An iteration-free finite element domain decomposition method (DDM) is proposed for the simulation of three-dimensional (3-D) electromagnetic problems. The finite element tearing and interconnecting (FETI) with Robin-type transmission condition is introduced to construct a domain decomposition framework. Based on hierarchical (H-) matrix algorithm, the numerical Green’s function of each subdomain can be represented by a data-sparse matrix form. Subsequently, the original 3-D problem is reduced to a 2-D problem on the skeleton. Derived from the finite element discretisation of pseudo-differential operator, the skeleton matrix can also be efficiently approximated with an H-matrix by assembling all the numerical Green’s functions of subdomains. Based on H-LU factorization algorithm, the computational complexity and memory requirement for the direct solution of the skeleton equation can be reduced to be logarithmic linear. The resulting direct FETI (D-FETI) method completely depends on direct method without any iterative process. Hence, it does not suffer from the issue of convergence rate, and avoids redundant computations for multiple right-hand-side problems. Numerical examples demonstrate the effectiveness of the proposed method.

An efficient direct solution scheme is presented to solve the finite element-boundary integral (FEBI) system for the analysis of open-region electromagnetic problems in half-space. Data-sparse representation based on hierarichal (H-) matrix is employed to construct the direct solution framework. The FEBI system matrix is first represented to be an H-matrix form, in which the FE submatrices are accurately represented by H-matrices, while the H-matrix approximations of the BI submatrices are constructed by the adaptive cross approximation algorithm combined with singular value decomposition recompression (ACA-SVD). Based on the data-sparse formatted algorithm, the lower and upper (LU) triangular factors of the FEBI system matrix can be computed and stores as H-matrix forms with low computational costs. The resulting method, refered to as the direct FEBI method (D-FEBI), is free of convergence problem and well-suited for multiple right-hand side (RHS) computations. The performance of the D-FEBI is examined by two examples of monostatic electromagnetic scattering above a lossy half-space.

The photothermal properties of graphene plasmonic waveguides (GPWs) are numerically investigated, while most of existing studies focus on their optical properties. A three-dimensional (3D) coupled optical-thermal model based on finite element method (FEM) is presented. The graphene sheet is treated as an graphene equivalent impedance surface. Transient thermal responses and peak temperature of the GPWs are captured using time-domain FEM (TDFEM). The effectiveness of the proposed method is validated by two examples of hybrid GPWs. Numerical results present the main factors that influence the photothermal properties of the GPWs, including the conductivity of graphene, and the wavelength and power density of incident light. The findings unveil that the temperature increase is an underlying factor influencing the maximum integration density of GPWs in optical interconnect.

As a powerful variant of the dual‐primal finite‐element tearing and interconnecting (FETI‐DP) method in electromagnetics (EM), the FETI‐DPEM method shows excellent convergence properties and numerical scalability. A key factor affecting the performance of the FETI‐DPEM is the direct solution of sub‐domain FE systems. An efficient direct solver based on hierarchical (ℋ‐) matrix technique is proposed to solve the sub‐domain FE systems. ℋ‐matrix formatted lower‐upper (LU) decomposition with subsequent forward and backward substitution (FBS) can significantly reduce the computational costs of the direct solution with sufficient accuracy. The nested dissection technique is employed to further accelerate the ℋ‐LU decomposition and the ℋ‐FBS. Numerical examples demonstrate that the proposed method is very robust for the three‐dimensional EM simulation.

An efficient electromagnetic-thermal-stress modeling method based on the finite element domain decomposition method (DDM) is presented for the analysis and design of antenna arrays. The proposed method can be applied to detect the heat generated by electromagnetic losses, describe the temperature distribution, and calculate the thermal stresses and displacements of antennas. It provides an efficient way to implement parallel computing for the multiphysics modeling of large-scale antenna arrays. Numerical results demonstrate the accuracy and effectiveness of the proposed method.

Method of moments (MoMs) solution of the electric and magnetic current combined-field integral equation (JMCFIE) for penetrable objects generally resorts to iterative solvers, which suffer from the problems of convergence rate and redundant computation for multiple right-hand-sides (RHSs). In this communication, an efficient direct solver based on the hierarchical ( $\mathcal {H}$ -) matrix technique is presented to solve these problems. $\mathcal {H}$ -matrix formatted algorithms provide an efficient way to factorize the impedance matrix with low computational costs, which make the direct solution feasible. Examples of electromagnetic scattering from a dielectric object and optical scattering from a plasmonic nanostructure are shown to demonstrate the efficiency and accuracy of the proposed method.