Effectiveness of BiCGStab(2) method on AP1000

For solving the large and sparse non-symmetric linear systems of equations, BiCGStab method is known as one of the product type of iterative solvers. This method smoothes the residual norm of BCG method, using degree one MR (minimal residual) polynomial. The BiCGStab method is efficient in many cases and has been used for actual problems. Recently, BiCGStab2 method and GP-BiCG method which improved on the BiCGStab method, have been proposed. The BiCGStab(𝓁) method, which is proposed by Sleijpen and Fokkema, is generalized by these methods. This algorithm is also improved to decrease the amount of computational cost per iteration. In this paper, the BiCGStab(𝓁) method and other related methods are parallelized on distributed memory machine Fujitsu AP1000. Results obtained from the numerical experiments, i.e. boundary value problems of 2nd order partial differential equations, etc., show that BiCGStab(𝓁) algorithm is effective iterative method and suitable for parallel computing.