Topology optimization process
Performance considerations

In practical topology optimization, FE models may quickly become quite large because of the need to use rather small elements. This results in significant

• memory (RAM) and
• computational (CPU time)

requirements.

To mitigate the situation, it might be useful to consider that RAM and CPU time consumption are heavily influenced by the

• choice of the finite element type and
• operation mode of the FEA solver

Choosing the right finite element

Topology optimization typically requires very fine meshes (small elements). Note that this requirement can not be relaxed by using higher-quality finite elements; in other words: we have to use small elements even if we replace linear tetrahedrons by quadratic ones. To get a feeling for approximate memory (RAM) consumption of various element types, the figure below depicts the situation for a simple test structure, meshed by tetrahedrons (full material design; no void regions).

Figure. Approximate RAM consumption in GBytes of ProTOp's direct FEA solver for a tetrahedron meshed test model

Note that the scales are logarithmic, and the values shown are valid for the direct FEA solver which needs to decompose the structural stiffness matrix; much less memory is required by the iterative solver. The used labels have the following meaning:

• TTH4-SP - 4-noded tetrahedron FE (stiffness matrix decomposed in single precision)
• TTH4-DP - 4-noded tetrahedron FE (stiffness matrix decomposed in double precision)
• TTH10-SP - 10-noded tetrahedron FE (stiffness matrix decomposed in single precision)
• TTH10-DP - 10-noded tetrahedron FE (stiffness matrix decomposed in double precision)

The hexahedral HXH8 element can be roughly estimated to be somewhere between TTH4 and TTH10. If one additionally considers that hexahedral meshing may be quite tedious, it follows that when we have to deal with difficult real-life problems (large and complicated meshes), the TTH4 element is typically the only viable alternative.

Choosing the FEA solver operation mode

ProTOp's FEA solver can operate in three different modes, as follows:

• 0 - Auto - the actual (iterative or direct) mode is determined by ProTOp and may differ in each optimization cycle (default);
• 1 - Iterative - this is a low-memory-mode, which, may take less or more CPU time than the direct mode;
• 2 - Direct - this is high-memory-mode which can be very CPU time efficient under some circumstances, if enough RAM is available.

In Auto mode ProTOp tries to determine automatically the best mode. This is the default option and a good choice if the user is unsure which solver mode to select.

Iterative mode

In iterative mode, ProTOp's high-quality iterative solver is engaged. This solver supports multi-imaging, which means that several load cases may be solved synchronously by several solver instances. Unfortunately, often one can not be sure in advance whether the iterative solver will be better or worse than the direct solver. Therefore, only some general guidelines can be offered in order to make this decision easier.

In general, the following circumstances are promoting the choice of the iterative solver:

• RAM shortage. If the user knows that the available RAM will be insufficient for the direct solver, the iterative solver is a much better choice. Namely, if insufficient memory is available, the performance of the direct solver will degrade to practically unacceptable levels.
• Many load cases and a FEA model containing semi-contact and/or semi-plastic materials. Under such circumstances, the direct solver does not exhibit its best performance and the iterative solver may quickly turn out to be the better choice.
• Bulky and stiff structures. The performance of the iterative solver depends significantly on the condition of the structural stiffness matrix. Typically, a bulky and stiff structure exhibits a good stiffness matrix with a low condition number, which is well suited for the iterative solver. On the contrary, a slender and compliant structure typically exhibits a bad stiffness matrix with a high condition number; this situation is not well suited for the iterative solver.

Direct mode

In direct mode, ProTOp's high-quality direct solver is engaged. This solver performs a decomposition of the structural stiffness matrix, which is a very CPU- and RAM-consuming operation. Again, only some general guidelines can be offered in order to make this decision for the direct solver easier.

In general, the following circumstances are promoting the choice of the direct solver:

• RAM sufficiency. If the user knows that there is enough RAM available, the direct solver has a real potential to be a very good choice.
• Many load cases and a FEA model without semi-contact and semi-plastic materials. Under such circumstances, the direct solver exhibits its best performance and may be a much better choice than the iterative solver.
• Slender and compliant structures. A slender and compliant structure typically exhibits a bad stiffness matrix with a high condition number. This is a bad situation for the iterative solver and the direct one can be a much better choice.

Switching between modes

ProTOp allows to change the solver mode at any time during a running optimization process. So, the user is free to switch between all solver modes at any time; this does not require to stop or pause the running optimization process.