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Model Reduction Techniques for LS-DYNA ALE and Crash Applications

Model Reduction Techniques (MRT) are algebraic approximation solutions allowing for fast (real- time) interpolations (reconstruction) or extrapolations (prediction), based on previously existing DOE-type results, obtained either from FE computations or directly from constructions of reduced FE solutions. In a sense reduced models are subsets or decomposed domains of the solutions allowing for reconstruction of all spatial or temporal domain response. Contrary to FE where global interpolations are based on local "shape" (geometrical) functions, reduced models are based on basis functions which include not only geometrical but also material, boundary conditions and loading. This contributes greatly to fast solver solutions for on-board computing and may be used for time dependent approximations. Further, unlike response surface methods where smoothed solutions on certain criteria are obtained, MRT's provide complete solutions (reconstructions) of the space-time response of the original differential equation. Keywords – Model Reduction, POD, Non-linear explicit, Crash, Safety, ALE