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Woo, Gyungsoo,Kim, Seokchan The Youngnam Mathematical Society 2022 East Asian mathematical journal Vol.38 No.5
In [6, 7] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. They considered a partial differential equation with the input function f ∈ L<sup>2</sup>(Ω). In this paper we consider a PDE with the input function f ∈ H<sup>1</sup>(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.
On some properties of a hyperbolic metric
Woo, Gyungsoo,Shin, Chulho 昌原大學校 基礎科學硏究所 1997 基礎科學硏究所論文集 Vol.9 No.-
상반평면에서의 H-선분은 실축상에 중심을 가진 반원의 호이거나, 실축과 수직한 유클리드 선분임을 변분법을 사용하여 증명하고 적용예를 보였다.
THE SINGULARITIES FOR BIHARMONIC PROBLEM WITH CORNER SINGULARITIES
Woo, Gyungsoo,Kim, Seokchan The Youngnam Mathematical Society 2020 East Asian mathematical journal Vol.36 No.5
In [8, 9] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].
SIF AND FINITE ELEMENT SOLUTIONS FOR CORNER SINGULARITIES
Woo, Gyungsoo,Kim, Seokchan The Youngnam Mathematical Society 2018 East Asian mathematical journal Vol.34 No.5
In [7, 8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.
Woo, Gyungsoo,Kwon, Young-Sam American Institute of Mathematical Sciences 2014 COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Vol.13 No.1
In this paper we consider the magnetohydrodynamics flows giving rise to a variety of mathematical problems in many areas. We study the incompressible limit problems for magnetohydrodynamics flows under strong stratification on unbounded domains.
FINITE ELEMENT SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATION WITH MULTIPLE CONCAVE CORNERS
( Seokchan Kim ),( Gyungsoo Woo ) 호남수학회 2018 호남수학학술지 Vol.40 No.4
In [8] they introduced a new _nite element method for accurate numerical solutions of Poisson equations with corner sin- gularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the ori- gin, and compute the _nite element solution using standard FEM and use the extraction formula to compute the stress intensity fac- tor, then pose a PDE with a regular solution by imposing the non- homogeneous boundary condition using the computed stress inten- sity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple sin- gular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.
A FINITE ELEMENT METHOD USING SIF FOR CORNER SINGULARITIES WITH AN NEUMANN BOUNDARY CONDITION
Kim, Seokchan,Woo, Gyungsoo The Youngnam Mathematical Society 2017 East Asian mathematical journal Vol.33 No.1
In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.
FINITE ELEMENT SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATION WITH MULTIPLE CONCAVE CORNERS
Kim, Seokchan,Woo, Gyungsoo The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.4
In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.
Robert V. Namm,Gyungsoo Woo,Shu-Sen Xie,이수철 대한수학회 2012 대한수학회지 Vol.49 No.4
In this paper, the iterative Uzawa method with a modified Lagrangian functional is investigated to seek a saddle point for the semicoercive variational Signorini inequality.
LAGRANGE MULTIPLIER METHOD FOR SOLVING VARIATIONAL INEQUALITY IN MECHANICS
NAMM, ROBERT V.,WOO, GYUNGSOO Korean Mathematical Society 2015 대한수학회지 Vol.52 No.6
Lagrange multiplier method for solving the contact problem in elasticity is considered. Based on lower semicontinuity of sensitivity functional we prove the convergence of modified dual scheme to corresponding saddle point.