  Parametric optimization is an important product design technique, especially
in the context of the modern parametric feature-based CAD paradigm. Realizing
its full potential, however, requires a closed loop between CAD and CAE (i.e.,
CAD/CAE integration) with automatic design modifications and simulation
updates. Conventionally the approach of model conversion is often employed to
form the loop, but this way of working is hard to automate and requires manual
inputs. As a result, the overall optimization process is too laborious to be
acceptable. To address this issue, a new method for parametric optimization is
introduced in this paper, based on a unified model representation scheme called
eXtended Voxels (XVoxels). This scheme hybridizes feature models and voxel
models into a new concept of semantic voxels, where the voxel part is
responsible for FEM solving, and the semantic part is responsible for
high-level information to capture both design and simulation intents. As such,
it can establish a direct mapping between design models and analysis models,
which in turn enables automatic updates on simulation results for design
modifications, and vice versa -- effectively a closed loop between CAD and CAE.
In addition, robust and efficient geometric algorithms for manipulating XVoxel
models and efficient numerical methods (based on the recent finite cell method)
for simulating XVoxel models are provided. The presented method has been
validated by a series of case studies of increasing complexity to demonstrate
its effectiveness. In particular, a computational efficiency improvement of up
to 55.8 times the existing FCM method has been seen.
