Advantages of using a node-oriented sparse-matrix solver in nuclear plant dynamic analyses

Abstract

Nuclear plant dynamic analyses are commonly carried out by directly integrating the equations of motion of the model, or by using the free vibration characteristics with methods based on modal decomposition. In both approaches a large system of linear equations with little or no change in the coefficient matrix has to be solved repeatedly, either in the eigensolver or in the time integrator. The efficiency of the linear equation solver determines, to a large extent, the cost of the numerical production. The present linear equation solver has been designed to meet a number of objectives. The system matrices are assembled in terms of node-oriented submatrices instead of individual coefficients. Nodal quantities considered are not restricted to displacements. The Gauss elimination scheme is geared to sparseness rather than bandedness of the coefficient matrix. This eliminates trivial arithmetic and storage of zeroes. Matrix decomposition, and forward and backward substitutions, are separated. Thus, in an eigensolution iteration, or in a time integration, a sequence of right-hand-sides may be operated on with the coefficient matrix decomposed only once. Prescribed degrees of freedom are retained in the system of equations. Oblique excitations are treated directly through individual coordinate reference systems. Support forces are computed directly by multiplication of the unmodified coefficient matrix with the solution vector. Accuracy checks are conducted via comparison of total potential and kinetic energies. Application of the solution algorithm to a typical nuclear plant computer model is compared to other storage and solution schemes. The operation count of the present scheme indicates its performance advantage.