1 Introduction Field Precision finite-element programs cover a broad spectrum of physics and engineering applications, including charged particle accelerators and X-ray imaging. The core underlying most of our software packages is the calculation of electric and magnetic fields over three- dimensional volumes. To use our electric and magnetic fields software effectively, researchers should have a background in electromagnetism and should be able to make informed decisions about solution strategies. First-time users of finite-element software may feel intimidated by these requirements. My motivation in writing this book is to share my experience in field calculations.
I hope to build users’ knowledge and experience in steps so they can apply finite- element programs confidently. In the end, readers will be able to solve real-world problems with the following programs: EStat (2D electrostatics) HiPhi (3D electrostatics) PerMag (2D magnetostatics) Magnum (3D magnetostatics) To begin, it’s important to recognize the difference between 2D and 3D programs. All finite- element programs solve fields in three-dimensions, but often systems have geometric symmetries that can be utilized to reduce the amount of work. The term 2D applies to the following cases: Cylindrical systems with variations in r and z but no variation in θ (azimuth).
Planar systems with variations in x and y and a long length in z . Which brings us to the first directive of finite-element calculations: never use a 3D code for a calculation that could be handled by a 2D code. The 3D calculation would increase the complexity and run time with no payback in accuracy. We need to clarify the meaning of static in electrostatics and magnetostatics. The implica- tion is that the fields are constant or vary slowly in time. The criterion of a slow variation is that the systems do not emit electromagnetic radiation. Examples of electrostatic applications are power lines, insulator design, paint coating, ink-jet printing and biological sorting.
Magne- tostatic applications include MRI magnets, particle separation and permanent magnet devices. A following coarse will cover simulations of electromagnetic radiation ( e.g. , microwave devices). Secondly, it’s important to have a clear understanding of the purpose of computer calcula- tions of electric and magnetic fields. Numerical methods should be used when it is not possible to generate accurate results with analytic methods. Numerical solutions are necessary in the following circumstances: 4