Fast Integral Methods

Abstract

Adaptive cross approximation technique was first developed by M. Bebendorf to reduce the numerical complexity of both memory requirement and matrix-vector multiplication to O(N1.5). The biggest advantage of this method is that it is independent of Green’s function. This paper presents a simple and efficient multilevel algorithm of adaptive cross approximation technique. Through the application of this technique on ground plane designs, we will show this technique is a very effective as well as reliable tool for computer modeling of electromagnetic radiation and scattering problems.

Ground Plane Design


Figure 1: Ground plane with waveguide excitation.

Figure 1 shows some snapshots of the ground plane along with the excitation waveguide. We excite one port of the waveguide, and compute the antenna pattern. To demonstrate the effectiveness of the ground plane design, we first compute the antenna pattern of the waveguide alone (Figure 2), as shown in figure 3. The backlobe ripples are due to the edge diffraction of the flat plate. Figure 3 shows the antenna pattern of ground plane mounting on the excitation waveguide. The diffraction phenomenon has been eliminated. For both cases, good agreements between measurement and multilevel ACA results are observed.


Figure 2: Waveguide and input port.



Figure 3: Antenna pattern of excitation waveguide with only one port excited. (Left: E-plane, Right: H-Plane)



Figure 4: Antenna pattern of ground plane. (Left: E-plane, Right: H-Plane)



Figure 5: Computaional requirements. (Left: Memory, Right: CPU-time)



Microstrip Array


Figure 6: Current pattern for 8x16 microstrip array antenna.



Figure 7: Antenna pattern of 8x16 microstrip array. (Left: E-plane, Right: H-Plane)



Figure 8: Current pattern for 32x16 microstrip array antenna.



Figure 9: Antenna pattern of 32x16 microstrip array. (Left: E-plane, Right: H-Plane)



Figure 10: Computaional requirements. (Left: Memory, Right: CPU-time)



Figure 11: Performance