Efficient Algorithms For Electromagnetic Scattering Analysis Of Objects With Uncertain Shapes

In order to adapt to the rapid development of modem society,effective electromagnetic analysis method for objects in different practical situation is always a research emphasis in the field of computational electromagnetic.Because of manufacturing processes or human factors,the uncertainties of the electromagnetic objects are ubiquitous in the real life and the practical engineering applications.The uncertainties include geometrical shapes,material properties and so on.The effects of these uncertainties on the electromagnetic characteristic of objects can not be ignored directly,which should be judged through rigorous theoretical analysis.For this purpose,this dissertation develops a series of effective algorithms for the electromagnetic analysis of objects with uncertain geometric shapes.Firstly,an effective uncertainty quatification method based on method of moments(MoM)is proposed for the electromagnetic scattering analysis of 3-D objects with uncertain varying geomatrical shape.The uncertainties of the geometric shape are described by several random variables in the integral equations through the non-uniform rational B-spline(NURBS)surface modeling approach.All random variables are independent.And then the basis function(RWG basis function)on the NURBS surface can be expressed with the corresponding random variables.Therefore,the uncertainties of the geometric shape are derived into the integral equations with the random variables.Then the scattering properties of the 3-D objects with uncertain geometric shape can be quantified by perturbation approach.Secondly,a kernel-independent method,nalely nested complex source beam(NCSB)method,based on octree structure is proposed to ruduce the computational complexity of MoM to accelerate the uncertainty qualification method based on MoM for electromagnetic scattering analysis of three dimensional(3-D)objects with varying shape.At the finest level,the far field contribution of each basis function is expressed with that of complex source beams(CSBs)distributed on the equivalent sphere surface for every group.Furthermore,the far field radiated by CSBs of the source group at child level can be represented by that radiated by CSBs of the source group at parent level.Similarly,the received field of CSBs for each observation group at the parent level can be expressed with that of CSBs belong to their child level groups.An equivalent relationship of CSBs between every two adjacent levels is built to obtain the nested equivalent process for NCSB method,and only the CSBs at the finest level have the direct association with the basis fimctions in their group.The NCSB method is shown to be O(NlogN)computational eomplexity for both matrix vector product(MVP)time and memory storage by numerical examples with appropriate parameters.Because of the kernel-independent property,the NCSB can be derived into MLFMA to accelerate the MVPs between groups at low levels without restrictions of group size for the analysis of realistic electrically large-scale objects.Thirdly,due to the multiple right-hand vector problems and slow convergence problems for complex objects in the the uncertainty quatification method based on MoM,a parallelizable direct solution of integral equation methods is proposed.There are mainly two parts of the proposed direct solution:forward decomposition and backward substitution.For the forward decomposition,the dense impedance matrix is decomposed into the product of several block diagonal matrices implicitly,which is shown to be O(Nlog2N)for both memory and CPU time cost.The final solutions are obtained with several MVPs in the part of backward substitution with O(Nlog2N)complexity as well.Both forward decomposition and backward substitution are implemented by group without recursion operations.Therefore,both the two parts can be parallelized because of the group independence.Finally,a surrogate modeling technique for electromagnetic scattering analysis of 3-D objects with varying shape is presented by means of Gaussian process(GP)and Bayesian committee machine(BCM).The technique based on GP and BCM constructs surrogate models of 3-D objects with varying shape to reduce the expensive computational resource consumption of the electromagnetic scattering analysis.Based on the resample method,several subsets of training data are selected from the total training data set,and several sub surrogate models can be constructed by GP with these subsets.The predicted values from each sub surrogate model for a test input can be fused by BCM to obtain the final predicted output with high accuracy.If the geometric dimensions of objects are set as the inputs and the corresponding RCS results are set as ouputs.For different test inputs about the geometric dimensions of objects,the uncertainty scattering analysis of 3-D objects with varying shape will be achieved efficiently by statistically analyzing the predicted outputs of the created surrogate model.