## How to Solve for the Brachistochrone Curve Between Points

##### Chien Liu | October 20, 2015

The shortest route between two points isn’t necessarily a straight line. If by shortest route, we mean the route that takes the least amount of time to travel from point A to point B, and the two points are at different elevations, then due to gravity, the shortest route is the brachistochrone curve. In this blog post, we demonstrate how to use built-in mathematical expressions and the Optimization Module in COMSOL Multiphysics to solve for the brachistochrone curve.

Read More##### Temesgen Kindo | October 5, 2015

Previously on the blog, we introduced you to Linear Extrusion operators and demonstrated their use in mapping variables between a source and a destination. This approach, as explained earlier, is limited to cases in which the source and destination are related by affine transformations. Today, we will discuss General Extrusion operators, which are designed to handle nonlinear mappings and the mapping of variables between geometric entities of different dimensions.

Read More##### Temesgen Kindo | September 29, 2015

In many simulation tasks, it is necessary to transfer variables from one region of a computation domain (the source) to another region or component (the destination). In COMSOL Multiphysics, this functionality is achieved by defining a point-to-point map, called an extrusion operator, that relates a set of destination points with a set of source points. Once a mapping is established by an extrusion operator, all variables defined at the source can be accessed from the destination using the same operator.

Read More##### Walter Frei | September 8, 2015

Good competitive paddling requires strength, timing, consistency, and teamwork. Initially, this may seem quite easy. Simply stick your paddle in the water and make the water go backward so that the boat moves forward. As it turns out, there are actually many different paddling strokes you can use depending on the situation.

Read More##### Walter Frei | September 7, 2015

When using the finite element method, we often want to model solid objects that are rotating and translating within other domains. The deformed mesh interfaces in COMSOL Multiphysics can be used to model these movements. In this blog post, we will look at the modeling of large linear translations and rotations of domains within other domains, while introducing efficient modeling techniques for addressing such cases.

Read More##### Walter Frei | September 4, 2015

COMSOL Multiphysics includes two interfaces for manually defining the deformation of finite element mesh, the Deformed Geometry interface and the Moving Mesh interface. In this blog post, we will address when to use these interfaces and how to use them to efficiently model translational motion.

Read More##### Walter Frei | September 2, 2015

Modeling geometries with high aspect ratios can be one of the more challenging tasks for the finite element analyst. You want to have a mesh that will accurately represent the geometry and the solution, but you do not want too many elements, as solving your models would then require excessive computational resources. Here, we will look at using swept meshing to generate efficient and accurate finite element meshes in the context of some common modeling cases.

Read More##### Chien Liu | August 24, 2015

Today we continue our discussion on the weak formulation by looking at how to implement a point source with the weak form. A point source is a useful tool for idealizing the situation where a source is concentrated in a very small region of the modeling domain. We will find that it is very convenient to set up such a point source using the weak form.

Read More##### Walter Frei | August 11, 2015

In the course of building multiphysics models, we often encounter situations in which the solution to one physics is periodic — or very nearly so — while the solutions to other physics of interest are nonperiodic. If we know this ahead of time, it is possible to exploit the periodicity to reduce computational requirements. Here, we will demonstrate how to accomplish this using the General Extrusion component couplings in COMSOL Multiphysics.

Read More##### Walter Frei | August 5, 2015

One useful — but in my experience, rarely used — capability available within COMSOL Multiphysics is the ability to compute design sensitivities. Assuming that you have a single objective function that is computed based on your finite element model, you can easily compute how sensitive this objective function is with respect to any model input, using only the core COMSOL Multiphysics package. In this blog post, we will look at how to use this functionality.

Read More##### Temesgen Kindo | July 27, 2015

How do we check if a simulation tool works correctly? One approach is the Method of Manufactured Solutions. The process involves assuming a solution, obtaining source terms and other auxiliary conditions consistent with the assumption, solving the problem with those conditions as inputs to the simulation tool, and comparing the results with the assumed solution. The method is easy to use and very versatile. For example, researchers at Sandia National Laboratories have used it with several in-house codes.

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