SINGULA can simulate **large phased array antennas**. These can be used for electronic steering of beams. Considering the mutual coupling between any two elements of the array, estimating the radiation characteristics of a large array leads to a very complex model. Using advanced **Fast Fourier Transform** (FFT) methods, the problem illustrated below was solved.

These antennas are used in wide variety of applications:

- Aerospace and defense industry
- Satellite communication
- Remote sensing
- Synthetic aperture radar (SAR)
- Moving target indicator

### Objective

This benchmark will demonstrate how to analyze large microstrip phased arrays.

### Geometry

The basic patch antenna is from the JINA2006-testcase2 example. See the following figures.

Figure: 1 Figure: 2

The relative permittivity and permeability of the substrate are **e _{r}=2.2**,

**µ**.

_{r}=1The structure of The 10 × 10 arrays and 20 × 20 arrays with perfectly conducting box is illustrated below:

### Database

The database files are entitled with:

1 – JINA2006_test2_10X10_SP_rad[8GHz]_LU.dbs

2 – JINA2006_test2_10X10_DP_rad[8GHz]_FFT.dbs

3 – JINA2006_test2_20X20_DP_rad[8GHz]_FFT.dbs

### Results

The results are obtained by different methods using different precisions.

Directive gain obtained from FFT method (left) Directive gain obtained from direct solver (right)

Directive gain in 2D and 3D patterns obtained from FFT method

### Comments

1 – The running time for JINA2006_test2_10X10_SP_rad[8GHz]_LU.dbs with 154140 unknowns using direct solver in single precision on two Xeon E5430 Quad CPUs , 32GB RAM is **46:15:05**.

2 – The running time for JINA2006_test2_10X10_DP_rad[8GHz]_FFT.dbs with 146820 unknowns using FFT iterative method in double precision on iterative accuracy 0.001 on two Xeon E5430 Quad CPUs , 32GB RAM is **01:24:34**.

**From the results, it is clear that use of FFT iterative method can reduce solution time significantly without losing accuracy.**

3 – The running time for JINA2006_test2_20X20_DP_rad[8GHz]_FFT.dbs with 692923 unknowns using FFT iterative method in double precision on iterative accuracy 0.001 on two Xeon E5430 Quad CPUs , 32GB RAM is **32:22:58**.