For the analysis of magnetic fields, I highly recommend a finite element analysis program called "FEMM" (Finite Element Methods Magnetics). This very useful program was written by Dr. David Meeker and version 3.1 is available free at his
web site. Be sure to get the tutorial by
Ian Stokes-Rees. This tutorial has very detailed step-by-step examples using FEMM. If you have been using version 2, version 3 has some new features that you'll fine useful and the data files are formated to make them easier to read, in case you want to change a parameter with a text editor. The .fem files are plain text, so you can view and edit them with any text editor, such as Notepad. It also includes a very powerful scripting capability.
The project editor incorporated in FEMM is good, however, if you make changes to an existing project file, you may want to save it with a different name before running the analysis in case you decide to revert back to the original design. FEMM as the peculiarity of writing the source file to disk with the original file name before it does an analysis.
The FEMM message board is an excellent source of additional information about magnetic problems.
Here is another example using FEMM, with graphical and numerical results.