Kedi Zhang

A 3-D Interface-Enriched Generalized FEM for Electromagnetic Problems With Nonconformal Discretizations

An interface-enriched generalized finite-element method (IGFEM) is introduced for efficient 3-D electromagnetic analysis of heterogeneous materials. Without using meshes that conform to the material microstructures, which greatly lessens the burden of mesh generation, the method assigns generalized degrees of freedom (DOFs) at material interfaces to capture the discontinuities of the field and its derivatives. The generalized DOFs are supported by enriched vector basis functions (VBFs), which are constructed through a linear combination of the VBFs from the subelements. Several verification examples are provided to show that the IGFEM is not sensitive to the quality of the subelements and maintains the same level of solution accuracy and computational complexity as the standard finite-element method (FEM) based on conformal meshes. The potential of the proposed IGFEM is demonstrated by simulating some engineering problems with complex, periodic internal structures, including composite materials with randomly distributed spherical particles and ellipsoidal inclusions and microvascular channels.

A General Scheme for the Discontinuous Galerkin Time-Domain Modeling and S-Parameter Extraction of Inhomogeneous Waveports

A general numerical scheme is proposed for the waveport modeling and scattering-parameter (S-parameter) extraction of inhomogeneous waveports with the discontinuous Galerkin time-domain method. In this scheme, the waveports are truncated with perfectly matched layers with a hybrid mesh automatically extruded from the mesh of the physical device to be simulated. The waveports are then excited by a total-field/scattered-field technique, with which the incident and scattered waves can be obtained for an accurate calculation of the S-parameters. A novel eigenmode solver is also developed to calculate the required modal profiles for the eigenmodes in both homogeneous and inhomogeneous waveports. Special attention is paid to the S-parameter extraction for evanescent modes, which has been a difficult task for time-domain simulations. Numerical examples are given to validate the proposed numerical scheme.

An MPI-accelerated multi-solver algorithm for electromagnetic modeling of complex objects

A multi-solver (MS) algorithm is accelerated on distributed computing systems to simulate the electromagnetic scattering from large and complex objects. In this algorithm, the targeted object with its background is decomposed into multiple subdomains which are modeled by either the finite element method or the method of moments. Different from conventional parallelized domain decomposition methods, where the subdomains are handled in parallel, the MS algorithm is parallelized by applying the parallelization to individual subdomains. The employed multilevel fast multipole algorithm is also parallelized to enable computation on many processors. Numerical examples are given to show the parallel efficiency of the proposed strategy.

Transient analysis of resonant waveguide devices using a hybrid FETD-GSM algorithm

A hybrid algorithm that combines the finite-element time-domain (FETD) method with the generalized scattering matrix (GSM) method is introduced to model resonant waveguide devices. The device is divided into several subdomains with each truncated with the waveguide port boundary condition (WPBC) to suppress resonance and therefore reduce the total number of time-marching steps. The subdomains are analyzed by the FETD method and characterized by broadband GSMs. The GSM of the original device is recovered by cascading the subdomain GSMs. A numerical example is presented to demonstrate the accuracy and efficiency of this algorithm.

Broadband monostatic scattering calculation of deep open cavities

A domain decomposition scheme is presented to analyze broadband scattering by deep open cavities using the finite-element time-domain (FETD) and generalized scattering matrix (GSM) methods. The cavity is decomposed into less resonant subdomains, and each subdomain is characterized by a GSM which is obtained by the fast Fourier transform of the FETD solutions. The subdomain GSMs are then cascaded to form the broadband GSM of the cavity. After that, incident waves are expanded by the modes at the cavity aperture to calculate scattered waves using the global GSM and then the monostatic scattering cross-section. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed scheme.

A Hybrid FETD-GSM Algorithm for Broadband Full-Wave Modeling of Resonant Waveguide Devices

An efficient hybrid algorithm that combines the finite-element time-domain (FETD) method with the generalized scattering matrix (GSM) technique is proposed to characterize the properties of wave propagation in highly resonant waveguide devices. To alleviate the problem of an extremely large number of time steps required for a highly resonant device, the algorithm first divides the device into several less resonant or resonant-free subdomains to reduce the number of time steps and the computational complexity of the FETD solver. The subdomain interfaces, which are assumed to be homogeneous, are modeled with an accurate waveguide port boundary condition (WPBC) to absorb any impinging waveguide modes. Each subdomain is then represented by a broadband GSM, which is computed by the fast Fourier transform of the FETD solutions. Finally, the subdomain GSMs are cascaded to form the global GSM of the original resonant device. The formulation and implementation of the FETD method with the WPBC, its required general waveguide modal analysis, and the cascading of GSMs are discussed in detail. Three numerical examples are presented to demonstrate the accuracy and efficiency of the proposed hybrid algorithm.

Far-field light scattering from sub-wavelength wafer patterns using a parallel FETI-DP algorithm

The dual-primal finite-element and interconnecting algorithm (FETI-DP) is efficiently applied in parallel to compute the far-field scattering from a wafer with sub-wavelength patterns. As a nonoverlapping domain decomposition method for solving large-scale problems, the FETI-DP algorithm formulates a global interface problem, whose iterative solution is accelerated by solving a global corner problem. To maintain good parallel scaling efficiency, global communication is minimized by using an iterative classical Gram-Schmidt scheme for the global interface problem and a communication-avoiding approach for the global corner problem. In addition, a preconditioner for the corner system matrix is implemented to improve iterative convergence. After computing the far-field data, digital postprocessing is used to remove the background signal and improve the detection sensitivity of isolated defects.

Gradient-based shape optimization for electromagnetic problems using IGFEM

A gradient-based shape optimization scheme combined with an interface-enriched generalized finite-element method (IGFEM) is proposed to efficiently optimize electro-magnetic (EM) problems. To avoid mesh distortion or the expensive process of repeatedly creating a conformal mesh for each design configuration, the problem geometry is projected onto a fixed background mesh that is not necessarily conformal to the geometry. The IGFEM, with an enriched solution space in nonconformal elements, is adopted for an accurate EM simulation. An analytical sensitivity analysis is presented to compute the derivatives of the objective and constraint functions. Because of the fixed background mesh, the design velocity field term in the sensitivity analysis is evaluated only at the geometry interfaces, and the efficiency of this method is significantly enhanced. An optimization of the radius of a dielectric cylinder to achieve the desired echo width is presented for verification.

An interface-enriched generalized FEM for EM analysis of composites with nonconformal meshes

An interface-enriched generalized finite-element method (IGFEM) is presented for accurate and efficient electromagnetic analysis of complex composite materials. Without using meshes that conform to the material interfaces, the IGFEM enriches the solution space at the material interfaces to capture the discontinuities of the field and its derivatives. Two verification examples and one engineering problem are provided to respectively demonstrate the accuracy of the IGFEM and its potential in modeling composites with intricate and randomly distributed internal structures.

Parallel FETI-DP algorithm for defect detection in large-area nanopatterned wafers

An efficient parallelization of the dual-primal finite-element tearing and interconnecting algorithm (FETI-DP) is presented for detecting defects in large-area nanopatterned wafers. To reduce global communication, iterative solvers with an iterative classical Gram-Schmidt scheme and a communication-avoiding approach are implemented to solve the interface and the coarse corner problems, respectively. A preconditioner is developed to improve the iterative convergence of the coarse problem. Electromagnetic analysis of a wafer is presented to show the scalability and capability of the method for accurate defect detection.