Fast analysis of three‐dimensional electromagnetic problems using dual‐primal finite‐element tearing and interconnecting method combined with ℋ‐matrix technique

Abstract

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.

Efficient Prediction and Analysis of Optical Trapping at Nanoscale via Finite Element Tearing and Interconnecting Method

“…2 b, which can be chosen as the cluster tree of the original edge-based basis function set and that of the testing basis function set in Galerkin’s method. Next, we need to introduce an admissibility condition based on the nested dissection to distinguish full blocks, low-rank decomposition blocks and off-diagonal zero blocks in T I × I [23]. Thus, can be produced by filling the corresponding blocks with the non-zero entries of .…”

“…It enforces a transmission condition at the subdomain interfaces to ensure the filed continuity, and introduces a dual variable to reduce original three-dimensional (3D) problem to be a two-dimensional (2D) problem by Lagrange multiplier. Primal variables at the subdomain corners are extracted to accelerate the convergence rate of iterative solution of the dual problem [23–26]. A low-rank sparsification approach is developed to improve the performance of the FETI-DP.…”

A review on the design and optimization of antennas using machine learning algorithms and techniques

“…For instance, Direct FE solver has been proposed for better accuracy with 3D structures, but also suffers from CPU time and memory storage requirements 39 . Dual prime, 40 which can be used with 3D structure problems, Vivaldi arrays, and other array problems, has a faster convergence time but also suffers from a trade‐off between accuracy and computational cost 41 . Element Tearing and interconnecting full‐dual‐primal have been also proposed for the analysis of 3D large‐scale problems, but also suffer from memory and CPU time requirements 42 .…”