Fast Methods for Solving High Accuracy Surface Modeling

Abstract

High accuracy surface modeling (HASM) is a novel surface modeling method. The well known preconditioned conjugate gradient (PCG) method is used to solve the equations produced by HASM. In this paper, in order to improve the convergence rate of PCG, we use two preconditioners: incomplete Cholesky decomposition conjugate gradient method (ICCG) and symmetric successive over relaxation-preconditioned conjugate gradient method (SSORCG), which have not previously been available for use with HASM. Furthermore, we give adequate storage scheme of the large sparse matrix and optimize the performance of sparse matrix-vector multiplication. We test the proposed method on a Dell OP990 machine. Numerical tests show that ICCG has the fastest convergence rate of HASM. We also find that both ICCG and SSORCG have much faster convergence rates than some available solvers.