Multiple Iterative Solution of Linear Algebraic Systems with a Partially Varying Matrix

Abstract

An iterative algorithm for solving a series of linear algebraic systems with partially varying coefficient matrix is suggested. Simple formulas for evaluating the speed up obtained are derived and used in choosing the related parameters. As examples, the choice of the drop tolerance and initial guesses are considered. Multiple solutions of linear systems of orders 708, 1416, 3540, 4425 arising in computing (by the method of moments) the electric capacity of two strips on a dielectric layer above a perfect conductive plane in the range of dielectric permeability is analyzed. As compared with Gaussian elimination, a 49 times speed up in solving 1000 linear systems of order 4425 is achieved. Bibliography 8 titles.

New Developments for Improved Simulation of Interconnects Based on Method of Moments

“…The algorithm for multiple iterative solution of the linear system with partially changing matrix was presented in [7]. In this algorithm, the preconditioner matrix M is formed from the first linear system.…”

Analytic Evaluation of the Computational Costs for Solving Systems of Linear Algebraic Equations in Multiple Computing of the Capacitance Matrix in a Range of the Dielectric Permittivity of Dielectrics

“…In order to obtain an analytic expression for the resulting acceleration, consider (as in [7]) the ratio (β) of the total time of solving m linear algebraic systems by the original algorithm (based on the pointwise LU factorization) to the time of solving them by the improved algorithm (based on the block LU decomposition). We have…”

“…Numerical values of the acceleration for N =1000 computed in accordance with (7) for N C =100, 500, 900 with N COND =1, 2, 10 and m=1, 100, 200, . .…”

Multiple Solution of Systems of Linear Algebraic Equations by an Iterative Method with Recomputed Preconditioners

“…In the above algorithm, the classical ILU(0) factorization is used, and no prefiltering is carried out because, for a large number of linear systems, this algorithm is efficient only if the zero drop tolerance value is used [5]. The initial preconditioner M is computed at Step 1.…”