# Scattering by Obstacles by Alexander G. Ramm

By Alexander G. Ramm

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Example text

For the general magnetic medium, the magnetization effect will vanish when the applied magnetic field is canceled, although another kind of magnetic medium, called a permanent magnet material, can retain the magnetization effect, even after the applied magnetic field is canceled. 1 Magnetization of Magnetic Media In classical electromagnetism, magnetization is the vector field that expresses the density of the permanent or induced magnetic dipole moments in a magnetic material. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the spins of the electrons or the nuclei.

Functional construction. We need to first construct the functional and make its extremum problem equivalent to the boundary problem of the unknown partial differential equation. There are two classical methods to form the basis of the transformation method in the modern FEM, that is, the Ritz variational method and Galerkin’s method. 2. Discretization or subdivision of the solution domain. The discretization of the domain is accomplished by dividing the solution domain into small elements according to geometrical and physical characteristics, such as line elements in a one-dimensional domain, triangular or quadrilateral elements in a two-dimensional domain, and tetrahedral elements, triangular prisms, or rectangular bricks in a three-dimensional solution domain.

3: 1  dtq 7 jðrq Þ Â rq  5 rp À rq  ð2:31Þ Practical Design of Magnetostatic Structure Using Numerical Simulation 26 With the help of r Â ðuFÞ ¼ ur Â F À F Â ru, we can obtain the integral form: ! ððð m 1  dt q À 0 jðrq Þ Â rp  4p rp À rq  tq m ¼ 0 4p ¼ m0 4p ððð rp Â tq ! ððð jðrq Þ rp Â jðrq Þ m   dt q À 0   r p À r q  rp À rq  dt q 4p Vq 8 > < m ððð ! 35) means that the total flux through any closed surface is zero. 2 Curl of Magnetic Induction and Ampere’s Loop Law The divergence of the magnetic vector potential Aðrp Þ is derived from the following equations.