• Journal of Magnetics
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• v.16 no.1
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• pp.77-82
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• 2011

This paper presents a new self-adjoint material sensitivity formulation for optimal designs and inverse problems in the high frequency domain. The proposed method is based on the continuum approach using the augmented Lagrangian method. Using the self-adjoint formulation, there is no need to solve the adjoint system additionally when the goal function is a function of the S-parameter. In addition, the algorithm is more general than most previous approaches because it is independent of specific analysis methods or gridding techniques, thereby enabling the use of commercial EM simulators and various custom solvers. For verification, the method was applied to the several numerical examples of dielectric material reconstruction problems in the high frequency domain, and the results were compared with those calculated using the conventional method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.4
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• pp.18-27
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• 2002

Aerodynamic shape optimization of two-dimensional airfoils in inviscid compressible flows is performed using a continuous adjoint formulation on unstructured meshes. Accurate evaluation of the gradient is achieved by using a reconstruction scheme based on the Laplacian averaging. A least-square method with extended stencil is used for flow gradient calculations. Proper convergence criterion is studied on Euler and adjoint equations for efficient design. The present method has been applied to RAE2822 and NACA0012 airfoils such that wave drag can be minimized by removing the shock wave. An inverse design is also performed to recover the shock wave on the designed RAE2822 airfoil.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.161-171
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• 1999

Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

• International Journal of Automotive Technology
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• v.7 no.3
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• pp.283-288
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• 2006

A mathematical methodology is proposed for designing nozzle hole shapes producing controlled geometric cavitation. The proposed methodology uses an unstructured RANS flow solver, with the ability to compute sensitivity derivatives via an adjoint algorithm. The adjoint formulation for the N-S equations is presented while variation of the turbulence viscosity is not taken into account during the geometry modifications. The sensitivities are calculated in a mode independently of the shape parameterisation. The method is used to develop and evaluate conceptual shapes for nozzle hole cavitation reduction. The localized region at the hole inlet producing cavitation, is parameterised using its radius of curvature, while a cost function is formulated to eliminate the negative pressures present at this location. Sensitivity derivatives are used to assess the dependence of the localized region on the minimum pressure, and to drive the geometry to the targeted shape. The results show that the computer model can provide nozzle hole entry shapes that produce predefined flow characteristics, and thus can be used as an inverse design tool for nozzle hole cavitation control.

• Geophysics and Geophysical Exploration
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• v.2 no.1
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• pp.54-62
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• 1999

This paper describes a datuming scheme for a prestack dataset which uses wavefield depth extrapolation. The formulation of the prestack datuming algorithm is performed by finding the adjoint operator to the corresponding forward prestack wavefield extrapolation from a flat surface to an irregular surface. Here I used double-square-root (DSR) equation to extrapolate wavefield in prestack sense. This correspond to the forward model of the well known `survey sinking` prestack imaging algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.123-130
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• 2002

A general formulation for shape design sensitivity analysis over three dimensional beam structure is developed based on a variational formulation of the beam in linear elasticity. Sensitivity formula is derived based on variational equations in cartesian coordinates using the material derivative concept and adjoint variable method for the displacement and Von-Mises stress functionals. Shape variation is considered for the beam shape in general 3-dimensional direction as well as for the orientation angle of the beam cross section. In the sensitivity expression, the end points evaluation at each beam segment is added to the integral formula, which are summed over the entire structure. The sensitivity formula can be evaluated with generality and ease even by employing piecewise linear design velocity field despite the bending model is fourth order differential equation. For the numerical implementation, commercial software ANSYS is used as analysis tool for the primal and adjoint analysis. Once the design variable set is defined using ANSYS language, shape and orientation variation vector at each node is generated by making finite difference to the shape with respect to each design parameter, and is used for the computation of sensitivity formula. Several numerical examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. The results are found excellent even by employing a simple linear function for the design velocity evaluation. Shape optimization is carried out for the geometric design of an archgrid and tilted bridge, which is to minimize maximum stress over the structure while maintaining constant weight. In conclusion, the proposed formulation is a useful and easy tool in finding optimum shape in a variety of the spatial frame structures.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.2 s.152
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• pp.130-138
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• 2007

A coupled variational equation for fluid-structure interaction (FSI) problems is derived from a steady state Navier-Stokes equation for incompressible Newtonian fluid and an equilibrium equation for geometrically nonlinear structures. For a fully coupled FSI formulation, between fluid and structures, a traction continuity condition is considered at interfaces where a no-slip condition is imposed. Under total Lagrange formulation in the structural domain, finite rotations are well described by using the second Piola-Kirchhoff stress and Green-Lagrange strain tensors. An adjoint shape design sensitivity analysis (DSA) method based on material derivative approach is applied to the FSI problem to develop a shape design optimization method. Demonstrating some numerical examples, the accuracy and efficiency of the developed DSA method is verified in comparison with finite difference sensitivity. Also, for the FSI problems, a shape design optimization is performed to obtain a maximal stiffness structure satisfying an allowable volume constraint.

• Journal of Mechanical Science and Technology
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• v.16 no.5
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• pp.710-719
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• 2002

This study investigates a nonlinear inverse convection problem for a laminar-forced convective flow between two parallel plates. The upper plate is exposed to unknown heat flux while the lower plate is insulated. The unknown heat flux is determined using temperature measured on the lower plate. The thermophysical properties of the fluid are temperature dependent, which renders the problem nonlinear. The sequential gradient method is applied to this nonlinear inverse problem in order to solve the problem efficiently. The function specification method is incorporated to stabilize the sequential estimation. The corresponding adjoint formalism is provided. Accuracy and stability have been examined for the proposed method with test cases. The tendency of deterministic error is investigated for several parameters. Stable solutions are achieved eve]1 with severely impaired measurement data.

• International Journal of Aeronautical and Space Sciences
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• v.4 no.1
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• pp.45-52
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• 2003

A three-dimensional aerodynamic shape optimization technique in inviscid compressible flows is developed by using a parallel continuous adjoint formulation on unstructured meshes. A new surface mesh modification method is proposed to overcome difficulties related to patch-level remeshing for unstructured meshes, and the effect of design sections on aerodynamic shape optimization is examined. Applications are made to three-dimensional wave drag minimization problems including an ONERA M6 wing and the EGLIN wing-pylon-store configuration. The results show that the present method is robust and highly efficient for the shape optimization of aerodynamic configurations, independent of the number of design variables used.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.8
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• pp.175-184
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• 2003

A method of the shape design sensitivity analysis based on the boundary integral equation formulation is presented for two-dimensional inhomogeneous thermal conducting solids with multiple domains. Shape variation of the external and interface boundary is considered. A sensitivity formula of a general performance functional is derived by taking the material derivative to the boundary integral identity and by introducing an adjoint system. In numerical analysis, state variables of the primal and adjoint systems are solved by the boundary element method using quadratic elements. Two numerical examples of a compound cylinder and a thermal diffuser are taken to show implementation of the shape design sensitivity analysis. Accuracy of the present method is verified by comparing analyzed sensitivities with those by the finite difference. As application to the shape optimization, an optimal shape of the thermal diffuser is found by incorporating the sensitivity analysis algorithm in an optimization program.