448 research outputs found
Excessive Memory Usage of the ELLPACK Sparse Matrix Storage Scheme throughout the Finite Element Computations
Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method. ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage scheme becomes negligible for large scale problems. On the other hand, our analyses show that the redundancy is still considerable for the occasions where facet or edge elements have to be used
Parallel Implementation of the Discrete Green's Function Formulation of the FDTD Method on a Multicore Central Processing Unit
Parallel implementation of the discrete Green's function formulation of the finite-difference time-domain (DGF-FDTD) method was developed on a multicore central processing unit. DGF-FDTD avoids computations of the electromagnetic field in free-space cells and does not require domain termination by absorbing boundary conditions. Computed DGF-FDTD solutions are compatible with the FDTD grid enabling the perfect hybridization of FDTD with the use of time-domain integral equation methods. The developed implementation can be applied to simulations of antenna characteristics. For the sake of example, arrays of Yagi-Uda antennas were simulated with the use of parallel DGF-FDTD. The efficiency of parallel computations was investigated as a function of the number of current elements in the FDTD grid. Although the developed method does not apply the fast Fourier transform for convolution computations, advantages stemming from the application of DGF-FDTD instead of FDTD can be demonstrated for one-dimensional wire antennas when simulation results are post-processed by the near-to-far-field transformation
Simulation of Metasurfaces in Finite Difference Techniques
We introduce a rigorous and simple method for analyzing metasurfaces, modeled
as zero-thickness electromagnetic sheets, in Finite Difference (FD) techniques.
The method consists in describing the spatial discontinuity induced by the
metasurface as a virtual structure, located between nodal rows of the Yee grid,
using a finite difference version of Generalized Sheet Transition Conditions
(GSTCs). In contrast to previously reported approaches, the proposed method can
handle sheets exhibiting both electric and magnetic discontinuities, and
represents therefore a fundamental contribution in computational
electromagnetics. It is presented here in the framework of the FD Frequency
Domain (FDFD) method but also applies to the FD Time Domain (FDTD) scheme. The
theory is supported by five illustrative examples
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