple Operator Splitting Technique For Phase Field Model Of Vesicle Membranes

This paper aimed to explore new algorithm in the Elastic BendingEnergy Model by Phase Field Method for Vesicle Membranes, usingOperator Splitting Technique. Two major parts of both theoretical derivationand numerical simulation had been researched, including Phase Field Modeland our Triple Operator Splitting Algorithm. In detail, Normal OperatorSplitting Method for Allen-Cahn Equation, the variation from the BasicEnergy Model, had been discussed; Elastic Bending Energy Model had beenbuilt then, compared with Helfrich Free Energy Model in liquid crystal,based on the asymptotic properties of Basic Energy Model and its variationwhen parameter. And then we created the Triple Operator SplittingTechnique to solve the Elastic Bending Energy Model with Gradient FlowMethod, and analyzed the advantages of this technique and its stabilityconditions of parameters after. At last, numerical simulations of eachoperator and six special cases had been compared and discussed in detail,which proved the effectivity of the method we created above.