When designing and simulating periodical structures, like arrays, the engineer wants to have a reliable tool, that doesn’t require hours of setting up. Simulation time plays a significant role here as well – when working with arrays we have structures much bigger than wavelength with millions of mesh cells.

Recently I have been actively using Domain Decomposition Solver (DDM) in CST Studio Suite. In this short article I would like to share my opinion on it, provide comparison with Time Domain Solver and draw some general conclusions about the new solver.

What is Domain Decomposition Solver?

DDM is essentially Frequency Domain Solver, that we have been using in CST for a long time. The difference is in meshing, as it fractions the structure into smaller blocks – domains – and adapts meshing for each domain.

Figure 1. Cavity array with domains view.

On figure 1 you can see 2 colors of domains: orange color means base blocks, that fill the boundary box evenly; pink color means element blocks, that contain an array of elements inside and have first priority.

Why the need for an alternative solver?

Modern mm-wave applications often require big number of antenna elements in arrays. For example, some RADAR arrays consist of hundreds of elements, which makes the simulation model heavy for simulation.

Figure 2. Dual-polarized cavity antenna array.

Let’s look at a simple cavity mm-wave antenna array, that works in the 24-32GHz range. It is a 4×4 array, that gives us 16 elements in total, or 16 ports. Most mm-wave applications require dual-polarization, which multiplies the number of ports by 2, resulting in 32.

Time Domain Solver calculates each port sequentially. It means that the more ports you have, the longer simulation time you get. When the count goes on hundreds, it can result in days of simulation.

On the contrary, simulation time with Frequency Domain Solver is independent of the number of ports in the structure. It comes with a price, of course. Direct Frequency Solver requires a big amount of RAM for managing big simulations, and sometimes you just do not have enough to work with.

By dividing the structure into smaller domains DDM solver gives a good simulation speedup, as domains can be solved in parallel, depending on the number of cores. If your structure contains geometrically identical elements – like antenna arrays – DDM solver allows setting up of repetitions.

Good news – with DDM solver the peak memory relates to the number and size of domains per core. By making the domains smaller the peak memory can also be lowered.

Let’s compare

Hardware in use: 2×18 cores, 128Gb RAM

Solver type Time Domain Solver Domain Decomposition Solver
Simulation time per port 9 minutes
Total simulation time 16 hours 4.5 hours
Mesh cells 7.2 million 1.7 million
Peak memory 45.6Gb 110Gb

Figure 3. Radiation efficiency comparison

Figure 4. Radiation pattern comparison

In conclusion

Here are some pros and cons that I have noticed while working with Domain Decomposition Solver:

Simulates all ports without increasing runtime The more frequency points, the more runtime
Uses less memory that direct FD Uses more memory than TD
Allows repetitions Requires more initial settings for the model

As always, each time engineers should decide which tool to use in order to achieve better results. Every option comes with a tradeoff. In my opinion, the DDM solver is a good way of simulating periodic structure, which allows using the full potential of the solver.

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