| e apply orthogonal spline collocation to a class of second-order, self-adjoint, elliptic eigenvalue equations on a rectangle, using piecewise Hermite bicubics as a basis. The inverse iteration and spectral transform Lanczos methods solve the discrete eigenvalue problem, using the preconditioned conjugate gradient method to solve the linear systems. The linear systems are preconditioned by the discretizations of special separable operators which are inverted using a fast matrix decomposition algorithm employing fast Fourier transforms. All the algorithms are highly amenable to parallel processing. These techniques were tested on the Schrodinger equations for the two-dimensional simple harmonic oscillator and the... |
