Application of accelerated iterative methods for solution of thermal models of spacecraft

Abstract

Lumped parameter thermal network formulation is widely used for constructing mathematical models of spacecraft. For steady-state analysis, the mathematical model is a system of coupled nonlinear algebraic equations. Generally, Newton's method is used for the solution of nonlinear systems. This is an iterative method in which a linear system is to be solved at every iteration. A direct method such as Gaussian elimination is commonly employed for this purpose. However, for large order systems, conventional direct methods are impractical because of the required high storage and computation time. The coefficient matrix associated with the mathematical model of spacecraft, in most cases, is sparse. Iterative methods offer special advantages over direct methods in solving large, sparse linear systems. They are easy to code and do not require explicit storage of the coefficient matrix. Moreover, certain acceleration schemes speed up considerably the convergence of the basic iterative methods. The Ng accelerated Jacobi method and successive overrelaxation method employing Carre's algorithm for an estimate of the optimum relaxation parameter are some of the powerful iterative techniques. Results of numerical experiments conducted on various methods indicate that accelerated iterative techniques seem to be an efficient way of solving large mathematical models.