Active region adaptations for design domains in topology optimizations

1. A method comprising:

by a computing system:

identifying a design domain for which to optimize a topology based on an objective function, the design domain comprising a bounding box for an unknown topology discretized into multiple design elements;

determining an active region for the design domain, the active region comprising a selected set of active design elements in the design domain, wherein determining the active region for the design domain comprises:

performing finite element analysis (FEA) for design elements in the bounding box based on the objective function;

computing sensitivity values for design elements in the bounding box; and

selecting, as the active design elements of the active region, design elements in the bounding box that exceed a bounding sensitivity threshold;

iteratively adapting the active region, including by, for a given adaptation cycle:

expanding the design domain to include branch design elements within a threshold element distance from the active design elements in the active region;

performing the FEA on the expanded design domain based on the objective function, including computing a respective sensitivity value based on the objective function for the design elements of the expanded design domain;

determining an adapted active region by:

activating, as active design elements, any of the branch design elements with a computed sensitivity value that exceeds an active sensitivity threshold; and

deactivating, from the active region, any active design element with a design variable value that changes less than a threshold amount from a previous adaptation cycle; and

setting the adapted active region as the active region for a subsequent adaptation cycle; and

continuing to iteratively adapt the active region until an optimization ending criterion is satisfied.

2. The method of claim 1 , wherein the optimization ending criterion is satisfied when a difference between a value of the objective function between adaptation cycles is less than an optimization process ending value.

3. The method of claim 1 , wherein the optimization ending criterion is satisfied when the active region does not include any active design elements.

4. The method of claim 1 , wherein the active sensitivity threshold is a function of the computed sensitivity values for the active region of a previous adaptation cycle.

5. The method of claim 1 , wherein the bounding sensitivity threshold is different from the active sensitivity threshold.

6. The method of claim 1 , comprising performing multiple iterations of the FEA in the given adaptation cycle prior to determining the adapted active region.

7. A system comprising:

an initial design space engine, comprising hardware, configured to

identify a design domain for which to optimize a topology based on an objective function, the design domain comprising a bounding box for an unknown topology discretized into multiple design elements; and

determine an active region for the design domain, the active region comprising a selected set of active design elements in the design domain, including by:

performing finite element analysis (FEA) for design elements in the bounding box based on the objective function;

computing sensitivity values for design elements in the bounding box; and

selecting, as the active design elements of the active region, design elements in the bounding box that exceed a bounding sensitivity threshold; and

an active region adaptation engine, comprising hardware, configured to:

iteratively adapt the active region, including by, for a given adaptation cycle:

expanding the design domain to include branch design elements within a threshold element distance from the active design elements in the active region;

performing the FEA on the expanded design domain based on the objective function, including computing a respective sensitivity value based on the objective function for the design elements of the expanded design domain;

determining an adapted active region by:

activating, as active design elements, any of the branch design elements with a computed sensitivity value that exceeds an active sensitivity threshold; and

deactivating, from the active region, any active design element with a design variable value that changes less than a threshold amount from a previous adaptation cycle; and

setting the adapted active region as the active region for a subsequent adaptation cycle; and

continue to iteratively adapt the active region until an optimization ending criterion is satisfied.

8. The system of claim 7 , wherein the optimization ending criterion is satisfied when a difference between a value of the objective function between adaptation cycles is less than an optimization process ending value.

9. The system of claim 7 , wherein the optimization ending criterion is satisfied when the active region does not include any active design elements.

10. The system of claim 7 , wherein the active sensitivity threshold is a function of the computed sensitivity values for the active region of a previous adaptation cycle.

11. The system of claim 7 , wherein the bounding sensitivity threshold is different from the active sensitivity threshold.

12. The system of claim 7 , wherein the active region adaptation engine is configured to perform multiple iterations of the FEA in the given adaptation cycle prior to determining the adapted active region.

13. A non-transitory machine-readable medium comprising instructions that, when executed by a processor, cause a computing system to:

identify a design domain for which to optimize a topology based on an objective function, the design domain comprising a bounding box for an unknown topology discretized into multiple design elements;

determine an active region for the design domain, the active region comprising a selected set of active design elements in the design domain, including by:

performing finite element analysis (FEA) for design elements in the bounding box based on the objective function;

computing sensitivity values for design elements in the bounding box; and

selecting, as the active design elements of the active region, design elements in the bounding box that exceed a bounding sensitivity threshold;

iteratively adapt the active region, including by, for a given adaptation cycle:

expanding the design domain to include branch design elements within a threshold element distance from the active design elements in the active region;

performing finite element analysis (FEA) on the expanded design domain based on the objective function, including computing a respective sensitivity value based on the objective function for the design elements of the expanded design domain;

determining an adapted active region by:

activating, as active design elements, any of the branch design elements with a computed sensitivity value that exceeds an active sensitivity threshold; and

deactivating, from the active region, any active design element with a design variable value that changes less than a threshold amount from a previous adaptation cycle; and

setting the adapted active region as the active region for a subsequent adaptation cycle; and

continue to iteratively adapt the active region until an optimization ending criterion is satisfied.

14. The non-transitory machine-readable medium of claim 13 , wherein the optimization ending criterion is satisfied when a difference between a value of the objective function between adaptation cycles is less than an optimization process ending value.

15. The non-transitory machine-readable medium of claim 13 , wherein the optimization ending criterion is satisfied when the active region does not include any active design elements.

16. The non-transitory machine-readable medium of claim 13 , wherein the active sensitivity threshold is a function of the computed sensitivity values for the active region of a previous adaptation cycle.

17. The non-transitory machine-readable medium of claim 13 , wherein the bounding sensitivity threshold is different from the active sensitivity threshold.