Direct simulation for CAD models undergoing parametric modifications

We propose a novel approach—direct simulation—for interactive simulation with accuracy control, for CAD models undergoing parametric modifications which leave Dirichlet boundary conditions unchanged. This is achieved by computing offline a generic solution as a function of the design modification parameters. Using this parametric expression, each time the model parameters are edited, the associated simulation solution for this model instance can be cheaply and quickly computed online by evaluating the derived parametric solution for these parameter values. The proposed approach furthermore works for models undergoing topological changes, and does not need any mesh regeneration or mesh mapping. These results are achieved by use of the proper generalized decomposition model reduction technique, in combination with R-functions. We believe this is the first approach that can interactively simulate the physical properties of a CAD model, even undergoing topological change, without expensive re-computation. The approach is demonstrated for linear elasticity analysis; numerical results demonstrate its simulation accuracy and efficiency in comparison with the classic FE method.