KR20190031803A - Method for Developing Function Algorithm of RLW Equation using Integral Equation Formalism - Google Patents
Method for Developing Function Algorithm of RLW Equation using Integral Equation Formalism Download PDFInfo
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Abstract
Description
본 발명은 RLW 방정식의 해석에 관한 것으로, 구체적으로 RLW(Regularized Long Wave) 방정식을 적분방정식 정식화를 이용하여 해석하여 복잡도를 줄이고 시간을 단축할 수 있도록 한 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법에 관한 것이다.The present invention relates to the analysis of RLW equations and more specifically to the development of a function algorithm of an RLW equation using an integral equation formulation for reducing complexity and time by analyzing RLW (Regularized Long Wave) equations using integral equation formulation For example.
대형 구조물의 구조해석에서는 신뢰성 및 안정성을 얻기 위한 정확한 응력 해석 및 정확한 구조물의 거동 해석이 필수적이다.In the structural analysis of large structures, accurate stress analysis and accurate structural behavior analysis are essential to obtain reliability and stability.
그러나 그로 인해 많은 미지수 증가가 수반되며 이런 미지수의 증가는 필요 메모리 또는 계산시간 등의 계산비용의 증가를 수반한다.However, this is accompanied by a large increase in unknowns, and this increase in unknowns is accompanied by an increase in computational costs such as memory required or computation time.
이와 같은 어려움 때문에 적은 미지수만으로 효과적으로 정확한 수치 해를 얻을 수 있는 방법에 대한 연구가 계속적으로 수행되어 왔으며 이런 연구의 일환으로 격자 없이 수치해의 높은 정확성을 보장할 수 있는 무요소법에 대한 연구가 활발히 진행되어 왔다.As a result of this difficulty, research has been carried out on methods to obtain an accurate numerical solution effectively with a small number of unknowns. As part of this research, studies on the elementless method that can guarantee high accuracy of numerical solution without lattice are actively conducted come.
무요소법에서는 요소의 연결성을 필요로 하지 않고 절점들의 정보들만을 가지고 형상함수를 구성하기 때문에 요소의 뒤틀림, 격자 생성 등에 수반되는 어려움을 해결할 수 있을 뿐만 아니라 근사함수의 연속성을 자유롭게 조절할 수 있는 장점을 가지고 있다.In the elementless method, since the shape function is composed only of the information of the nodes without requiring the connectivity of the elements, it is possible to solve the difficulties associated with element distortion and grid generation, and to freely control the continuity of the approximate function Have.
그러나 유한요소법과 달리 무요소법에서 구성된 형상 함수가 다항함수가 아니기 때문에, 수치적분에 어려움이 존재한다.However, unlike the finite element method, since the shape function constructed in the elementless method is not a polynomial function, there is a difficulty in numerical integration.
이러한 무요소법의 단점을 극복하기 위하여 새로 제안된 절점활성화 기법은 유한요소 절점들 가운데 필요한 부분의 절점만을 활성화하여 무요소 근사기법으로 활성커널을 구성하고 이를 유한요소 형상함수로 재보간하여 문제를 해석할 수 있다.In order to overcome the disadvantages of this elementless method, the newly proposed node activation method activates only necessary nodal points of the finite element nodes, constructs the active kernel by the elementless approximation method, reinterpolates the kernel into the finite element shape function, can do.
종래 기술에서는 RLW(regularized long wave) 방정식을 해석하기 위해 parametric spline 해법, Galerkin 유한요소법, 최소자승 유한요소법, 선형 유한요소법 등을 개발하였다.In the prior art, a parametric spline solution, a Galerkin finite element method, a least squares finite element method, and a linear finite element method have been developed to analyze RLW (regularized long wave) equations.
여기서, 유한요소법(finite element method,FEM)의 개념은 미분방정식의 근사법에 해당한다.Here, the concept of the finite element method (FEM) corresponds to the approximation of differential equations.
Ritz법은 변분유한요소법(Variational Approach to FEM)이고, 가중오차법(Weighted Residual Method)은 Glaerkin 유한요소법이다.The Ritz method is a Variational Approach to FEM and the Weighted Residual Method is a Glaerkin finite element method.
이러한 종래 기술들의 방법은 모든 경계치 문제에 대하여 변분이론을 적용할 수 있는 것은 아니다.These prior art methods are not applicable to the theory of variability for all boundary value problems.
즉, 경계치 문제에 따라서는 범함수가 존재하지 않을 수 있다. In other words, the boundary function may not exist according to the boundary value problem.
그리고 다른 문제는 일반적으로 시도함수를 구하기가 쉽지 않다. 특히 이차원 및 삼차원 문제의 경우, 필수경계조건을 만족하는 시도함수를 사실상 구할 수 없다. And the other problem is that it is usually not easy to get an attempt function. In particular, in the case of two-dimensional and three-dimensional problems, it is practically impossible to obtain an attempt function satisfying the essential boundary condition.
이와 같이 종래 기술에서의 RLW(regularized long wave) 방정식을 해석하기 위한 방법들은 해법의 복잡성과 매 시스템의 해석에 대해 많은 시간과 노력이 필요하였다.Thus, methods for analyzing RLW (regularized long wave) equations in the prior art have required much time and effort for solution complexity and analysis of each system.
따라서, 이러한 한계점을 극복할 수 있는 새로운 기술의 개발이 요구되고 있다.Therefore, development of a new technology capable of overcoming these limitations is required.
본 발명은 이와 같은 종래 기술의 RLW(regularized long wave) 방정식을 해석하는 방법들의 문제를 해결하기 위한 것으로, RLW(Regularized Long Wave) 방정식을 적분방정식 정식화를 이용하여 해석하여 복잡도를 줄이고 시간을 단축할 수 있도록 한 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법을 제공하는데 그 목적이 있다.The present invention solves the problem of methods of interpreting regularized long wave (RLW) equations of the prior art. The present invention analyzes RLW (Regularized Long Wave) equations using integral equation formulation to reduce complexity and shorten the time The objective of this paper is to provide a method for developing a function algorithm of RLW equation using an integral equation formulation.
본 발명의 목적들은 이상에서 언급한 목적들로 제한되지 않으며, 언급되지 않은 또 다른 목적들은 아래의 기재로부터 당업자에게 명확하게 이해될 수 있을 것이다.The objects of the present invention are not limited to the above-mentioned objects, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.
이와 같은 목적을 달성하기 위한 본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법은 RLW 방정식을 Laplace 변환과 역변환및 Fourier 변환 및 역변환을 통해,In order to achieve the above object, a method for developing a function algorithm of an RLW equation using an integral equation formulation according to the present invention is characterized in that RLW equations are transformed through Laplace transform, inverse transform, Fourier transform,
으로 적분방정식을 정식화하는 것을 특징으로 한다.To formulate an integral equation.
이와 같은 본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법은 RLW(Regularized Long Wave) 방정식을 적분방정식 정식화를 이용하여 해석하여 복잡도를 줄이고 시간을 단축할 수 있도록 한 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘을 제공한다.The method for developing the function algorithm of the RLW equation using the integral equation formulation according to the present invention is characterized in that the RLW (Regularized Long Wave) equation is analyzed using the integral equation formulation to form an integral equation for reducing the complexity and shortening the time The function of the RLW equation is presented.
도 1 내지 도 4는 본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법을 설명하기 위한 도면1 to 4 are diagrams for explaining a method for developing a function algorithm of an RLW equation using integral equation formulation according to the present invention
이하, 본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법의 바람직한 실시 예에 관하여 상세히 설명하면 다음과 같다.Hereinafter, a preferred embodiment of a method for developing a function algorithm of the RLW equation using the integral equation formulation according to the present invention will be described in detail as follows.
본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법의 특징 및 이점들은 이하에서의 각 실시 예에 대한 상세한 설명을 통해 명백해질 것이다.The features and advantages of the method for developing the function algorithm of the RLW equation using the integral equation formulation according to the present invention will be apparent from the following detailed description of each embodiment.
도 1 내지 도 4는 본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법을 설명하기 위한 도면이다.FIGS. 1 to 4 are diagrams for explaining a method for developing a function algorithm of the RLW equation using the integral equation formulation according to the present invention.
본 발명은 RLW(Regularized Long Wave) 방정식을 적분방정식 정식화를 이용하여 해석하여 복잡도를 줄이고 시간을 단축할 수 있도록 한 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법을 제공하기 위한 것이다.The present invention is to provide a method for developing a function algorithm of an RLW equation using an integral equation formulation for reducing complexity and time by interpreting RLW (Regularized Long Wave) equations using integral equation formulation.
아래의 수학식 1은 본 발명에서 다루고 있는 RLW(regularized long-wave)방정식의 형태를 나타낸 것이다.Equation (1) below shows a form of a regularized long-wave (RLW) equation that is dealt with in the present invention.
이러한 방정식은 Laplace 변환과 역변환및 Fourier 변환 및 역변환을 통해 수학식 2에서와 같이, 적분방정식을 정식화할 수 있다.These equations can formulate the integral equation as in equation (2) through Laplace transform, inverse transform and Fourier transform and inverse transform.
이러한 연성 적분방정식은 
이와 같은 수학식 2에서와 같은 적분방정식 형태를 본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법을 적용한 결과 수식은 수학식 3에서와 같다.Equation (3) is applied to a method for developing a functional algorithm of the RLW equation using the integral equation formulation according to the present invention as shown in Equation (2).
이와 같은 본 발명에 따른 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법은 RLW 방정식의 해석을 위하여 RLW(Regularized Long Wave) 방정식을 적분방정식 정식화를 이용하여 해석하여 복잡도를 줄이고 시간을 단축할 수 있다.The method for developing the function algorithm of the RLW equation using the integral equation formulation according to the present invention is to analyze the RLW (Regularized Long Wave) equation using the integral equation formulation to reduce the complexity and shorten the time .
본 발명에 따른 이와 같은 방법에 의해 안정적인 해법을 제시하고 있으며 그 해석의 정도도 상당히 좋은 것으로 확인할 수 있다.A stable solution is proposed by this method according to the present invention, and the degree of interpretation is also remarkably good.
이상에서의 설명에서와 같이 본 발명의 본질적인 특성에서 벗어나지 않는 범위에서 변형된 형태로 본 발명이 구현되어 있음을 이해할 수 있을 것이다.As described above, it will be understood that the present invention is implemented in a modified form without departing from the essential characteristics of the present invention.
그러므로 명시된 실시 예들은 한정적인 관점이 아니라 설명적인 관점에서 고려되어야 하고, 본 발명의 범위는 전술한 설명이 아니라 특허청구 범위에 나타나 있으며, 그와 동등한 범위 내에 있는 모든 차이점은 본 발명에 포함된 것으로 해석되어야 할 것이다.It is therefore to be understood that the specified embodiments are to be considered in an illustrative rather than a restrictive sense and that the scope of the invention is indicated by the appended claims rather than by the foregoing description and that all such differences falling within the scope of equivalents thereof are intended to be embraced therein It should be interpreted.
Claims (2)
으로 적분방정식을 정식화하는 것을 특징으로 하는 적분방정식 정식화를 이용한 RLW 방정식의 함수 알고리즘 개발을 위한 방법.Through the Laplace transform and the inverse transform and the Fourier transform and the inverse transform of the RLW equation,
A method for developing a function algorithm of an RLW equation using an integral equation formulation.
The method according to claim 1,
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| KR20120132101A (en) | 2011-05-27 | 2012-12-05 | 부산대학교 산학협력단 | Method for measuring nonharmonic periodic excitation forces in nonlinear damped systems |
| KR20160009462A (en) | 2014-07-16 | 2016-01-26 | 부산대학교 산학협력단 | Analyzing method by an integral equation for solving the nonlinear Klein-Gordon equation |
| KR20170075537A (en) | 2015-12-23 | 2017-07-03 | 부산대학교 산학협력단 | Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach |
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| KR20120132101A (en) | 2011-05-27 | 2012-12-05 | 부산대학교 산학협력단 | Method for measuring nonharmonic periodic excitation forces in nonlinear damped systems |
| KR20160009462A (en) | 2014-07-16 | 2016-01-26 | 부산대학교 산학협력단 | Analyzing method by an integral equation for solving the nonlinear Klein-Gordon equation |
| KR20170075537A (en) | 2015-12-23 | 2017-07-03 | 부산대학교 산학협력단 | Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach |
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