The Matrix Market

Home Search Browse Resources

CRYSTAL: Diffusion Model Study for Crystal Growth Simulation

from the NEP Collection

Source: C. Yang, Rice University
Discipline: Material science

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.

1/(eta^2+xi^2)[d^2U/dxi^2 +d^2U/deta^2+2P(eta*dU/deta-xi*dU/dxi)]=lambda U; -1/(1+xi^2)[dU/deta+4P^2N+2P(N+xi*dN/dxi)]=lambda N; U=2PN at eta=1

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:

The Matrix Market is a service of the Mathematical and Computational Sciences Division / Information Technology Laboratory / National Institute of Standards and Technology.

[ Home ] [ Search ] [ Browse ] [ Resources ]

Last change in this page: Wed Sep 22 13:37:24 US/Eastern 2004 [Comments: ]