Study of stiff converging problems in magnetic field calculation
This thesis is mainly devoted to the numerical solutions of stiff converging problems in magnetic fields. Stiff problems are the ones whose converging process in iterative methods is extremely slow. The solution of many micromagnetic problems lead to unbounded nonlinear partial differential equations. A standard technique to convert these problems to boundary value problems is to assume that the geometry is periodic and then limit the solution to a bounded region. This can be done by introducing Dirichlet boundary conditions at points of odd symmetry and Neumann boundary conditions at points of even symmetry. These problems are then solved numerically using iterative techniques. It is shown that introducing Neumann boundary condition in any form slows down the convergence of the iterative process. A technique is introduced to give a measure of the degree of stiffness in linear cases. A numerical model for Barkhausen coercivity, which is an elliptic type nonlinear partial differential equation with stiff converging property, is used to calculate the coercivity of a garnet material known as Ca-Ge substituted YIG. This particular garnet, grown by liquid phase epitaxy is used in bubble memory devices and is believed to be the perfect magnetic material. A complete analysis is performed to measure the sensitivity of calculated coercivity to input parameters and the result of this calculation will be compared to experiment.
- Research Organization:
- Wayne State Univ., Detroit, MI (USA)
- OSTI ID:
- 5190885
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY-VALUE PROBLEMS
CONVERGENCE
DIRICHLET PROBLEM
GARNETS
MAGNETIC FIELDS
MAGNETIC PROPERTIES
MINERALS
NUMERICAL SOLUTION
OXYGEN COMPOUNDS
PHYSICAL PROPERTIES
PHYSICS
SILICATES
SILICON COMPOUNDS
SOLID STATE PHYSICS