Abstracts - Dipartimento di Elettronica Applicata

Meta 2010 & FEM 2010 – Rome, 13-15 December 2010
C-Language-Based 2D-Optical Mode Solver
C. Molardi, 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 discard 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
cladding 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
Edition, (Cambridge University Press 2007).
[4] S. Selleri, L. Vincetti, A. Cucinotta, M. Zoboli “Complex FEM modal solver of optical waveguides with PML boundary
conditions”, Optical and Quantum Electronics 33: 359, 2001
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