A survey is provided of shape parameterization techniques for multidisciplinary optimization, and some emerging ideas are highlighted. The survey focuses on the suitability of available techniques for multidisciplinary applications of complex con gurations using high-delity analysis tools such as computational uid dynamics and computational structural mechanics. The suitability criteria are based on the ef ciency, effectiveness, ease of implementation, and availability of analytical sensitivities for geometry and grids. A section on sensitivity analysis, grid regeneration, and grid deformation techniques is also provided. NomenclatureB = Bernstein polynomial N c = polynomial coef cients N D = grid perturbations J = cell Jacobian k = spring stiffness N = B-spline basis function N P = coordinates of nonuniform rational B-spline (NURBS) control point N R = coordinates of deformed model N r = coordinates of baseline model t = response N U = design vector u = independent parameter coordinate V = baseline cell volume N v = design variable vector W = NURBS weights " = small positive number Subscripts f = eld (volume) grid g = geometry i; j = control point indices k = grid-point index m = element index n = basis vector index p = degree of Bernstein polynomial and B-spline basis function s = surface grid Superscripts i = polynomial power n = number of design variables

This paper presents a free-form deformation technique suitable for aerodynamic shape optimization. Because the proposed technique is independent of grid topology, we can treat structured and unstructured computational fluid dynamics grids in the same manner. The proposed technique is an alternative shape parameterization technique to trivariate volume technique. It retains the flexibility and freedom of trivariate volumes for CFD shape optimization, but it uses a bivariate surface representation. This reduces the number of design variables by an order of magnitude, and it provides a much better control for surface shape changes. The proposed technique is simple, compact, and efficient. The analytical sensitivity derivatives are independent of the design variables and are easily computed for use in a gradient-based optimization. The paper includes the complete formulation and aerodynamics shape optimization results. * Senior Research Scientist, jamshid.a.samareh@nasa.gov, http://mdob.larc.nasa.gov, AIAA Associate Fellow

This paper presents a general three-dimensional algorithm for data transfer between dissimilar meshes. The algorithm is suitable for applications of fluid-structure interaction and other high-fidelity multidisciplinary analysis and optimization. Because the algorithm is independent of the mesh topology, we can treat structured and unstructured meshes in the same manner. The algorithm is fast and accurate for transfer of scalar or vector fields between dissimilar surface meshes. The algorithm is also applicable for the integration of a scalar field (e.g., coefficients of pressure) on one mesh and injection of the resulting vectors (e.g., force vectors) onto another mesh. The author has implemented the algorithm in a C++ computer code. This paper contains a complete formulation of the algorithm with a few selected results.

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