Efficient Solution of Spacecraft Thermal Models Using Preconditioned Conjugate Gradient Methods

摘要

The thermal mathematical models of spacecraft are usually constructed using a lumped parameter network formulation. The governing equations under the steady-state condition are a system of nonlinear algebraic equations, often large and sparse. Generally, the quadratic convergent Newton's method is used to solve nonlinear systems, in which a linear system with a Jacobian coefficient matrix is solved at each iteration. It is necessary to solve this linear system in an efficient and economical way, exploiting the sparsity of the coefficient matrix in storage as well as in computation. The conjugate gradient method with appropriate preconditioners is a very successful tool to solve large, sparse, linear systems. Numerical experiments were conducted to investigate the effectiveness of preconditioned conjugate gradient methods for large spacecraft thermal problems. The results are compared with those of sparse elimination methods and the successive overrelaxation method. It has been found that the conjugate gradient method with the symmetric successive overrelaxation preconditioner is a simple and efficient method to solve large-order problems.