Hi all, I need help with numerical solution of motion equation. From the numerical point of view and in the real of the finite element method, which method is recommended for the solution of damped ( proportional damping) linear motion equation? I have been trying three common methods; Modal decomposition, time integration ( Newark method), and frequency domain method ( for steady state solution). I faced a problem with the accuracy of modal decomposition method as I don't and can not use all the modes. In addition , if the displacements of all nodes are desired, the method turns out to be more time consuming than the time integration method. The frequency domain method is another choice when steady-state solution is sought but, in my code , it may need too much memory. So, I found the time integration to be the best and it is fast if we use an iterative matrix solver and use the solution of the previous time-step as the initial value of the current step. But isn't this contrary to claims that the modal decomposition method is the method of choice for linear motion equation? Your help would be highly appreciated. Thanks.