| What is the function of finite-element software? Finite-element programs calculate quantities that vary over a region of space (fields) - examples include electric fields, magnetic fields and temperature distributions. These quantities are governed by partial differential equations. You can solve the equations analytically for simple systems, but numerical methods are more effective for real-world geometries or when materials exhibit complex behavior. For a solution on a digital computer, the differential equations must be converted to a large set of linear equations. The strategy is to divide space into small pieces (elements) so that field variations over a single piece are relatively simple. This activity is called mesh generation. The finite-element method is one way to generate the linear-equation set. In contrast to finite-difference methods, the finite-element procedure can handle conformal meshes where elements closely fit the boundaries of objects. The resulting advantage is higher accuracy with fewer operations. Numerical computer codes are powerful tools. In a few hours, you can find solutions for complex systems that would require weeks of effort by mathematicians or theoretical physicists. Nonetheless, it is important to remember that numerical calculations have their own challenges. The efficiency of solutions and the quality of results depend on your judgment. To help, we have put considerable effort into documentation and user interfaces. Experienced researchers can add numerical methods to their capabilities with a few days effort. |