A reduced-basis discretization method for chemical vapor deposition reactor simulation

Abstract

A computational technique for producing reduced-order models of distributed parameter systems is developed in the context of a tungsten chemical vapor deposition (CVD) simulation problem. The reduced-order simulations are formulated in terms of a reduced-basis Galerkin projection of the CVD system thermal dynamics model, where the trial functions are defined globally over the spatial domain and the entire processing cycle, reducing the simulation problem to the solution of a relatively small number of nonlinear algebraic equations. The biorthogonal, reduced basis is computed using the Karhunen-Loéve decomposition, where the two-point spatial and temporal correlation functions are determined from an eigenfunction expansion solution to a linearized approximation of the nonlinear CVD system. A subset of the parameters in the linearized system are represented as random variables so that the reduced basis remains accurate as the parameters are changed in simulations performed using the reduced model. We find that the number of floating point operations required for the generating the reduced basis and the subsequent full-Galerkin discretization of the nonlinear system is one order of magnitude less than the computational effort required for direct, semidiscrete Galerkin projection simulations of the CVD system model.