Abstract: This paper presents simiimplicit Runge-kutta type parallel direct integration methods to solve structural dynamic problems using 3-stage-3-order semi-implicit Runge-kutta method and using polynomial preconditioned conjugate gradient method for solving relevant systems of linear algebraic equations. Compared with relevant serical algorithm RK33S on YH-1 computer, parallel algorithm RK33P's speed up is 24~27 when linear systems of equations involved is of order 10³~10⁴.

Key words: parallel direct integration method, Runge-kutta type parallel method, polynomial preconditionings for the conjugate gradient method