This is a large nonsymmetric standard eigenvalue problem that arises from the stability analysis of a crystal growth problem. To determine the stability of the interfacial crystallization of a piece of solid crystal solidifying into some undercooled melt, solutions of the following equations are sought.

Zero Dirichlet boundary condition is imposed at infinity. The variable U in the above equations represents the temperature perturbation of the liquid, and N describes the interface perturbation in a transformed (parabolic) coordinate system. The constant P is the Peclet number. The second equation is satisfied only at the interface eta=1. Eigenvalues with largest real parts are of interest. They indicate the growth or decay of the initial disturbance at the solid-liquid interface. A change of variable is used to map the partial differential equation from an infinite domain to a finite box [0,1] × [0,1]. The matrix eigenvalue problem follows from discretization using the standard second order finite difference formulae. The Peclet number used here is P=0.05.

Matrices in this set:

CRY10000 (real unsymmetric, 10000 by 10000, 49699 entries)

CRY2500 (real unsymmetric, 2500 by 2500, 12349 entries)