Abstract: In this paper a general matrix decomposition scheme as well as an element-by-clement relaxation algorithm combined with step-by-step integration method is presented for transient dynamic problems thus the finite element method can be fromforming global stiffness matrix global mass matrix as well as solyin large scale sparse equations Theory analysis and numerical results show that the presented matrix decomposition scheme is the optimal one The presented algoithm has else physicalmeaning and can be busily applied to finite element codes

Key words: finite element method, step-hy-step integration matrixdecomposition, element-by-element relaxation