Fast And Accurate Electromagnetic Simulation Methods For Microstructures

This dissertation focuses on the fast and accurate simulation methods for two kinds of microstructures.The first kind of microstructure is a typical one,i.e.,the micro-or nano-particle illu-minated by light.For a given particle or particle assemble,the characteristics of the exerted radiation pressure force depend greatly on the incident light beam,which can be described by a set of controlling parameters,such as the illumination angle,beam centre,and beam waist for the Gaussian beam.In order to reach accurate prediction of the force,it is always neces-sary to compute the force within a large range of parameter space.Therefore,the computation involves solving of a linear matrix system of multiple right-hand sides(RHS).Suppose the characteristic size of the microstructure is D,the number of the unknowns in the associated linear matrix system N is proportional to D²for the surface mesh case,or to D³for the volume mesh case.If the incident light is of plane wave form,the number of RHSs m is proportional to D².However,if the incident is Gaussian beam,m?D².For such case,although the computation for one RHS may be finished in acceptable time,the total cost of the whole multiple RHS system can be extremely time consuming since m can be very large.To treat this problem,this work proposed the skeletonization scheme based on the interpola-tive decomposition to speed up the computation.In this scheme,interpolative decomposition is firstly carried out on the RHS matrix consisting of all the RHS vectors to figure out m_skelskeleton RHSs.Then,the skeletonized solution matrix corresponding to the skeleton RHSs is obtained by solving the matrix system by the traditional manner,typically by an iterative solver.With the skeletonized solution matrix,we finally recover the whole solution matrix by the interpolative decomposition.Because m_skelis generally much smaller then m and the in-terpolative decomposition is very efficient,the acceleration rate of solving the multiple-RHS system can be very large.To obtain optical force with high accuracy,this work makes use of the Maxwell tensor which involves computing scattered fields from the equivalent currents.For each incident,computation of scattered fields is of complexity N².Therefore,the asso-ciated computation for m incidents is of complexity m N².To accelerate the computation,we compute all the scattering fields associated with the skeleton RHSs instead of the whole RHS matrix,and then recover the whole set of scattering fields.The second kind of microstructure of interest is the electrically small structure on large platforms.Such problem is characterized by the multi-scale property,which is always very challenging.Domain decomposition method(DDM)has been proved to be a suitable solu-tion for multi-scale problems.In this work,we are interested in the discontinuous Galerkin(DG)implementation of DDM for surface integral equations.DG employs the half-RWG basis function to discretized the surface integral equation,which introduces the line charge to satisfy the continuity of the current.The line charge produces two additional terms in the matrix elements of the method of moments(Mo M),which require special singularity treatment.This work proposed one efficient and accurate singularity technique based on the Duffy's transformation.Numerical experiments show that the efficiency and the accuracy of the singularity computation is improved by the proposed method compared with the tradi-tional singularity subtraction method.The DDM method does NOT solve the low frequency breakdown in terms of the small structure.To handle the low frequency breakdown,this work combined the DG with the Augmented Electric Field Integral Equation(AEFIE)and proposed the AEFIE-DG method.Numerical experiments validated the effectiveness of the AEFIE-DG.The proposed singularity treatment is also applied to the AEFIE-DG,where the accuracy on near-and far-field computation is investigated.