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Open Access Dissertation
Doctor of Engineering (DEng)
Electrical and Computer Engineering
Year Degree Awarded
Month Degree Awarded
Marinos N. Vouvakis
Electromagnetics and Photonics
Numerical modeling of electromagnetic (EM) phenomenon has proved to become an effective and efficient tool in design and optimization of modern electronic devices, integrated circuits (IC) and RF systems. However the generality, efficiency and reliability/resilience of the computational EM solver is often criticised due to the fact that the underlying characteristics of the simulated problems are usually different, which makes the development of a general, ''black-box'' EM solver to be a difficult task.
In this work, we aim to propose a reliable/resilient, scalable and efficient finite elements based domain decomposition method (FE-DDM) as a general CEM solver to tackle such ultimate CEM problems to some extent. We recognize the rank deficiency property of the Dirichlet-to-Neumann (DtN) operators involved in the previously proposed FETI-2$\lambda$ DDM formulation and apply such principle to improve the computational efficiency and robustness of FETI-2$\lambda$ DDM. Specifically, the rank deficient DtN operator is computed by a randomized computation method that was originally proposed to approximate matrix singular value decomposition (SVD). Numerical results show a up to 35\% run-time and 75% memory saving of the DtN operators computation can be achieved on a realistic example. Later, such rank deficiency principle is incorporated into a new global DDM preconditioner (W-FETI) that is inspired by the matrix Woodbury identity. Numerical study of the eigenspectrum shows the validity of the proposed W-FETI global preconditioner. Several industrial-scaled examples show significant iterative convergence advantage of W-FETI that uses 35%-80% matrix-vector-products (MxVs) than state-of-the-art DDM solvers.
Wang, Wei, "Randomized Computations for Efficient and Robust Finite Element Domain Decomposition Methods in Electromagnetics" (2016). Doctoral Dissertations. 635.