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Performing Optimization in COMSOL Multiphysics^®

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Optimization is the mathematical process of finding the optimal version of a design or process. This is achieved through a series of iterations where specific design aspects are varied, such as the dimensions, material properties, operating conditions, etc., in order to meet an objective, such as the performance of a design, the need to fall under a specific criteria, etc. An example of this could be minimizing the amount of material needed to support a structure while maintaining structural integrity. In this 10-part course, you will get an introduction to optimization, learn how to perform multiple types of optimization using the COMSOL Multiphysics^®software and the Optimization Module add-on, and, in the process, learn about the benefits of combining multiphysics simulation with optimization. You will also learn how to perform parameter estimation, where we estimate the values of the input parameters to a model from experimental data.

The COMSOL Multiphysics UI showing the Model Builder with the Optimization solver selected, the corresponding Settings window, and the Graphics window showing the optimal cooling model's concentration profile. In Part 5 of this course, you will perform an optimization study to adjust the cooling stream temperature of a reactor in order to maximize the production of an intermediary product.

The focus of this course is how optimization is incorporated with a completed, solved model. In some examples, we will complete a full model build from start to finish before implementing the optimization analysis. In most exercises, however, we will start with a model where only the optimization is missing. Note that each part of this course will include demonstrations as well as downloadable model files so that you can gain hands-on experience. With this, you will apply optimization to a variety of different problems in different application areas.

Note: This course is meant for users that are familiar with COMSOL Multiphysics^®. If you are new to the software, we strongly recommend either attending alive, introductory trainingand/or completing theintroductory tutorial seriesbefore starting this Learning Center course.

You can find a synopsis of the topics covered in each part below.

Part 1:Introduction to Optimization

• Optimization terminology
• Types of optimization problems
• Common optimization tasks
• Parametric sweep & batch sweep

Part 2:Using Parametric Sweeps to Perform Optimization

• Parametric optimization
  • Preparing the forward model simulation for optimization analysis
  • Parametric Sweepstudy set up

Part 3:Using the Optimization Study Step

• Introduction to performing optimization using the software
• Optimization workflow
  • Setting up optimization in COMSOL Multiphysics^®
  • How to approach setting up the optimization problem
  • Formulating the objective function
  • Selecting the optimization solver

Part 4:Using Optimization Studies to Perform Parameter Optimization

• Adding, setting up, and computing an optimization study
  • Important settings in theOptimizationstudy node
  • Using various optimization solver methods
• Parameter optimization

Part 5:Optimizing Multiple Parameters and Understanding Optimization Solvers

• Multiparameter optimization
• Optimization application examples
• Optimization solvers
  • Understanding various solvers
  • Gradient-based solvers
  • Comparison of algorithms
  • Derivative-free solvers
  • Optimization Tutorials app

Part 6:Using the Shape Optimization Interface and Study Step

• Introduction to shape optimization
  • Parametric representation of boundaries
  • Regularization
  • Built-in features for shape optimization

Part 7:Using the Curve Fitting and Parameter Estimation Study Steps

• Introduction to parameter estimation
  • General Parameter Estimation app
  • Steady state, time dependent, or frequency domain
  • Curve Fittingstudy versusParameter Estimationstudy

Part 8:Performing Parameter Estimation and Introduction to Topology Optimization

• Parameter estimation
  • Important settings
  • Fitting measured data to estimate material properties
  • Weighted objective functions
• Introduction to topology optimization
  • Key implementation issues
  • Built-in features for topology optimization

Part 9:Using the Topology Optimization Interface and Study Step

• Topology Optimizationinterface
  • Settings and physics feature nodes
  • Density Modelfeature
• Topology Optimizationstudy
  • Setup and settings
  • Topology Linknode under materials
• Exporting the optimized topology & validation

Part 10:Topology Optimization Applications and Comparing Optimization Techniques

• Topology optimization examples
• Comparison of methods
  • Dimensional optimization
  • Shape optimization
  • Topology optimization
• Miscellaneous topics related to optimization
  • Features introduced in version 6.0
  • Multistudy optimization
  • Optimization with LiveLink™ for CAD

The COMSOL Multiphysics UI showing the Model Builder with expanded Filer options, the corresponding Settings window, and the Graphics window with the MBB beam model. The optimized topology for an MBB beam is exported into a new component for analysis. Example from Part 9 of this course.

After completing the course, you will understand what optimization is and know about the different types of optimization and the related terminology. You will also understand how optimization is performed and know which solver methods are best suited for different problems. Moreover, you will be familiar with the optimization capabilities and features within COMSOL Multiphysics^®and the Optimization Module.

Please note that the videos featured in this course were taken from a past event; because of this, some slides feature a daily agenda that is not relevant to this course.