An Iteration-Free Domain Decomposition Method for the Fast Finite Element Analysis of Electromagnetic Problems

Fast and Accurate Prediction of Light Scattering from Plasmonic Nanoarrays in Multiple Directions

“…An H-matrix formatted LU factorization can be defined by recursively performing Equation ( 13) and replacing additions and multiplications in it with H-matrix-formatted additions and multiplications (⊕ and ⊗). The H-matrix method can significantly reduce the computational costs of the traditional dense matrix solution method [23][24][25][26]. Once the H-LU factors are obtained, they can be stored, and the H-matrix formatted forward-andbackward substitution (H-FBS) can then be performed very quickly for each RHS vector b in (9).…”

On the Design of Complex EM Devices and Systems through the System-by-Design Paradigm -- A Framework for Dealing with the Computational Complexity

“…Initialization -Generate D 0 = Ω (s) ; Φ (s) ; s = 1, ..., S 0 by sampling the input space via LHS and initialize the loop index (j = 1); . (6) According to the reference literature [47], the number of candidates is set to a value in the range C ∈ [50, 200] × K.…”

A Rigorous Code Verification Process of the Domain Decomposition Method in a Finite Element Method for Electromagnetics

“…Garcia-Castillo are with the Department of Signal Theory and Communications, University Carlos III of Madrid, 28911, Leganes, Spain (e-mail: aamor@ing.uc3m.es, legcasti@ing.uc3m.es) O. Floch, L.L. Toth, and R. Dyczij-Edlinger are with the Lehrstuhl für Theoretische Elektrotechnik, Universität des Saarlandes, Saarbrücken [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42]. All these references can be divided into three groups: i) optimized Schwarz methods, focused on the optimization of the so-called transmission conditions, [16], [25], [30]; ii) cement element methods, which use transmission conditions through the definition of cement variables with physical meaning, [13], [14], [17], [18], [19], [20], [21], [22]; iii) finite element tear and interconnecting (FETI) methods, which use Lagrange multipliers to obtain a reduced system of equations, [15], [23], [26], [27], [24], [32],…”