Abstract
A magnetostatics problem arises when searching for the distribution of the magnetic field generated by magnet systems of many physics research facilities, e.g., accelerators. The domain in which the boundary-value problem is solved often has a piecewise smooth boundary. In this case, numerical calculations of the problem require consideration of the solution behavior in the corner domain. In this work we obtained an upper estimation of the magnetic field growth using integral formulation of the magnetostatic problem and propose a method for condensing the differential mesh near the corner domain of the vacuum in the three-dimensional space based on this estimation.
Highlights
Many physics research facilities use magnetic systems of various configurations, e.g., a system of spectrometric magnets
The problem is reduced to the formulation of a magnetostatics problem of finding the distribution of the magnetic field generated by the magnetic system under consideration
Based on the estimation obtained we propose to condense the mesh approaching the corner point
Summary
Many physics research facilities use magnetic systems of various configurations, e.g., a system of spectrometric magnets. It is very important to know with a good accuracy the distribution of the magnetic field generated by this system. The problem is reduced to the formulation of a magnetostatics problem of finding the distribution of the magnetic field generated by the magnetic system under consideration. Since the magnetic system has a complicated configuration, the solution to the problem is usually sought using numerical methods. This paper discusses the case when the domain over which a boundary value magnetostatics problem is solved has piecewise smooth boundary. In this case, the solution to the problem or the derivative solutions can have a singularity, the numerical search for the solution requires the use of special methods
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