特異な非対称行列を係数とする連立1次方程式での各種反復解法の収束特性と流れの数値シミュレーションへの応用

抄録

The consistency of a singular system of linear equations are discussed, where the coefficient matrix is nonsymmetric, and the convergence properties of the bicon-jugate gradient, conjugate gradient squared, and conjugate residual methods are discussed. Numerical experiments are presented for a Laplace equation with Neumann boundary conditions. Next, the consistency theory of a singular system is applied to numerical simulation of fluid flow. In order to ensure convergence of the solution of the pressure equation, this paper proposes the perturbation removal method using the eigenvector of the transposed coefficient matrix corresponding to the eigenvalue 0. Thermal convection of a Boussinesq fluid is simulated in a square cavity. The pressure equation is solved using the proposed method. The convergence rates of the iterative methods are compared. The simulation result is in good agreeement with a benchmark solution.