## 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##### 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##### 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##### 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.

Read More##### Temesgen Kindo | July 28, 2014

In a previous blog entry, we discussed the join feature in COMSOL Multiphysics in the context of stationary problems. Here, we will address parametric, eigenfrequency, frequency domain, and time-dependent problems. Additionally, we will compare and contrast the built-in with and at operators versus solution joining.

Read More##### Temesgen Kindo | July 1, 2014

In engineering analysis, the need to compare solutions obtained under different circumstances frequently arises. Some possible scenarios include comparing the effect of different load or parameter configurations, and enveloping results to find the worst or best case at each point of the domain. In each of these and other similar cases, you need access to more than one data set. Here’s how to accomplish such tasks using COMSOL Multiphysics.

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