However, trying to design experiments that allow you to extract the desired parameters with analytical methods can be challenging.Ī solution to these problems is to use the parameter estimation functionality of the Optimization Module to find the set of parameters of a model that minimizes the deviation between the physical and the simulated experiment. To account for nonlinearities, you might need to perform experiments. Method of moving asymptotes (both MMA and GCMMA)Ī model is only as accurate as the input, but it can be difficult to source accurate material parameters from suppliers.The gradient-based methods included in the Optimization Module are: The gradient-based methods simultaneously compute all analytic derivatives, whereas the derivative-free methods have to approximate each derivative and will take more time as the number of design variables increases. This is often the case for shape or topology optimization, where the design variables represent field quantities that are distributed throughout space and represented by different values in each mesh element. Gradient-based optimization can be used with thousands, even millions, of design variables. This is thanks to the core technology of COMSOL Multiphysics ® that features symbolic differentiation, which also provides the flexibility needed for solving custom multiphysics problems. This is possible for custom objectives or constraints, as long as these are differentiable. Gradient-based optimization methods are used when the derivatives can be computed efficiently using the adjoint method. The optimal and smoothed design is made available in the STL, 3MF, or PLY file formats for further use in another software or for verification analysis within COMSOL Multiphysics ®. In addition, just like with shape optimization, remeshing is not required for topology optimization. It is therefore common to introduce manufacturing constraints, because this enables the optimized design to be produced using extrusion or milling. The extreme design freedom associated with topology optimization can result in designs that cannot be manufactured with conventional methods. A dedicated user interface and study are available for topology optimization. This method typically results in an organic-looking design, and is a popular method for light-weighting. This approach allows for material removal and addition during the optimization process, allowing for holes to be created in the geometry not originally present in the design. Topology optimization represents even greater freedom in geometry variation than both parameter and shape optimization. This requires the CAD Import Module, Design Module, or one of the LiveLink™ products for CAD. The optimal solution is always a true CAD part that can be immediately exported to industry-standard CAD formats. When running a parameter optimization with parameters that define geometry dimensions, remeshing is needed at each iteration - a process that is fully automatic with the Optimization Module. Whereas a parametric sweep will give you an overview of the design parameter space, a parameter optimization will give you the optimal parameters and objective function values. The parameters that you use for parameter optimization can be the same that were used to set up the model in the first place, such as geometry dimensions, material properties, or boundary loads. An associated settings window prompts you to add an objective function, control variables and parameters, and constraints. To set up a parameter optimization in COMSOL Multiphysics ®, you only need to add a general-purpose Optimization study. Any inputs to the model - whether they be geometric dimensions, part shapes, material properties, or material distribution - can be treated as design variables, and any model output can be used as the objective function, which is then minimized or maximized. Starting with an objective function to improve and a set of design variables to change, along with an optional set of constraints, the software will search for an optimal design. You can optimize geometric dimensions when combined with the CAD Import Module, Design Module, or any of the LiveLink™ products for CAD. Used together with other modules from the COMSOL product suite, you can optimize devices and processes that involve phenomena such as electromagnetics, structural mechanics, acoustics, fluid flow, heat transfer, and more. The Optimization Module, an add-on to COMSOL Multiphysics ®, provides tools for parameter, shape, and topology optimization, as well as parameter estimation.
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