A new method for Ewald summation in planar/slablike geometry, i.e., systems where periodicity applies in two dimensions and the last dimension is “free” (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast particle mesh Ewald (PME)-type method suitable for large-scale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PME-type method for the 2P k-space Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.

Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems.

A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast PME-type method suitable for large-scale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PME-type method for the 2P k-space Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.

Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems

This paper presents a new approach to derive far-field data needed in antenna and EMI/EMC testing from near-field measurements. An exact integral equation solution to the wave propagation problem is used to transform the near-field data to the far field. The method requires near-field measurements on two closed surfaces enclosing all sources and inhomogeneities. The approach is validated with numerical simulation of measurements of fields radiated from a known antenna. >

Far-field predictions from near-field measurements using an exact integral equation solution

A new highly accurate fast algorithm is proposed for computing the Fourier transform integrals of discontinuous functions (DIFFT) by employing the analytical Fourier transforms of Gauss-Chebyshev-Lobatto interpolation polynomials and the scaled fast Fourier transform. This algorithm can achieve the exponential accuracy for evaluation of Fourier spectra at the whole frequency range with a low computational complexity. Furthermore, the algorithm allows the adaptive sampling densities for different sections of a piecewise smooth function. Numerical experiments are shown for the applications in computational electromagnetics.

DIFFT: A Fast and Accurate Algorithm for Fourier Transform Integrals of Discontinuous Functions

An adaptive integration algorithm for the computation of the Sommerfeld-type integral has been developed. The algorithm allows the user to specify the precise location of the desired range sample points and change the integration contour. In addition, the algorithm can be used to recompute the Sommerfeld-type integral with different range resolutions without recomputing the integrand. It is also shown how the algorithm can be used to adaptively increase the number of integration points required to evaluate the Sommerfeld-type integral. Numerical results show that the algorithm is useful in many interesting areas. >

Adaptive evaluation of the Sommerfeld-type integral using the chirp z-transform

A new technique that significantly minimizes the aliasing error encountered in the conventional use of the fast Fourier transform (FFT) algorithms for the efficient evaluation of Fourier transforms of spatially limited functions (such as those that occur in the radiation pattern analysis of reflector antennas and planar near field to far field (NF-FF) transformation) is presented and illustrated through a typical example. Employing this technique and a discrete Fourier series (DFS) expansion for the integrand, a method for computing the radiation integrals of reflector antennas and planar NF-FF transformation integrals at arbitrary observation angles with optimum use of computer memory and time is also described.

M. Karthikeyan

Papers

Evaluation of Fourier transform integrals using FFT with improved accuracy and its applications