Abstract
To satisfy the need for network parallel computing in the whole time domain, a penalized weighted residual formulation for the second-order initial value problems is developed and its time finite element approximation is presented. To impose properly both the initial displacement and velocity, the initial velocity is imposed to the weighted residual equation as a penalized form that is constructed such that the approximated initial velocity can satisfy the initial condition in the average sense. By this procedure, the penalized weighted residual formulation makes it possible to handle the whole time domain of investigation and to use the conventional-displacement-based finite element technique without any other artificial routine. Through several numerical tests, it is confirmed that the present method gives very accurate solutions for various systems arising in the second-order initial value problems and presents promising characteristics for network parallel computation in the whole time domain of investigation.
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