Accelerating Isogeometric Boundary Element Analysis For 3-dimensional Elastostatics Problems

The high performance simulation is an important issue for advanced flight vehicle structural design.High performance here means the well balance in accuracy and efficiency.The integration of IGA and BEM gives a new dawn in both CAD and CAE.The unified model representation in both geometry and analysis will keep the integrity of geometry information,fully eliminate the meshing process and improve the geometry precision of simulation model.And on this basis,a new algorithm framework is proposed aiming to accelerate the IGABEM computation which is helpful for the future practical application.Firstly,the efficiency in design state evolution needs to be improved.A reduced order computational framework of IGABEM is proposed.Through the POD,an a priori model reduction strategy is established which can predict the evolutionary state in a short time.Meanwhile,the PGD is introduced in IGABEM to realize an online response computation.The results show that the relative error is about 0.2% and the computational speed is three orders higher than before,which validate the method with good efficiency and accuracy.Secondly,the efficiency in coefficient matrix assembling comes into view.A kernel independent FMM IGABEM computational framework is constructed which realize the application of bbFMM in solving three dimensional elastostatics problems.Through the PGD,the M2 L operation can be further accelerated.This will obviously shorten the time of preprocessing of FMM.The results show that,the precision can be kept compared with conventional IGABEM,the computational time can be reduced into a linear computation complexity and the memory request is only half of conventional IGABEM.Moreover,the small and medium models are also suitable for this method.The related computational parameters are further discussed and recommended value ranges are provided which will be helpful for the application in other areas.Thirdly,the focus changes to the dense/asymmetric matrix solving.A fast iteration method is proposed.Through the Krylov subspace,the recycling,augmenting and updating algorithms is realized for enhancing convergent property.The results show that the method can reduce the number of iterations one order of magnitude.Meanwhile,the computational stability can be further reinforced.The recommended value ranges of parameters are also listed.Finally,the ultimate goal is to provide a fast optimization method.Through the RBF,an adaptive SVD-Krylov hybrid algorithm is proposed.The a priori knowledge is successfully introduced into the optimization process which can well balance the efficiency and accuracy.The results show that,the numbers of iteration will be three orders less than before.This is further applied into the shape optimization process of engineering structural components.The related works in this thesis will effectively promote IGABEM in industry application.Meanwhile,it is a guidance for the BEM software developing with our own intellectual-property rights.This gives a bright prospect for future IGABEM studies.