## Integrals with Moving Limits and Solving Integro-Differential Equations

##### Temesgen Kindo | October 6, 2016

In a previous blog post, we discussed integration methods in time and space, touching on how to compute antiderivatives using integration coupling operators. Today, we’ll expand on that idea and show you how to analyze spatial integrals over variable limits, whether they are prescribed explicitly or defined implicitly. The technique that we will describe can be helpful for analyzing results as well as for solving integral and integro-differential equations in the COMSOL Multiphysics® software.

Read More##### Temesgen Kindo | October 5, 2016

Cylindrical coordinates are useful for efficiently solving and postprocessing rotationally symmetric problems. The COMSOL Multiphysics® software has built-in support for cylindrical coordinates in the axisymmetry physics interfaces. When defining custom partial differential equations (PDEs) using the mathematical interfaces, paying close attention to their meaning is important. The PDE interfaces assume partial differentiation in a Cartesian system, requiring manual coordinate transformations to change to a cylindrical system. See how to account for such coordinate transformations when using your own PDEs.

Read More##### Björn Bretz | September 27, 2016

To help optimize your modeling processes, we are continuously striving to enhance the quality of our meshing capabilities. The recent improvements to the algorithm for generating tetrahedral meshes in the COMSOL Multiphysics® software are one such example. Follow along as we guide you through the process of generating a tetrahedral mesh to highlight this improved functionality and its correlating features, while discussing its role in helping you obtain better simulation results.

Read More##### Amelia Halliday | September 20, 2016

To optimize your modeling processes, there are a number of built-in materials available for you to use in the COMSOL Multiphysics® software. Along with these materials are features and functionality that allow you to efficiently assign materials to geometric entities in your model. These tools help expedite the process of assigning materials, specifying material properties, and even comparing the impact of different materials on your simulation results. Here, we’ll highlight three tutorial videos that showcase how to use such tools.

Read More##### Hanna Gothäll | September 14, 2016

When addressing your geometry- and mesh-related support questions, we’ve noticed an increased use of STL files originating from 3D scan sources and meshes in NASTRAN® file format as bases for geometries. Performing simulations on these realistic objects can be challenging, particularly when preparing the geometry. Dealing with these files is now easier thanks to updates in the COMSOL Multiphysics® software. Learn how to utilize this functionality as well as how to achieve good results when importing STL and NASTRAN® files.

Read More##### Magnus Ringh | September 2, 2016

A COMSOL Multiphysics® simulation typically includes one or more field quantities in its output. Depending on the number of field quantities, the geometry’s complexity, and the mesh density required for valid results, simulations can include millions of degrees of freedom (DOFs). Oftentimes, storing one or more scalar quantities or the results on a small geometry part is sufficient. Here, we explore tools for storing selected output quantities and minimizing model file sizes and the time required to display this data.

Read More##### Temesgen Kindo | September 1, 2016

Suppose you take a piece of metal — a thin sheet, for example — and apply some mechanical loads. The metal will deform and take on a new shape that differs from the original undeformed configuration. Say you now want to use this deformed object as part of a new geometry construction. You can then solve another physics problem on the new composite domain. Today, we’ll demonstrate how to use a deformed object as an input to a geometry sequence.

Read More##### Temesgen Kindo | August 30, 2016

Have you ever wanted to integrate your COMSOL® software apps with external data files? These files can contain material properties, geometric dimensions, or other model inputs, and such data can derive from internal company standards or be provided by a vendor. Built-in methods in the Application Builder simplify reading from these files and displaying options read. To show this procedure, we will build an app that populates a combo box with material properties from a comma-separated values (CSV) file.

Read More##### Caty Fairclough | August 18, 2016

Does your simulation take a large amount of computational time to solve? One potential reason for this is that your mesh is using too many elements. In cases such as this, you may want to switch to user-controlled mesh to manually build and edit the meshing sequences available in the COMSOL Multiphysics® software as an alternative to using the default meshing sequence. As we’ll highlight with a tutorial example, this can help reduce memory requirements while providing accurate results.

Read More##### Walter Frei | August 11, 2016

Extending our discussion on modeling the harmonic excitations of linear systems, we will now shift focus to nonlinear systems. We will look at problems where the loading on the system has some sinusoidal components as well as cases where the material properties or loads and constraints depend directly on the solution. As you will see, COMSOL Multiphysics can address these apparently nonlinear cases with some very efficient solution algorithms. Let’s find out how.

Read More##### Walter Frei | August 10, 2016

In many engineering situations, we can assume that excitations on the system of interest and the responses are sinusoidal over time. When this assumption holds, we can use a so-called frequency-domain analysis, which leads to some very efficient solution techniques. Let’s go over a few basic concepts and the conditions under which we can make this assumption, while exploring various solution approaches to take.

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