COMSOL Multiphysics^® 6.2 Release Highlights

Optimization Module Updates

For users of the Optimization Module, COMSOL Multiphysics^® version 6.2 introduces the ability to export the covariance matrix associated with parameter estimation, a new Stationary Then Eigenfrequency study step, and new mirror and sector symmetry features for shape and topology optimization. Read more about these features below.

Stationary Then Eigenfrequency Study Step

A new Stationary Then Eigenfrequency study step allows for consecutively solving a Stationary and an Eigenfrequency study in a single study step. This functionality, by default, uses the Stationary Solver to solve the dependent variables associated with the shape and topology optimization interfaces and uses the Eigenfrequency Solver to solve the dependent variables associated with the physics interfaces. This functionality is generally applicable and could be used to maximize the lowest eigenfrequency for an application in structural mechanics or to design band gaps. Note that the new Stationary Then Eigenfrequency study step solves for different sets of dependent variables in the stationary and eigenfrequency solvers, making it unsuitable for the maximization of, for example, buckling loads.

The new Stationary Then Eigenfrequency study step is combined with the Free Shape Shell feature to maximize the eigenfrequency of a shell. The model also uses the new Mirror Symmetry feature.

Parameter Estimation

The Global Least-Squares Objective feature and the Parameter Estimation study step now provide a Variance column for specifying the variance of individual measurements. Alternatively, the variance can be estimated automatically, and, in either case, the results can be used to estimate the uncertainty of the output from parameter estimation. The simplest approach is to compute confidence intervals for the estimated parameters, but the resulting intervals may be inapplicable if the parameters are correlated. Therefore, the ability to export the covariance matrix has been added and is available with the Levenberg-Marquardt optimization method. This capability provides a more detailed assessment of output uncertainty than using the confidence intervals of the estimated parameters. Additionally, support for bounds has been added to the Levenburg-Marquardt optimization method, and this can improve robustness for nonlinear models.

The computation of the covariance matrix can be enabled in the Output While Solving section of the Optimization and Parameter Estimation study nodes. The new Parameter Estimation with Covariance Analysis model verifies that the covariance matrix provides a tighter representation of the uncertainty than the confidence intervals (represented with black lines in the image).

Topology and Shape Optimization Updates

For topology optimization, new Mirror Symmetry and Sector Symmetry features have been added to simplify the setup of models where a symmetric design is required but where the effects of certain physics phenomena are not expected to be symmetric. In some cases, these features can be used to reduce the number of solutions or load cases per iteration, leading to improved performance. Additionally, the shape optimization features now include the ability to set the maximum displacement for individual components, and it is also possible to enforce a Euclidean interpretation of the maximum displacement, instead of the previous taxicab (box-like) interpretation.

New shape optimization settings for maximum displacement are demonstrated within the Wheel Rim — Stress Optimization with Fatigue Evaluation model and the new Shape Optimization tab in the ribbon.

General Purpose Updates

• The Control Variable Field feature includes support for grouping adjacent entities using the new geometric constant discretization.
• The settings for the Control Function feature include additional options and improved consistency between polynomial functions and Helmholtz regularization.
• New Shape Optimization, Topology Optimization, and Parameter Estimation ribbon tabs appear when the features are in use, providing better consistency with the Model Builder tree.
• The Control Function and Control Variable Field features have been moved to the Definitions branch in the Model Builder tree.

New boundary conditions for the Control Function feature are shown in the Shape Optimization of a Rectangular Loudspeaker Horn in 3D model. The Control Variable Field and Control Function features can be accessed from the Control Variables button in the Definitions tab.

New and Updated Tutorial Models

COMSOL Multiphysics^® version 6.2 brings several new and updated tutorial models to the Optimization Module.

Tweeter Dome and Waveguide Shape Optimization

Shape optimization is used to elicit a uniform response for an acoustic tweeter with respect to frequency as well as angle. The model has been simplified because acoustic far-field calculations now support optimization in axisymmetric models.

Application Library Title:
tweeter_shape_optimization
Download from the Application Gallery

Wheel Rim — Stress Optimization with Fatigue Evaluation

This model uses shape optimization to reduce stress in a wheel rim without increasing the mass or decreasing the stiffness. Fatigue behavior, shown by different colors, is assessed before and after optimization, suggesting its potential as a heuristic method for fatigue optimization. While the image displays only a single spoke of the wheel being optimized, the whole wheel is modeled in every iteration. Using the new Sector Symmetry feature in the Shape Optimization interface makes it simpler to impose sector symmetry.

Application Library Title:
rim_fatigue_optimization
Download from the Application Gallery

Wheel Rim — Topology Optimization with Milling Constraints

This model uses the Density Model feature to optimize the stiffness of a wheel subjected to a mass constraint and milling constraints along its axis. Sector symmetry is enforced to reduce the number of required load cases, and this aspect has been simplified with the new Sector Symmetry feature in the Topology Optimization interface. Furthermore, the geometry of the model has been changed, and a nonzero diffusion length is used to improve stability.

Application Library Title:
wheel_topology_optimization_milling
Download from the Application Gallery

Maximizing the Eigenfrequency of a Shell

This model maximizes the lowest eigenfrequency of a shell by combining the Free Shape Shell feature with the new Stationary Then Eigenfrequency study step. The previous version of this model used the Polynomial Shell feature, but that feature cannot preserve the continuity of normal vectors across edges.

Application Library Title:
shell_eigenfrequency_shape_optimization
Download from the Application Gallery

Optimal Control for Heating of a Rod

This model for optimal heating of a rod uses the Control Function feature and has been extended with more boundary conditions for increased flexibility and consistency.

Application Library Title:
optimal_heating_control
Download from the Application Gallery

Optimization of a Waveguide Iris Bandpass Filter — Transformation Version

This model uses the Transformation feature, available in the Shape Optimization interface, to design an RF bandpass filter. This feature includes the option to either set the center of the scaling manually or set it based on the average. It is now possible to choose different options for the individual coordinates, and that has allowed the setup of this model to be simplified. The model has also been simplified by replacing equation-based modeling with the new Sector Symmetry feature.

Application Library Title:
waveguide_filter_optimization_transformation
Download from the Application Gallery

Optimization of a Photonic Crystal for Signal Filtering

In this model, shape optimization is used to design a filter for a wave optics application. The positions of GaAs pillars (circles) are optimized using the Transformation feature, available in the Shape Optimization interface. The model has been changed to allow the pillars to move a maximum distance instead of having box-shaped displacement constraints.

Application Library Title:
photonic_crystal_filter_optimization
Download from the Application Gallery

Maximizing the Eigenfrequency of a Beam

This model maximizes the lowest eigenfrequency of a beam by combining the Density Model and Mirror Symmetry features in the Topology Optimization interface with the Stationary Then Eigenfrequency study step.

Application Library Title:
beam_eigenfrequency_topology_optimization
Download from the Application Gallery

Bracket — Eigenfrequency Shape Optimization

This model demonstrates maximization of the lowest eigenfrequency using the Free Shape Boundary feature in the Shape Optimization interface. This approach requires using the new Stationary Then Eigenfrequency study step.

Application Library Title:
bracket_eigenfrequency_shape_optimization
Download from the Application Gallery

Ten-Bar Truss Optimization

The model demonstrates a simple case of truss optimization and uses the Control Variable Field feature to control the truss areas. The model has been updated to use a new discretization for the Control Variable Field, as it is now possible to choose a discretization that is constant over geometric entities.

Application Library Title:
ten_bar_truss
Download from the Application Gallery

Parameter Estimation with Covariance Analysis*

This model demonstrates the use of the covariance matrix and verifies the functionality by solving the same optimization many times with different noise levels.

Application Library Title:
parameter_estimation_covariance
Download from the Application Gallery
*Requires the Nonlinear Structural Materials Module