Variational and D-N approaches for a magnetostatic Cauchy problem

摘要

The purpose of this paper is to propose two numerical methods for a magnetostatic Cauchy problem. In this problem, the Cauchy data are prescribed on a part of the boundary of a bounded domain. Based on the variational method, the proper boundary value on the rest of the boundary and the corresponding magnetic field in the domain are determined. Another method is based on the Dirichlet-Neumaun (D-N) alternating method. After computations by using these two numerical methods, it is concluded that our variational algorithm is stable, and the numerical solution is in good agreement with the exact one. The D-N algorithm is better than the variational algorithm in the cost of computations.