Multigrid Preconditioners Applied to Three Dimensional Parabolic Equation Type Models

摘要

The numerical solution of three dimensional standard parabolic equation (SPE) and high angle parabolic equation (HAPE) approximations of the Helmholtz equation is investigated. The model is discretized using an unconditionally stable, implicit finite difference scheme based on the Crank-Nicolson method in the range direction. The discretization in the transverse direction is based on a standard finite difference or finite element method. The use of an implicit scheme in range requires the solution of a large, sparse, nonselfadjoint system of equations at each range step of the marching algorithm. This system is solved by preconditioning the matrix and then applying the conjugate gradient method to the normal equations (PCGN). The main result is the development of a preconditioner that significantly reduces the condition number of the original matrix and is efficiently implemented into the marching algorithm. 15 refs. (ERA citation 11:042273)