Finite-element methods for Maxwell's equations with stationary magnetic fields and Galerkin-wavelets methods for two-point boundary-value problems

Miscellaneous · Tue Jan 01 00:00:00 EST 1991

OSTI ID:5256557

Shann, Weichang

This thesis consists of two parts. In the first, the author studies numerical methods for solving a class of partial different equations of the Sobolev type. For the semidiscretization scheme (namely, only the spatial variables are approximated by finite element method) he proves its stability and its a priori error estimates in H{sup 1}, L{sup 2} and L{sup {infinity}} norms. For piecewise linear finite element spaces, the uniform convergence is proved by a superapproximation result. The induced system of ordinary differential equations can be solved in detail. Numerical experiments are presented. In the second part, a new class of methods, the Galerkin-wavelets methods, is studied. First introduced are the wavelets with compact supports. Then the trial function space of the Galerkin method is constructed by anti-derivatives of wavelets. He derives approximation properties of these spaces and the error estimates of the Galerkin-wavelets methods in H{sup 1} and L{sup 2} norms. The methods are applied to solve two-point boundary value problems. The conjugate gradient method is proved to be very efficient for solving the induced linear system; a preconditioner is also constructed. By changing bases, the full matrices are reduced to sparse ones. Numerical experiments are also presented.

• Research Organization: Pennsylvania State Univ., University Park, PA (United States)
• OSTI ID: 5256557
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MAXWELL EQUATIONS
FINITE ELEMENT METHOD
BOUNDARY-VALUE PROBLEMS
CONVERGENCE
ERRORS
GALERKIN-PETROV METHOD
MAGNETIC FIELDS
MATRICES
NUMERICAL SOLUTION
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
PARTIAL DIFFERENTIAL EQUATIONS
990200* - Mathematics & Computers