# COMSOL Blog

## Part 2: Mapping Variables with General Extrusion Operators

##### 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.

### Accessing Nonlocal Variables with Linear Extrusion Operators

##### 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.

### Verify Simulations with the Method of Manufactured Solutions

##### 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.

### Solution Joining for Parametric, Eigenfrequency, and Time-Dependent Problems

##### 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.

### How to Join Solutions in COMSOL Multiphysics

##### 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.