May 2, 2024 9:30–15:15 CEST

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COMSOL Day: Optimization

See what is possible when multiphysics modeling is combined with optimization

Modeling and simulation is highly beneficial for understanding, designing, and optimizing devices and processes across many research areas and industries.

While most software focus on structural mechanics when it comes to optimization, COMSOL Multiphysics® offers the ability to consider many different physics phenomena while leveraging state-of-the-art optimization techniques such as topology and shape optimization. For this reason, COMSOL Multiphysics® has become widely used for design and optimization.

COMSOL Multiphysics® features a wide range of capabilities for the exploratory phase of development and design as well as advanced yet user-friendly features for optimization involving phenomena such as heat transfer, fluid flow, electromagnetics, acoustics, and structural stresses and strains.

Join us for this COMSOL Day to get an overview of the software’s capabilities for topology optimization, shape optimization, and parameter optimization and estimation. You will hear from keynote speakers about their use of the optimization features in COMSOL®. Additionally, a COMSOL-led session on topology optimization will include real-world examples of how leading automotive companies are using topology optimization for the design of components.



Engineers and scientists are using the optimization methods available in COMSOL Multiphysics® to optimize devices and processes that involve a wide range of physics phenomena, including acoustics, electromagnetics, fluid flow, heat transfer, and more.

In this session, we will discuss the latest optimization technology that is driving this trend as well as the wide variety of applications for its use. We will go over the optimization techniques available and give an overview of the optimization functionality introduced in the latest versions of the software, including:

  • Shape optimization for maximizing eigenfrequencies
  • Manufacturing constraints in topology optimization, including milling constraints as well as mirror and sector symmetry
  • For parameter estimation, support for computing the covariance of parameter uncertainty
Keynote Speaker
Inverse Design and Characterization of Compact, Broadband, and Low-Loss Chip-Scale Photonic Power Splitters

Rasmus Ellebæk Christiansen, Technical University of Denmark

The use of photonic devices and components in various technological solutions is continually growing, having found use in a wide range of applications, such as data transfer and processing. Future adoption of integrated nanophotonics in scalable on-chip devices hinges on realizing small-footprint extremely low-loss optical components. This is true for both classical and quantum applications. To attain the required extreme performance of small-footprint photonic components, inverse design realized by topology optimization has proven to be effective for several applications in recent years where intuition and standard design rules have fallen short.

This keynote talk will center around the use of topology optimization for the design of one such important integrated photonic component: the power splitter, an essential building block for interferometric devices. Rasmus Ellebæk Christiansen will present recent work on the inverse design and characterization of compact, broadband, and low-loss chip-scale photonic power splitters, focusing on the experimental realization of an inversely designed ultracompact (2000 x 3000 nm) broadband (exceeding 300 nm at 0.5 dB) power splitter.

The talk will touch on all aspects of the study, from the mathematical formulation of the problem, numerical simulations, and topology optimization conducted utilizing COMSOL Multiphysics® to the fabrication and experimental realization of the device. The study was recently published in Material for Quantum Technology by IOP Publishing (DOI 10.1088/2633-4356/ad2521).


Parameter estimation is a crucial step when validating models with experimental data. COMSOL Multiphysics® includes dedicated functionality for parameter estimation, which is often used to extract properties and model parameters in the modeling and simulation of batteries, non-Newtonian fluids, and nonlinear materials in structural mechanics, to mention a few.

In this session, we will demonstrate parameter estimation and parameter optimization and how they can be used together with a wide range of combinations of physics phenomena. We will demonstrate how to:

  • Estimate and validate material and model parameters from experimental data
  • Optimize geometric parameters with respect to arbitrary design goals

The shape optimization functionality in COMSOL Multiphysics® allows for descriptions of arbitrary shapes that result from the optimization process by adjusting the position, orientation, and shape of each boundary. The functionality is used to design processes and devices involving a wide range of physics phenomena and combinations of physics phenomena (i.e., multiphysics); COMSOL users have applied shape optimization to designs ranging from loudspeaker drivers to filters and diplexers in electromagnetics applications to the shape of valves in microfluidics.

In this session, we will demonstrate shape optimization techniques, including:

  • Maximization of the lowest eigenfrequency
  • Stress and fatigue optimization of mechanical components
  • Advanced methods for controlling the shape change to fit the design freedom for a given application
Lunch Break
Introduction to COMSOL Multiphysics®

Learn the fundamental workflow of COMSOL Multiphysics®. This introductory demonstration will show you all of the key modeling steps, including drawing the geometry, setting up the materials and physics models, meshing, solving, and evaluating and visualizing the results.

Keynote Speaker
Optimizing Battery Pack Lifetime: 3D Modeling of Degradation Fitted to Experimental Data

André Gugele Steckel, Resolvent P/S

Batteries play a vital role in a zero-emission future, and modeling battery systems can provide significant benefits for battery efficiency and lifetime. The difficulty in simulating, and finding optimal solutions for, battery systems stems from the many orders of magnitude of scale of such problems — from the chemistry in the individual battery layers to the degradation patterns across entire battery packs and battery modules. In this keynote talk, André Gugele Steckel will discuss how Resolvent P/S used the COMSOL Multiphysics® software to develop a battery pack degradation model, highlighting the role that the Optimization Module played in the process.


The topology optimization functionality in COMSOL Multiphysics® has been used to design rotors in electric motors as well as cooling channels for power electronics in hybrid vehicles. Because topology optimization has the most extreme design impact of the optimization methods, it is typically used early in the design phase. In the latest versions of the COMSOL® software, manufacturing constraints can be introduced to the optimization formulation, making designs compatible with conventional methods for mass production. Furthermore, the analysis can account for eigenfrequencies and transient aspects in addition to stationary studies.

Join this session to learn how COMSOL® users benefit from incorporating topology optimization and multiphysics modeling into their research, development, and design projects. We will show you how to get started with the software and demonstrate:

  • Topology optimization for an eigenfrequency problem
  • Verification using body-fitted meshes and other techniques for avoiding common pitfalls

A surrogate model can yield high accuracy with very little computational effort once it is properly trained. The latest version of COMSOL Multiphysics® features functionality for creating data-driven surrogate models based on advanced function approximation enabled by deep neural networks and Gaussian process regression. This functionality can be used to approximate any physics or multiphysics phenomenon in the software. Thanks to their minimal computational cost, surrogate models are well suited for use in uncertainty quantification — where many computations of a model may be required — and in simulation apps — where interactivity and speed may be expected.

Join this session to:

  • Get an overview of the functionality for creating surrogate models in COMSOL Multiphysics®
  • Learn how it can serve as an efficient environment for generating physics-based training data via design-of-experiments
  • Learn how surrogate models can be used in the Uncertainty Quantification Module to perform screening, sensitivity analysis, uncertainty propagation, and reliability analysis
Closing Remarks

Register for COMSOL Day: Optimization

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COMSOL Day Details

Local Start Time:
May 2, 2024 | 9:30 CEST (UTC+02:00)
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Invited Speakers

Rasmus Ellebæk Christiansen Technical University of Denmark, Department of Civil and Mechanical Engineering, Section for Solid Mechanics

Rasmus Ellebæk Christiansen received his PhD from the Technical University of Denmark (DTU) in 2016 for his work on topology optimization for frequency-domain applications. As part of his research career, he has held visiting appointments at both École Polytechnique Fédérale de Lausanne and Massachusetts Institute of Technology. He has become an expert in the field of inverse design through his continued focus, and today he works in the Topology Optimization group at DTU as an associate professor.

Christiansen's primary research interest is inverse design applied to problems within electromagnetics and acoustics. A key aspect of his work is the push to ensure highly accurate experimental realization of inversely designed blueprints through integration of fabrication constraints into the design process. Done right, this approach enables direct fabrication of highly optimized devices using standard tools, replicating numerically predicted performance nearly 1–1 without requiring postprocessing.

André Gugele Steckel Resolvent P/S

André Gugele Steckel is a modeling specialist at the COMSOL-certified engineering consultancy Resolvent P/S, located in Denmark. Steckel uses his background in physical engineering to cover a broad range of multiphysics subjects that combine modeling fields of various natures. With a PhD from DTU Physics in modeling acoustofluidics in the COMSOL Multiphysics® software and an MSc in physics and nanotechnology, Steckel has extensive experience in modeling and simulation of fluid mechanics, electromechanical, piezoelectricity, time-harmonic vibrational mechanics, and acoustofluidics systems in COMSOL Multiphysics®. At Resolvent P/S, he leverages his experience for the simulation of solid oxide fuel and electrolysis cell stacks, battery modeling, reduced-order modeling, and microfluidics simulation and device development.