A central difference time stepping algorithm has been used to discretize the governing equilibrium equation in time. Written in an incremental form, it leads to the following relation

where . The is load vector and is vector of real internal forces at time . From given displacement increment vectors and , the corresponding vectors of velocities and accelerations can be easily computed using

Particularly, the use of diagonal mass matrix and dumping matrix expressed in the form of ( ) is assumed. This significantly simplifies the solution of the problem and leads to an efficient implementation of the proposed parallel algorithm.

*Daniel Rypl
2005-12-03*