Meta 2010 & FEM 2010 – Rome, 13-15 December 2010 C-Language-Based 2D-Optical Mode Solver C. Molar<strong>di</strong>, E. Coscelli, F. Poli, A. Cucinotta, S. Selleri Information Engineering Department, University of Parma, I-43124 Parma, Italy stefano.selleri@unipr.it Finite Element Method (FEM), based on edge elements, approach to the modal analysis of modern optical structures leads to a generalized eigenvalue problem, that involves several resolutions of a linear equations system in order to span a basis of the Krylov subspace, in which we find eigensolutions. The matrix of this system is large, sparse, symmetric and not positive definite, so we can <strong>di</strong>scard every iterative method for resolution. The only way to proceed is to perform a sparse factorization, that carries on the well known numerical problem called fill-in. A good factorization algorithm that preserves fill-in small is strongly required; despite this, the memory space to store matrix factors increases largely with the increase of mesh points, so a wise use of memory is the prime requisite. Fortran coded modal solver currently used in the department, suffers from an oversized use of memory space, so a new solver has been developed using the C programming language that offers an easy, powerful and dynamic memory allocation approach, furthermore, modern C compilers can generate highly optimized code and give programmers the possibility to include Fortran subroutines. In the new solver, the handling of memory and the framework algorithms are written in C, creating an efficient interface to Arpack subroutines to calculate the eigensolutions. In order to show the goodness of the work, for simulation an ytterbium doped large mode area PCF rod-type fiber with double clad<strong>di</strong>ng has been considered, searching for Fundamental Mode (FM) and Higher Order Mode (HOM) on various wavelenghts using a mesh with 89135 points. The new C modal solver results are compared with the old solver solutions. As shown in the table results fit. Then the number of mesh points has been gradually increased, comparing execution time and memory space needed by both solvers, on a 32-bit Intel Pentium4 2.80 GHz 2 GByte of RAM with a Linux operating system installed. C solver gains in speed using significantly less memory space as shown in Fig. 1(a) and (b) respectively. This give the abilities to simulate with a higher number of points, up to 360000 as reported in Fig. 1(c). Figure 1 – (a) Speed and (b) memory comparisons between C solver and Fortran solver. (c) Memory required by C solver. References [1] J. Jin, The Finite Element Method in Electromagnetics, (John Wiley & Sons Inc. 1993). [2] Z. Bai, J. Demmel, J. Dongarra, A. Rhue, H. van der Vorst, “Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide”, (Draft 1999). [3] W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, Third E<strong>di</strong>tion, (Cambridge University Press 2007). [4] S. Selleri, L. Vincetti, A. Cucinotta, M. Zoboli “Complex FEM modal solver of optical waveguides with PML boundary con<strong>di</strong>tions”, Optical and Quantum Electronics 33: 359, 2001 46
Session FEM-4 Design and applications Meta 2010 & FEM 2010 – Rome, 13-15 December 2010 Chairperson: S. Selleri, University of Florence 15:50-16:10 S. Ceccuzzi, S. Meschino, F. Mirizzi, L. Pajewski, C. Ponti, and G. Schettini A FEM analysis of microwave components for oversized waveguides 16:10-16:30 U. d’Elia, G. Pelosi, S. Selleri, R. Taddei Finite Element design of CNT-based multilayer absorbers 16:30-16:50 S. Coco, A. Laudani, G. Pulcini, F. Riganti Fulginei, A. Salvini Optimization of multistage depressed collectors by using FEM and METEO 16:50-17:10 D. Ramaccia, F. Bilotti, and A. Toscano Parametric bandwidth analysis of an Artificial Magnetic Conductor surface 47
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