Model reduction is a means to arrive at simplified dynamical descriptions of the behavior of a complex system that may be hard to model directly. Instead of attempting to model the overall behavior of such systems by considering all constituent degrees of freedom a simplified model is built with few degrees of freedom, but capable of modeling the observed behavior at a particular scale of interest using simulation or experimental data. In a multiresolution setting, aside from simplifying the geometry the attendant dynamics must also be simplified. This must occur in a controlled fashion with tight coupling between geometry and physics. We provide an explicit method of constructing reduced-order models of mechanical systems which preserves the Lagrangian structure of the original system. These methods may be used in combination with standard spatial decomposition methods, such as the Karhunen-Loève expansion, balancing, and wavelet decomposition. The model reduction procedure is implemented for three-dimensional finite-element models of elasticity, and we show that using the standard Newmark implicit integrator significant savings are obtained in the computational costs of simulation. In particular simulation of the reduced model scales linearly in the number of degrees of freedom, and parallelizes well. A few examples of how we apply these methods are in Model Reduction for Systems with Symmetry, or in this short Quick Time [Top | Home] |