One of the most important questions that are raised when using any analysis software is “Do I have enough elements for an accurate solution?” In addition to simplify the number of elements on a model, it is useful to be able to concentrate the elements where the field gradients are highest to ensure that computation is not wasted in regions where very little is happening. To a large degree, the self-adaptive feature of Integrated solvers addresses this question. Users can solve a model to a given degree of accuracy or use a given number of element refinement steps to generate the elements needed. In the end, however, the question of how the given accuracy relates to the accuracy in the computed value that is of most interest often remains.

A method has been introduced in version 7.0 of Integrated Software to allow users to refine one additional step and check results to gain confidence in the solution. This method is implemented by way of a simple command, “Refine Solution”. By calculating the values that are most interesting, using the “Refine Solution” command, and then recalculating the same values, you can have confidence that the solution is refined enough for your specific application and accuracy needs.

As an example, consider the simple magnetic catch found in the Amperes Quick Start Guide.

The catch is modeled using the symmetry in the X=0 and Y=0 planes.

We’ll start by solving the model self-adaptively with an accuracy criterion of 0.05. In this we might expect the accuracy of the force calculation to be around 5%, but we would like to confirm this.

After the model is solved with this criterion, the elements appear as in the image below on the left. The global error norm reported by the program is 0.00163. The elements generated after this, by the Refine Solution command, are displayed below on the right.

On the initially solved model, the force calculated on the bottom piece using “Amperian Force on Volume” is 3.483 N. The same force calculation with the refined model is 3.492, a difference of less than 0.5%. For the purpose of demonstration, graphs of the vertical component of the B-field between the two pieces are also compared below. The value of the field in the two graphs differ by about 2.5% on average.

Users should find that the Refine Solution method of verifying results will give them confidence in their solutions and help them to get a better feel for how many elements are necessary for their models and where they are most needed.