## Multiparameter Optimization with a Least-Squares Objective

##### Friedrich Maier October 19, 2017

Optimization is an efficient way to gain deeper knowledge of a model. Much like the different flowers in a colorful bouquet, you can perform a variety of different optimization projects using the Optimization Module. However, parameter estimation is also a widely used technique. Such an analysis is usually set as a least-squares problem based on measured data, but for a clear and unique answer, you might need multiple measurements. Today, learn how to estimate parameters using a multiparameter data set.

Read More##### Caty Fairclough September 12, 2017

When thinking about natural selection, antennas are probably not the first thing that comes to mind. But with genetic algorithms, we can use the basic principles of natural selection to solve antenna optimization problems. For example, genetic algorithms enabled one research group to optimize the geometry of an optical antenna. They implemented their study by using LiveLink™ for MATLAB®, an add-on product to the COMSOL Multiphysics® software.

Read More##### Bridget Cunningham August 28, 2017

Pipelines are used to transport petroleum products and natural gas across long distances in cold environments. Because of this, petroleum mixtures may need to be preheated after being transported in pipelines before a refining process can begin. However, as the oil is pumped through the pipeline, heat is generated from the fluid itself as it flows. To keep costs down and the heat inside the pipe, the pipeline insulation can be optimized using models and simulation.

Read More##### Caty Fairclough August 9, 2017

Studying vacuum system designs can be difficult, since some analysis methods only work when the relative speed of the gas molecules is very large compared to the velocity of the enclosing walls. This is not the case for turbomolecular pumps, which we can model and analyze using a Monte Carlo approach and the Rotating Frame feature in the COMSOL Multiphysics® software. Let’s check out one example below.

Read More##### Bridget Cunningham May 24, 2017

Inertial focusing is a useful technique for various applications, particularly within the medical field. Ensuring its effectiveness requires accurately describing the migration of particles as they flow through a channel. Version 5.3 of the COMSOL Multiphysics® software gives you the tools to generate reliable results that agree with experimental data on inertial focusing. Our new benchmark model highlights these capabilities.

Read More##### Walter Frei April 20, 2017

When designing electromagnetic coils, we may want to adjust the position of the coils to achieve a desired magnetic field strength within a particular region of space. This is possible to do within the COMSOL Multiphysics® software by using the add-on AC/DC Module and Optimization Module to combine parameter and shape optimization. Let’s find out how.

Read More##### Walter Frei April 10, 2017

If you design electromagnetic coils, the combination of the AC/DC and Optimization modules with the COMSOL Multiphysics® software gives you the power to quickly come up with improved design iterations. Today, we will look at designing a coil system to achieve a desired magnetic field distribution by changing the coil’s driving currents. We will also introduce three different optimization objectives and constraints. This topic is of interest to anyone who is modeling coils or curious about optimization.

Read More##### Hanna Gothäll February 1, 2017

Topology optimization can be a useful step in your design process, but the generated designs often require further analysis. With the COMSOL Multiphysics® software, you can create geometries out of your topology optimization result plots and easily export them to CAD software. In this blog post, we discuss how to do so, using both 2D and 3D examples.

Read More##### Guest René Christensen November 3, 2016

Today, guest blogger René Christensen of GN ReSound discusses the importance of acoustic topology optimization and how to apply it in COMSOL Multiphysics. Topology optimization is a powerful tool that enables engineers to find optimal solutions to problems related to their applications. Here, we’ll take a closer look at topology optimization as it relates to acoustics and how we optimally distribute acoustic media to obtain a desired response. Several examples will further illustrate the potential of this optimization technique.

Read More##### Christopher Boucher September 22, 2016

In the previous installment of this series, we explained two concepts needed to model the release and propagation of real-world charged particle beams. We first introduced probability distribution functions in a purely mathematical sense and then discussed a specific type of distribution — the transverse phase space distribution of a charged particle beam in 2D. Now, let’s combine what we’ve learned and find out how to sample the initial positions and velocities of 3D beam particles from this distribution.

Read More##### Christopher Boucher September 19, 2016

Previously in our Phase Space Distributions in Beam Physics series, we introduced probability distribution functions (PDFs) and various ways to sample from them in the COMSOL Multiphysics® software. Such knowledge of PDFs is necessary to understand how ion and electron beams propagate within real-world systems. In this installment, we’ll discuss the concepts of phase space and emittance as they apply to the release of ions or electrons in beams.

Read More