The special project addresses the following four aspects:FFT method[single]:The first student will be given an existing implementation of the FTT method and corresponding literature. The student will thenCarry out a literature reviewanalyze the computational complexity of the method analytically and for practical examples.analyze pros and cons of the methodpropose, rewrite and implement remediesFinite Cell Method (FCM) with Moment Fitting[single]:The second student will be given an existing implementation of the moment fitting method for a 2D finite element case and corresponding literature. The student will thenCarry out a short literature reviewAnalyze the computational complexity of the method analyticallyUnderstand and implement the moment fitting method in FCM and analyze the computational complexityPre-Integration[single]:The third student will work on implementing a pre-integration technique. Additionally, the student will prepare a given FEM framework for a meaningful comparison of the homogenization methods of student one and two. The tasks include:Carry out a short literature reviewAnalyze the computational complexity of the method analyticallyImplement the pre-integration method and analyze its computational complexityPrepare an interface to include the methods of student one and two.[team]:The three students will then jointly compare their results on benchmark examples in a written report and present their findings in a final presentation. The modified codes must be handed in along with the technical report.