Iterative‐solvers for numerical analysis of photonic devices

Abstract

An assessment of four linear‐system iterative solvers is carried out through the simulation of a key 2D photonic crystal structure. Among these solvers, the biconjugate gradient stabilized (BCGS) in conjunction with the incomplete LU (ILU) decomposition, shows the best performance and can be regarded as a promising candidate for large‐scale computation. In addition, the iterative solver with the best performance is applied to analysis of the directional optical coupler and transverse anisotropic waveguide. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1182–1186, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21571

Finite element method to improve the computational performance in optical devices analysis

“…The Tables 3 and 4 list the secondary nodes located on the mesh boundary and outside the boundary, respectively. The last column of these Tables (1)(2)(3)(4) shows the number of non-nulls values contributions in global matrix for each type nodes. Figure 2 presents the fFEM flowchart to represent the disassembling/assembling management process, which is applied in a TDBPM [5].…”

“…The contributions presented in Tables (1)(2)(3)(4) are important to determine the end loop to assembling/disassembling of the elements whose physical properties have been modified. Finally, the expressions used to calculate the contributions of each node can be proved by mathematical induction.…”

“…These strategies are related to manage the runtime ILUT preconditioner and the number of iterations of the biconjugate gradient stabilized (Bi‐CGSTAB) method . The first strategy considers the ILUT preconditioner runtime as a reference value.…”

Elementos finitos com resolução simplificada de sistemas de equações lineares para dispositivos fotônicos

“…Neste caso, avaliam-se várias possibilidades de reaproveitamento, a eficiência desta aproximação em relação ao desempenho computacional e a precisão da solução. Em [7] foi estudado o método iterativo Biconjugado Estabilizado Precondionado (BCGS) [9] e as particularidades em [8]. Em [8] fez-se um estudo comparativo completo entre os métodos iterativos baseados no espaço de Krylov.…”

“…Em [7] foi estudado o método iterativo Biconjugado Estabilizado Precondionado (BCGS) [9] e as particularidades em [8]. Em [8] fez-se um estudo comparativo completo entre os métodos iterativos baseados no espaço de Krylov. Neste estudo, o BCGS destacou-se como sendo o mais eficiente, o precondicionador empregado foi o Incomplete LU Thereshold (ILUT) [10], [11].…”