L.R. Hamilton

Numerical solution of 2-D scattering problems using high-order methods

We demonstrate that a method of moments scattering code employing high-order methods can compute accurate values for the scattering cross section of a smooth body more efficiently than a scattering code employing standard low-order methods. Use of a high-order code also makes it practical to provide meaningful accuracy estimates for computed solutions.

Scattering computation using the fast multipole method

The fast multipole method (FMM) computes scattering cross sections from large targets with several orders of magnitude reduction in the CPU time and memory storage compared to traditional method of moments (MoM) techniques. The authors compare the memory usage and CPU times for FMM with traditional MoM results using both direct and iterative solvers. It is shown that dramatic reductions in CPU and memory requirements can be realized by using the FMM to compute scattering and radiation from large objects. In the test cases considered, 2D objects with perimeters longer than about 12 wavelengths required less memory than using traditional MoM techniques. Using the FMM to compute scattering from objects with perimeters larger than about 30 wavelengths required less CPU time than using iterative solvers with a dense Z matrix.<<ETX>>

3D method of moments scattering computations using the fast multipole method

The fast multipole method (FMM) dramatically reduces the time and memory required to compute radar cross sections and antenna radiation patterns compared to dense matrix techniques. We have implemented the FMM in a method of moments (MoM) program to compute electromagnetic scattering from large bodies of arbitrary shape. We compare the memory and time required using the FMM to that for direct and iterative solutions using a dense impedance matrix.<<ETX>>

Electromagnetic scattering computations using high-order basis functions in the method of moments

Using high order basis functions in Galerkin method of moments calculations permits a significant reduction in the number of unknowns needed to achieve a given accuracy in modeling a scatterer or antenna [Hamilton et al., 1993]. The present authors have developed a set of vector valued basis functions of arbitrary order with a sparse overlap matrix. They demonstrate the reduction of computational effort for a given accuracy by computing the scattering from a sphere.

The importance of accurate surface models in RCS computations

The authors investigate the magnitude of the errors in the scattering cross section made by approximating 2-D targets by flat segments and by quadratic splines. These results were compared to computations using exact representations of the surface. A research program for scattering computation called Fast Scat was instrumental in computing the results. The importance of precise surface models for computing accurate scattering amplitudes and radiation patterns is shown. For the particular example of TM (transverse magnetic) scattering from an infinite PEC (perfectly electrically conducting) circular cylinder, the error made in approximating the surface by linear segments or quadratic splines was computed.<<ETX>>

Method of moments scattering computations using high-order basis functions

It is shown that using high-order basis functions in Galerkin method of moments calculations permits a significant reduction in the number of unknowns needed to achieve a given accuracy in modeling a scatterer or antenna. For instance, to model scattering from an infinite circular cylinder, six times as many unknowns are required to achieve 10/sup -6/ accuracy by using pulse basis functions than using higher-order basis functions on larger patches. Decreasing the size of the patches on the surface reduces the error by a power of the patch size. Increasing the number of basis functions makes the error exponentially smaller.<<ETX>>

FastScat™: An Object-Oriented Program for Fast Scattering Computation

FastScat is a state-of-the-art program for computing electromagnetic scattering and radiation. Its purpose is to support the study of recent algorithmic advancements, such as the fast multipole method, that promise speed-ups of several orders of magnitude over conventional algorithms. The complexity of these algorithms and their associated data structures led us to adopt an object-oriented methodology for FastScat. We discuss the programs design and several lessons learned from its C++ implementation including the appropriate level for object-orientedness in numeric software, maintainability benefits, interfacing to Fortran libraries such as LAPACK, and performance issues.

Comments on "Numerical solution of 2-D scattering problems using high-order methods" [with reply]

For original article by L.R. Hamilton et al. see ibid., vol.47, no.4, p.683-91 (Apr. 1999).