• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.30 no.4
• /
• pp.180-190
• /
• 2018

The preliminary study was carried out to utilize the rolling porous pendulum plate as a hybrid system combining blocking and extracting of wave energy. The Galerkin method suggested by Porter and Evans (1995) was used to solve the diffraction and radiation problems to obtain reflection and transmission coefficient, roll displacement, extracted power. The Galerkin method provides better convergence than the matched eigenfunction expansion method (MEEM), which improves the accuracy of the analytical solution even if the CPU time is shorter. The porous plate can not be said to be more effective than the impermeable plate in terms of wave energy extraction and wave blocking, but it has the advantage of reducing the wave load and exchanging seawater.

• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.267-284
• /
• 2014

The multiresolution analysis for Legendre multiwavelets are given, anti-derivatives of Legendre multiwavelets are used for the numerical solution of differential equations, a special form of multilevel augmentation method algorithm is proposed to solve the disrete linear system efficiently, convergence rate of the Galerkin methods is given and numerical examples are presented.

• International Journal of Safety
• /
• v.2 no.1
• /
• pp.17-22
• /
• 2003

In order to analyze general three dimensional cracks in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. A crack is modelled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems for three dimensional cracks in an infinite solid, as well as their growth under fatigue, are solved and the accuracy and efficiency of the method are demonstrated.

• Communications of the Korean Mathematical Society
• /
• v.15 no.1
• /
• pp.143-153
• /
• 2000

In [8], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we propose the block diagonal preconditioners. The preconditioned conjugate residual method is robust in that the convergence is uniform as the parameter, v, goes to $\sfrac{1}{2}$. Computational experiments are included.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.963-982
• /
• 2013

The Galerkin method has been developed mainly for 2nd order differential equations. To get numerical solutions, there are some choices of Riesz bases for the approximation subspace $V_j{\subset}L^2$. In this paper we shall propose a uniform approach to find suitable Riesz bases for higher order differential equations. Especially for the beam equation (4-th order equation), we also report numerical results.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.1-20
• /
• 2006

This paper presents the interior penalty discontinuous Galerkin finite element methods (DGFEM) for solving the rotating disk electrode problems in electrochemistry. We present results for the simple E reaction mechanism (convection-diffusion equations), the EC' reaction mechanism (reaction-convection-diffusion equation) and the ECE and $EC_2E$ reaction mechanisms (linear and nonlinear systems of reaction-convection-diffusion equations, respectively). All problems will be in one dimension.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.317-329
• /
• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• Proceedings of the KSME Conference
• /
• 2000.04a
• /
• pp.625-630
• /
• 2000

In this paper, the governing equation and the boundary conditions of deploying rods are derived by using Hamilton's principle. The Galerkin method using the comparison function of the instantaneous natural modes is adopted by which the governing equation is discretized. Based on the discretized equations, the time integration analysis is performed and the longitudinal vibrations for the deploying and the retrieving velocity are analyzed.

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.27-43
• /
• 2002

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
• /
• 1993.07a
• /
• pp.178-182
• /
• 1993

유속의 연직분포를 알기 위한 방안의 하나로 Galerkin 함수 전개모델에 대한 연구가 활발히 진행되어 왔다(Heaps, 1972； Davies, 1980； Cordon,1982； 최,1983；강등,1993). Galerkin 함수 이용 3차원 모델은 수직좌표상의 수평유속 성분을 수평좌표, 시간에 따라 변하는 계수 와 수심에 따라 변하는 함수군의 곱의 형태로 선형전개하며, 계수의 값은 Galerkin 방법을 써서구한다. (중략)