• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2005.11a
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• pp.169-174
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• 2005

In this paper, we proposed a new algorithm of the inverse scattering for the reconstruction of unknown dielectric scatterers using the finite-difference time-domain method and the design sensitivity analysis. We introduced the design sensitivity analysis based on the gradient for the fast convergence of the reconstruction. By introducing the adjoint variable method for the efficient calculation, we derived the adjoint variable equation. As an optimal algorithm we used the steepest descent method and reconstructed the dielectric targets using the iterative estimation. To verify our algorithm we will show the numerical examples for the two-dimensional $TM^2$ cases.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.5
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• pp.535-541
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• 2010

In this paper, we have derived a continuum-based adjoint design sensitivity of general performance functionals with respect to Young' modulus and heat conduction coefficient for steady-state nonlinear thermoelastic problems. An adjoint equation for temperature and displacement fields is defined for the efficient computation of the coupled field design sensitivity. Through numerical examples, we investigated the mesh dependency of the topology optimization method in the thermoelastic problems. Also, comparing the dominant loading cases of thermal and mechanical ones, the loading dependency of topology design optimization in coupled multi-physics problems is investigated.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.7
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• pp.18-27
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• 2006

The conventional reliability based design optimization(RBDO) methods require high computational cost compared with the deterministic design optimization(DO) methods, therefore it is hard to apply directly to large-scaled problems such as an aerodynamic shape design optimization. In this study, to overcome this computational limitation the efficient RBDO procedure with the two-point approximation(TPA) and adjoint sensitivity analysis is proposed, that the computational requirement is nearly the same as DO and the reliability accuracy is good compared with that of RBDO. Using this, the 3-D aerodynamic shape design optimization is performed very efficiently.

• Journal of Magnetics
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• v.16 no.3
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• pp.240-245
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• 2011

A new hybrid ON/OFF method is presented for the fast solution of electromagnetic inverse problems in high frequency domains. The proposed method utilizes both topological sensitivity (TS) and material sensitivity (MS) to update material properties in unit design cells. MS provides smooth design space and stable convergence, while TS enables sudden changes of material distribution when MS slows down. This combination of two sensitivities enables a reduction in total computation time. The TS and MS analyses are based on a variational approach and an adjoint variable method (AVM), which permits direct calculation of both sensitivity values from field solutions of the primary and adjoint systems. Investigation of the formulations of TS and MS reveals that they have similar forms, and implementation of the hybrid ON/OFF method that uses both sensitivities can be achieved by one optimization module. The proposed method is applied to dielectric material reconstruction problems, and the results show the feasibility and effectiveness of the method.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.1
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• pp.66-78
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• 2007

A multi-point aerodynamic shape optimization technique has been developed for helicopter rotor blades in hover based on a continuous adjoint method on unstructured meshes. The Euler flow solver and the continuous adjoint sensitivity analysis were formulated on the rotating frame of reference. The 'objective function and the sensitivity were obtained as a weighted sum of the values at each design point. The blade section contour was modified by using the Hicks-Henne shape functions. The mesh movement due to the blade geometry change was achieved by using a spring analogy. In order to handle the repeated evaluation of the design cycle efficiently, the flow and adjoint solvers were parallelized based on a domain decomposition strategy. A solution-adaptive mesh refinement technique was adopted for the accurate capturing of the wake. Applications were made to the aerodynamic shape optimization of the Caradonna-Tung rotor blades and the UH-60 rotor blades in hover.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.679-686
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• 2017

The present paper is devoted to self-adjoint cyclically compact operators on Hilbert-Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators is given. We use more simple and constructive method, which allowed to apply this result to compact operators relative to von Neumann algebras. Namely, a general form of compact operators relative to a type I von Neumann algebra is given.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.669-690
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• 1998

In this paper we develop a new theory of adjoint and symmetric method in the class of general implicit one-step fixed-stepsize methods. These methods arise from simple and natral def-initions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for meth-ods having these properties and show in particular that only the symmetric methods possess a quadratic asymptotic expansion of the global error. In addition we give a very simple test to identify the symmetric methods in practice.

• 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.

• Computers and Concrete
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• v.7 no.1
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• pp.63-81
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• 2010

We present the shape determination method of 3-D reinforcement corrosion based on observed temperature on concrete surface. The non-destructive testing for reinforcement corrosion in concrete using a heat image on concrete surface have been proposed by Oshita. The position of the reinforcement of corrosion or the cavity can be found using that method. However, the size of those defects can not be precisely measured based on the heat image. We therefore proposed the numerical determination system of the shape for the reinforcement corrosion using the observed temperature on the concrete surface. The adjoint variable method is introduced to formulate the shape determination problem, and the finite element method is employed to simulate the heat transfer problem. Some numerical experiments and the examination for the number of the observation points are shown in this paper.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.127-134
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• 2004

In this paper, using an adjoint variable method, we develop a design sensitivity analysis (DSA) method applicable to heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume, respectively. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with finite difference ones, requiring less than 0.3% of CPU time far the finite differencing. Also, the topology optimization yields physical meaningful results.