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Featured researches published by Kazuei Onishi.


Engineering Analysis With Boundary Elements | 2002

Direct method of solution for general boundary value problem of the Laplace equation

Keisuke Hayashi; Yoko Ohura; Kazuei Onishi

A general boundary value problem for two-dimensional Laplace equation in the domain enclosed by a piecewise smooth curve is considered. The Dirichlet and the Neumann data are prescribed on respective parts of the boundary, while there is the second part of the boundary on which no boundary data are given. There is the third part of the boundary on which the Robin condition is prescribed. This problem of finding unknown values along the whole boundary is ill posed. In this sense we call our problem an inverse boundary value problem. In order for a solution to be identified the inverse problem is reformulated in terms of a variational problem, which is then recast into primary and adjoint boundary value problems of the Laplace equation in its conventional form. A direct method for numerical solution of the inverse boundary value problem using the boundary element method is presented. This method proposes a non-iterative and unified treatment of conventional boundary value problem, the Cauchy problem, and under- or over-determined problems.


Journal of Computational and Applied Mathematics | 2003

Direct numerical identification of boundary values in the Laplace equation

Keisuke Hayashi; Kazuei Onishi; Yoko Ohura

An inverse boundary value problem for the Laplace equation is considered. The Dirichlet and the Neumann data are prescribed on respective part of the boundary, while there is the second part of the boundary where no boundary data are given. There is the third part of the boundary where the Robin condition is prescribed. This ill-posed problem of finding unknown values along the whole boundary is reformulated in terms of the variational problem, which is then recast into primary and adjoint boundary value problems of the Laplace equation in conventional forms. A direct method for numerical solution of the boundary value problems using the boundary element method is presented.


Engineering Analysis With Boundary Elements | 1997

Identification of boundary displacements in plane elasticity by BEM

Y. Ohura; Kinko Kobayashi; Kazuei Onishi

The purpose of this study is to present a possible application of BEM for numerical identification of the boundary conditions for Navier equations in plane elasticity with internal measurements, based on insufficient and noisy information for unique identification. The inverse problem is re-formulated as a minimization problem by the direct variational method. The minimization problem is then recast using the gradient method into successive primary and adjoint boundary value problems in the corresponding plane elasticity problem. For numerical solution of the elasticity problems, the conventional direct boundary element method is employed. From the simple numerical examples considered, it is concluded that our identification scheme is stable and the approximate solutions are convergent to the minimum.


Journal of Physics: Conference Series | 2005

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

Katsuyoshi Saito; Manabu Nakada; Kentaro Iijima; Kazuei Onishi

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.


Engineering Analysis With Boundary Elements | 2002

On identifying Dirichlet condition for under-determined problem of the Laplace equation by BEM

Yoko Ohura; Qingchuan Wang; Kazuei Onishi

The purpose of this paper is to present a numerical technique for the solution of an under-determined problem of the Laplace equation in two spatial dimensions. A resolution is sought for the problem in which the Dirichlet and Neumann data are, respectively, imposed on two disjoint parts of the boundary of the domain, so that the union of the two parts does not constitute the whole boundary. This under-determined boundary value problem can be regarded as a boundary inverse problem, in which the proper Dirichlet condition is to be identified for the rest of the boundary. The solution of this problem is not unique. The technique is based on the direct variational method, and a functional introduced is minimized by the method of the steepest descent. Since the functional is convex, the minimum is attained uniquely. The minimization problem is recast into successive primary and adjoint boundary value problems of the Laplace equation. The boundary element method is applied for numerical solution of the boundary value problems. Some empirical tricks are proposed for increasing the efficiency of the numerical method. A few simple examples show that the method yields a convergent solution which corresponds to the minimum of the functional.


Inverse Problems in Engineering Mechanics II#R##N#International Symposium on Inverse Problems in Engineering Mechanics 2000 (ISIP 2000) Nagano, Japan | 2000

Numerical solution of under-determined 2D laplace equation with internal information

Qingchuan Wang; Yoko Ohura; Kazuei Onishi

Publisher Summary This chapter provides a numerical treatment concerning an underdetermined problem of the Laplace equation in two spatial dimensions. The Dirichlet and Neumann data are respectively imposed on two parts of the boundary of the domain. Besides, the values of the unknown function are specified at n distinct internal points. This new problem is regarded as a boundary inverse problem because the proper boundary conditions are to be identified for the rest of the boundary. The treatment is based on the direct variational method. A functional is minimized by the method of the steepest descent. The minimization problem is transformed into iterative primary and dual boundary value problems of the Laplace equation. In simple numerical examples, this chapter compares numerical solution containing internal information with the numerical solution not containing internal information. It is concluded that adding internal information can significantly improve the numerical solution.


Inverse Problems in Engineering Mechanics#R##N#International Symposium on Inverse Problems in Engineering Mechanics 1998 (ISIP '98) Nagano, Japan | 1998

A numerical method for a magnetostatic inverse problem using the edge element

Takemi Shigeta; Kazuei Onishi

Publisher Summary The purpose of this chapter is to present a numerical method of solution for a magnetostatic inverse problem in two dimensions. On a part of the boundary of a bounded domain of the problem, the normal component of the magnetic flux density and the tangential component of the magnetic field are simultaneously imposed. The method aims at identifying the proper boundary condition for the rest of the boundary. The treatment is based on the method of least squares, and a functional is minimized by the steepest descent method. The direct variational method paraphrases the inverse problem to the primary and the adjoint boundary value problems. The mixed finite element method using the edge element and the conventional finite element method is applied to the numerical solutions of the boundary value problems. Based on numerical computations, it is concluded that estimated solutions agree with an exact solution.


Inverse Problems in Engineering Mechanics III#R##N#International Symposium on Inverse Problems in Engineering Mechanics 2001 (ISIP 2001) Nagano, Japan | 2002

Direct Method for Solution of Inverse Boundary Value Problem of the Laplace Equation

Kazuei Onishi; Yoko Ohura

The Laplace equation is considered in the domain enclosed by a smooth boundary, on which information about Dirichlet or Neumann data is incompletely specified so that the defined problem is not well-posed. A numerical method with no iterations is presented for finding an approximate solution of the problem. The method does not suffer from the instability of the inverse problem.


Numerical Functional Analysis and Optimization | 2001

NUMERICAL RECONSTRUCTION OF INTERNAL STATES BY BOUNDARY MEASUREMENTS FOR THE LAPLACE EQUATION

Qingchuan Wang; Kazuei Onishi

The purpose of the paper is to present a unified numerical method for problems consisting of the conventional boundary value problem. Cauchy problem, under-determined problem, and over-determined problem. The method is based on the direct variational approach, which paraphrases the problems into the primary and adjoint boundary value problems that can be tackled by commonly used computer programs for the numerical solution of the Laplace equation.


Inverse Problems in Engineering Mechanics#R##N#International Symposium on Inverse Problems in Engineering Mechanics 1998 (ISIP '98) Nagano, Japan | 1998

Impedance computed tomography for electrocardiogram application

Kenji Shirota; Gen Nakamura; Kazuei Onishi

Publisher Summary The inverse problem in electrocardiography reads: determine the distribution of electric current inside a heart by means of measurements of electric potential and current on a body surface. The problem concerned in this chapter consists of determining the surface distribution of electric potential of the heart in the situation that the electrical conductivity of the body tissue is not known. The purpose of this chapter is to present a hybrid method for numerical solution of the inverse problem in electrocardiography with unknown conductivity of the body. To determine unknown electric potential on the epicardium, we adopt the boundary value identification algorithm with assumed conductivity. To reconstruct unknown conductivity, we combine the alternating direction algorithm with the above identification algorithm.

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Yoko Ohura

Kyushu Institute of Information Sciences

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