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THPSC009 |
Boundary-Value Problem for Elliptic Equation in the Corner Domain in the Numerical Simulation of Magnetic Systems | |
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Modern particle accelerators and detectors* contain magnetic systems of complex geometrical configuration. Design and optimization of the systems led to the necessity of solving a nonlinear boundary-value problem of the magnetostatic. The considered region consists of two sub-domains namely: vacuum and ferromagnetic. In view of complexity of magnetic systems, the ferromagnetic/vacuum boundary can be non-smooth, i.e. it includes a corner point that separate two smooth curves belongs to different sub-domains and crossed in the corner point at some angle. A nonlinear differential equation of divergent type in the domain with a corner and the opportunity of existence of solutions with an unlimitedly growing module of gradient in the vicinity of the corner point have been considers in**. A theorem of limitation of the module of gradient of the solution in the vicinity of the corner point in the case of the magnetic permeability satisfying to certain conditions at high fields was proved. An upper estimate of the maximum possible growth of the magnetic field in the corner domain is presented in [4]. The method of designing the differential mesh near the corner domain allowed reducing considerably a relative error of calculating the magnetic field in the considered design problems. Examples of calculating some magnetic systems containing a domain with the corner point are given in [2-4].
* Perepelkin E. and ATLAS collaboration, Aad, JINST 2008, S08003, vol.3, p.437. ** Perepelkin E.E. et al. Estimation of magnetic field growth and construction of adaptive mesh in corner domain for magnetostatic problem. Physics of Particles and Nuclei Letters, V 13, Issue 6, 2016. |
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