Time Decomposition Method for Maxwell Transient Designs

If a Maxwell 2D or 3D transient design problem is too large to solve efficiently on one machine, Maxwell can use the Time Decomposition Method (TDM). The Time Decomposition Method (TDM) is an HPC distributed analysis type based on domain decomposition along the time axis (rather than the normal geometry division) to parallelize the transient solution. Instead of solving Maxwell transient problems sequentially for each timestep, TDM enables timesteps to be solved simultaneously in parallel. Thus, TDM can be implemented on distributed memory parallel platforms based on MPI. TDM has very good scalability, resulting in significant speed up for both 2D and 3D transient solutions.

Note: Maxwell 3D A-Phi transient solver supports only General Transient TDM.

Maxwell supports two time decomposition methods:

General Transient (Non-Periodic) – This method is intended for general transient applications.

For this method, TDM solves a collection of many timesteps simultaneously – a collection of many timesteps being defined as one time subdivision. For example, if the end time of the entire transient simulation is 4 seconds, and if we want to solve all time-step solutions together for every 1 second, then this 1 second is defined as one time subdivision, and the total time subdivisions is 4. For the same problem, we can also define every 2 seconds as one time subdivision. Accordingly, the total time subdivisions becomes 2.

Periodic – This method is intended for use in steady-state simulation. In such a case, all the setup and solutions at the first timestep will be the same as those at the last timestep of one period. Setup includes source, boundary, and position in electrical degrees. The solutions include all electrical and magnetic quantities. To use this method, all current in windings and all induced eddy currents in the conducting region should have the same time period. For example, an induction machine cannot be solved using this method because the time period of the currents in the stator winding is different from the time period of induced eddy current in the rotor bars.

You can also select a Half-periodic option if all physical quantities satisfy anti-periodic condition along Time axis. In this case, the memory usage can be cut to almost half.

Periodic TDM has the advantage that the problem just needs to be solved over one period of time, while General Transient TDM uses many cycles to reach steady state. But to enforce periodical condition along the Time axis, all timesteps over one period of time must be solved together. This may require extensive memory usage.

Using TDM

To use TDM, you must do the following:

Have and use the HPC license Workgroup option (Refer to Setting HPC and Analysis Options for Maxwell and RMxprt Designs).
Set the total number of Tasks, N, (at least three Tasks) for the solve workgroup. The actual number of Tasks for parallel computation is N-1 (dependent tasks) because the first Task is used as the independent task, which is responsible for task assembly, dependent task control, synchronization, etc.
Enable the Transient Solver distribution type in the Analysis Configuration dialog box (Refer to Editing Distributed Machine Configurations.)

Note: In Maxwell 2D, for General Transient TDM, the expression cache will be updated every 10 subdivisions, that is to say, every (task number - 1 )*10 timesteps. For Periodic TDM, the expression cache is updated after the entire solution is completed.

Limitations to using TDM

Mechanical transient is not supported. This means all moving positions for every timestep have to be known in advance so that FEA will take place at that predetermined position.
The solution at a timestep cannot depend on the arbitrary history of previous timesteps (allowed for previous couple of timestep solutions required due to the time integration scheme itself). Traditional core loss computation is supported because core loss computation is done in post-processing.

Strictly speaking, TDM cannot support hysteresis modeling. But for soft hysteresis materials, especially for lamination core loss computation, the hysteresis loop, or the coercivity Hc, is very small. In such a case, the impact of hysteresis on the nonlinear operating point can be ignored. This means we can decouple the nonlinear iteration process with consideration of hysteresis impact. For the first step of the nonlinear iteration process, distributed parallel TDM can still be applied. After the nonlinear iteration has converged, that is, the nonlinear problem has been linearized for all timesteps (or all timesteps in the sub-division), the second step is applied to take into account the impact of hysteresis. In such a case, the solution process is sequential – to consider the impact of hysteresis behavior from the previous time-step solution on the solution at current timestep. It can be expected that the results with TDM enabled and with TDM disabled might differ slightly due to ignoring the impact of hysteresis on the nonlinear operating point. However, from a practical application point of view, the solutions can be considered as sufficiently accurate –especially for lamination core loss computation.
The purpose of the demagnetization process in a transient simulation is to find the worst operating point during the entire transient simulation. After a new worst operating point is discovered, a linearized representation of the permanent magnet characteristic will be used to construct a new recoil line, which is applied to the simulation for subsequent timesteps. Thus, strictly speaking, TDM cannot support demagnetization modeling because all timesteps (or all timesteps in a subdivision) are solved simultaneously. However, as a reasonable approximation, we can solve all timesteps in one subdivision simultaneously based on distributed parallel TDM – and then search for the worst operating point among the solutions of these just-solved timesteps. Thereafter, this new worst operating point is used to construct a new recoil line, which is applied to all timesteps in the next subdivision. This means the impact of previous solutions on subsequent searches for the worst operating point is taken into account subdivision-by-subdivision, rather than timestep-by-timestep.

It can be expected that the results of the discovered final worst operating point might differ slightly between TDM- enabled solutions and TDM-disabled solutions. However, from a practical application point of view, the solutions can be considered as sufficiently accurate. This error can be reduced with the use of few timesteps in one subdivision.