TY - JOUR
T1 - A vector dual-primal finite element tearing and interconnecting method for solving 3-D large-scale electromagnetic problems
AU - Li, Yujia
AU - Jin, Jian Ming
N1 - Funding Information:
Manuscript received April 10, 2006; revised June 16, 2006. This work was supported in part by a grant from the Air Force Office of Scientific Research via the MURI Program under contract number FA9550-04-1-0326. The authors are with the Center for Computational Electromagnetics, Department of Computer and Electrical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2991 USA (e-mail: j-jin1@uiuc.edu). Color versions of Figs. 4–13 are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2006.882191
PY - 2006/10
Y1 - 2006/10
N2 - A Lagrange multiplier based non-overlapping domain decomposition method, referred to as the dual-primal finite element tearing and interconnecting (FETI-DP), is formulated for the finite element simulation of large, three-dimensional (3-D) electromagnetic problems. This formulation extends the FETI-DP for solving the scalar Helmholtz equation to the solution of the vector curl-curl wave equation using edge-based finite elements. It enforces the field continuity explicitly along the edges shared by more than two subdomains and implicitly at the interfaces between two subdomains through the use of Lagrange multipliers. With the aid of a direct sparse solver for each subdomain system, the large global problem is reduced to a much smaller interface problem, from which a Neumann boundary condition is obtained at the interfaces between all the subdomains. This Neumann boundary condition is then used to calculate the field within each subdomain. It is shown that the resulting FETI-DPEM method is scalable with respect to the size of finite elements and the number of subdomains. It is also scalable with respect to the size of the subdomains when the subdomains, with its surfaces enclosed by perfect magnetic conductors, cannot support any resonant modes. The FETI-DPEM method is applied to the electromagnetic simulation of array-type structures where the geometrical redundancy is fully exploited to speedup the simulation and reduce the memory requirement. Numerical results for the simulation of finite antenna arrays and photonic bandgap devices are presented to demonstrate the application, accuracy, efficiency, and capability of the FETI-DPEM method.
AB - A Lagrange multiplier based non-overlapping domain decomposition method, referred to as the dual-primal finite element tearing and interconnecting (FETI-DP), is formulated for the finite element simulation of large, three-dimensional (3-D) electromagnetic problems. This formulation extends the FETI-DP for solving the scalar Helmholtz equation to the solution of the vector curl-curl wave equation using edge-based finite elements. It enforces the field continuity explicitly along the edges shared by more than two subdomains and implicitly at the interfaces between two subdomains through the use of Lagrange multipliers. With the aid of a direct sparse solver for each subdomain system, the large global problem is reduced to a much smaller interface problem, from which a Neumann boundary condition is obtained at the interfaces between all the subdomains. This Neumann boundary condition is then used to calculate the field within each subdomain. It is shown that the resulting FETI-DPEM method is scalable with respect to the size of finite elements and the number of subdomains. It is also scalable with respect to the size of the subdomains when the subdomains, with its surfaces enclosed by perfect magnetic conductors, cannot support any resonant modes. The FETI-DPEM method is applied to the electromagnetic simulation of array-type structures where the geometrical redundancy is fully exploited to speedup the simulation and reduce the memory requirement. Numerical results for the simulation of finite antenna arrays and photonic bandgap devices are presented to demonstrate the application, accuracy, efficiency, and capability of the FETI-DPEM method.
KW - Antenna arrays
KW - Domain decomposition method (DDM)
KW - Finite element method (FEM)
KW - Finite element tearing and interconnecting (FETI)
KW - Photonic bandgap (PBG)
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U2 - 10.1109/TAP.2006.882191
DO - 10.1109/TAP.2006.882191
M3 - Article
AN - SCOPUS:33750123747
SN - 0018-926X
VL - 54
SP - 3000
EP - 3009
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 10
ER -