Oscar Borries

Multilevel Fast Multipole Method for Higher Order Discretizations

The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined.

Design and Optimization of a Single-Layer Planar Transmit-Receive Contoured Beam Reflectarray With Enhanced Performance

This paper presents the design and optimization of a 1.2-meters single-layer planar contoured beam reflectarray in Ku-band. The reflectarray is optimized to fulfill the requirements of a Direct Broadcast Satellite mission, which covers a South American coverage in both transmit and receive frequency bands for dual linear polarization. The reflectarray is designed using a direct optimization approach where all the array elements are optimized simultaneously, thus resulting in a design with enhanced performance compared to designs obtained using a phase-only optimization approach. The reflectarray fulfills all the coverage requirements in both transmit and receive frequency bands and the performance is validated by means of full-wave Method of Moments simulations.

Large-scale optimization of contoured beam reflectors and reflectarrays

Designing a contoured beam reflector or performing a direct optimization of a reflectarray requires a mathematical optimization procedure to determine the optimum design of the antenna. A popular approach, used in the market-leading TICRA software POS, can result in computation times on the order of days, due to the optimization algorithm. The present paper discusses recent improvements, allowing reductions in optimization time by two orders of magnitude or more on several application examples.

Fast full-wave analysis of challenging reflector antenna problems

We apply two algorithms to full-wave analysis of electrically large reflector antennas with complex surroundings. The new algorithms are a higher-order MLFMM, yielding a considerably faster solution than a low-order MLFMM, and a fast algorithm for current integration. The new techniques allow a significant reduction of the computational burden, thereby extending the range of problems that can be solved on commodity computer hardware. The examples include two challenging reflector antenna problems; ESAs Planck space telescope and a detailed model of a telecommunication satellite.

Solution of electrically large scattering problems on a laptop

We consider the application of full-wave methods to electrically large structures with emphasis on an implementation that allows modest computing resources to be used even for very large problems. First, we highlight the recent development of a Multi-level Fast Multipole Method (MLFMM) implementation based on Higher-Order (HO) basis functions, which allow significant time and memory reductions as compared to previous MLFMM implementations. Second, we show how the use of the harddisk for some of the more memory demanding components in MLFMM can allow us to solve much larger problems than the memory of the computing platform makes room for, with only a modest increase in computational time.

Gaussian translation operator for Multi-Level Fast Multipole Method

Results using a new translation operator for the Multi-Level Fast Multipole Method are presented. Based on Gaussian beams, the translation operator allows a significant portion of the plane-wave directions to be neglected, resulting in a much faster translation step.

A Novel Accurate Pattern Fitting of Noisy Irregular Beam Data for the Planck Space Telescope

Fitting using Kriging, originally developed for geological exploitation, has here been applied for fitting an expected pattern to noisy, irregular, in-flight measurements of a satellite antenna. The noise level in in-flight measurements is often so high that only the central part of the main beam appears. Using the Kriging method, a characteristic function - the regression model - was first fitted to the measurements. For the main beam, this was chosen to be described by a general second-order polynomial. To this was added a more-detailed correlation model, which represented realistic deviations from the regression model but filtered out the fast variations of the noise. The method was applied to simulated measurements of the Planck RF telescope. The results presented showed a considerable reduction of the noise floor of the pattern: even beam details invisible in the original measurements (a shoulder) were revealed by the pattern fitting.

Efficient surface optimization of large dual reflector systems

Surface shaping of reflector antennas for creating a contoured beam is an ubiquitous task in the design of modern communication satellites. In this paper, we highlight two major improvements to the state-of-the-art that provides a major increase in computational efficiency — a modern mini-max optimisation algorithm for large-scale problems and the implementation of analytical derivatives for simultaneous shaping of the surface of both reflectors in a dual reflector system.

Memory-efficient, full-wave analysis of waveguide scattering parameters for multiple reflector feeds mounted on electrically large satellite platforms

A Higher-Order Multilevel Fast Multipole Method (HO MLFMM) is presented for the efficient calculation of waveguide scattering parameters in cases where several reflector feeds are mounted on electrically large satellite platforms. The efficiency is obtained by: 1) using a Block Krylov method for solving the HO MLFMM problem for the required large number of right-hand sides and 2) implementing an out-of-core solution, taking into account the fact that the memory distribution of HO MLFMM is different from the standard low-order MLFMM.

Higher-Order method of moments analysis for unconnected quadrilateral meshes

A higher-Order (HO) quadrilateral mesher is presented along with a HO method of moments formulation for unconnected meshes. A numerical example is presented to validate the new formulation.