线性瞬态涡流电磁场定解问题解的唯一性和稳定性

Uniqueness and stability of solution to the linear transient eddy current electromagnetic field problem for determining solution

线性瞬态涡流电磁场定解问题的主要特点是边界条件使用磁感应强度的法向分量边界条件代替了电场强度的切向分量边界条件,约束方程中忽略了位移电流.这种具有特殊性的定解问题的解是否唯一和稳定对于求解瞬态涡流电磁场而言是一个基本问题.本文在非涡流区引入标量位函数,证明了在推导过程中起重要作用的辅助函数的存在性.通过推导线性瞬态涡流电磁场定解问题的能量估计式,证明了该定解问题的解是唯一的,并且关于初始条件和外源项是稳定的.本结果对于线性瞬态涡流电磁场的求解有一定的指导意义.作为应用,给出了通有单脉冲电流的单匝圆环线圈与球形导体共轴的涡流问题的解析解.

The linear transient eddy current electromagnetic field problem for determining solution is characterized by replacing the interface condition of the tangential component of the electric field intensity by the interface condition of the normal component of the magnetic flux density, and ignoring the displacement current in the constraint equations. In is a fundamental theoretical problem whether the solution to the irregular problem for determining solution in unique and stable. In this paper, we introduce a scalar potential function in the nonconducting region, and prove the existence of an auxiliary function which is important to the problem. After deriving the energy estimate inequality, the uniqueness and stability of the solution to the linear transient eddy current electromagnetic field problem for determining solution are proved. The results of the paper can provide theoretical basis for analyzing and calculating the linear transient eddy current electromagnetic field problem. As an application example, we present the analytical solution to the eddy current problem that a single-turn coil driven by solitary pulse current is arranged coaxially with a spherical conductor.