• 대한수학회지
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• 제59권5호
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• pp.891-909
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• 2022

The main objective of this paper is to develop a concrete inverse formula of the system induced by the fourth-order finite difference method for two-point boundary value problems with Robin boundary conditions. This inverse formula facilitates to make a fast algorithm for solving the problems. Our numerical results show the efficiency and accuracy of the proposed method, which is implemented by the Thomas algorithm.

• The Journal of the Acoustical Society of Korea
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• 제23권1E호
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• pp.3-9
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• 2004

An important inverse problem in the field of acoustics is that of reconstructing the strengths of a number of sources given a model of transmission paths from the sources to a number of sensors at which measurements are made. In dealing with this kind of the acoustical inverse problem, strengths of the discretised source distribution can be simply deduced from the measured pressure field data and the inversion of corresponding matrix of frequency response functions. However, deducing :he solution of such problems is not straightforward due to the practical difficulty caused by their inherent ill-conditioned behaviour. Therefore, in order to overcome this difficulty associated with the ill-conditioning, the problem is replaced by a nearby well-conditioned problem whose solution approximates the required solution. In this paper a microphone array are identified for which the inverse problem is optimally conditioned, which can be robust to contaminating errors. This involves sampling both source and field in a manner which results in the discrete pressures and source strengths constituting a discrete Fourier transform pair.

• 한국통신학회논문지
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• 제21권5호
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• pp.1317-1324
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• 1996

An angular spectral inverse technique, applying the moment method procedure with a series expansion for the induced field in each enlarged cell, is suggested to reconstruct permittivity profiles of inhomogeneous dielectric objects and to reduce the ill-posedness inherent to inverse scattering problems. The angular spectral inverse scattering using the pulse basis function in enlarging the scatterer has the ill-posedness due to the input data of higher spectra. To reduce the number of higher spectra, enlarging the cell size and averaging over the cell with a suitable weighting function are found to play improtant roles for the reduction of ill-posedness of the angular spectral inverse scattering problems.

• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.353-369
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• 2024

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

• Journal of Magnetics
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• 제16권3호
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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.

• Journal of Magnetics
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• 제16권1호
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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.

• 지구물리와물리탐사
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• 제2권2호
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• pp.112-121
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• 1999

This article reviews the development of geophysical inverse theory. In a series of articles published in 1967, 1968, and 1979, G. Backus and F. Gilbert a trade-off between model resolution and estimation errors in geophysical inverse problems, and gave a criterion to compromise the reciprocal relation. Although the criterion was not clear in the physical point of view, it had been extensively used in the interpretation of geophysical date in the 1970s. This was the starting point of the fruitful development of inverse theory in geophysics. A reasonable criterion to compromise the reciprocal relation was derived to solve linear problems by D. D. jackson in 1979, introducing the concept of a priori information about unknown model parameters. This Jackson's approach was extended to solve nonlinear problems on the basis o probabilistic approach to the inverse problems formulated by A. Tarantola and B. Vallete in 1982. At the end of 1980s ABIC (Akaike Bayesian Information Criterion) was introduced for selecting a more reasonable model in geophysics. Now the date inversion is regarded as the process of extracting new information from observed data, combining in with a priori information about model parameters, and constructing a more clear image of model.

• 대한수학교육학회지:수학교육학연구
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• 제18권1호
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• pp.103-121
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• 2008

본 연구는 비례 추론의 중요성을 바탕으로 5, 6, 7학년 학생들의 비례추론 능력을 알아보고자, 다양한 유형의 비례 문제와 비례가 아닌 문제로 구성된 검사지를 이용하여 5학년 155명, 6학년 153명, 7학년 190명의 반응을 분석하였다. 분석 결과, 비례문제 유형별로는 정비례 상황의 미지값 구하기 문제, 수리적 비교, 반비례 상황의 미지값 구하기 문제, 질적 예측 및 비교의 순으로 성취 정도가 높게 나타났으며, 비례가 아닌 문제에서는 비례 상황이 아님에도 불구하고 전체 약 34%의 학생들이 비례관계를 적용하는 오류를 범하였다. 문제유형별로 학년별 학생들의 반응을 비교 분석함으로써 비와 비율 및 비례와 관련한 교수 학습 방향에 대한 시사점을 도출하였다.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.161-173
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• 2009

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others.

• 한국공간정보시스템학회:학술대회논문집
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• 한국공간정보시스템학회 2004년도 춘계 학술발표회 논문집 제1권1호(통권1호)
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• pp.29-36
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• 2004

In this paper, a study of damage detection for 2-Dimensional Truss Structures using the parametric projection filter theory is presented. Many researchers are interested in inverse problem and one of solution procedures for inverse problems that are very effective is the approach using the filtering algorithm in conjunction with numerical solution methods. In filtering algorithm, the Kalman filtering algorithm is well known and have been applied to many kind of inverse problems. In this paper, the Parametric projection filtering in conjunction with structural analysis is applied to the identification of damages in 2-D truss structures. The natural frequency and modes of damaged truss model are adopted as the measurement data. The effectiveness of proposed method is verified through the numerical examples.