• Journal of the Society of Naval Architects of Korea
• /
• v.33 no.1
• /
• pp.90-97
• /
• 1996

The optimal mesh refinement has a meaning that error of the every element is within an allowable level and in uniformly distributed. The adaptive mesh generation may be required to achieve the optimal mesh generation. For the purpose of optimal mesh generation, an error estimation and an adaptive mesh refinement are required. Using the adaptive mesh generation the second finite element analysis is performed with the result of the first analysis. In the process the error estimation is required. In this study the adaptive mesh generation program for triangular element is developed, and for a posteriori error estimation the stress projection approach is considered. It has been found the multigrid technique, where the error estimation and the mesh generation are combined in multi-step of analysis, may be used efficiently in the finite element analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.849-856
• /
• 2006

This paper is to examine the applicability of ordinary Kriging interpolation(OK) to the p-adaptivity of the finite element analysis that is based on variogram. In the p-refinement, the analytical domain has to be refined automatically to obtain an acceptable level of accuracy by increasing the p-level non-uniformly or selectively. In case of non-uniform p-distribution, the continuity between elements with different polynomial orders is achieved by assigning zero higher-order derivatives associated with the edge in common with the lower-order derivatives. It is demonstrated that the validity of the proposed approach by analyzing results for stress singularity problem.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.19 no.4 s.74
• /
• pp.429-440
• /
• 2006

This paper comprises two specific objectives. The first is to examine the applicability of ordinary kriging interpolation(OK) to the p-adaptivity of the finite element method that is based on variogram modeling. The second objective Is to present the adaptive procedure by the hierarchical p-refinement in conjunction with a posteriori error estimator using the modified S.P.R. (superconvergent patch recovery) method. The ordinary kriging method that is one of weighted interpolation techniques is applied to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by experimental and theoretical variograms for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In the p-refinement, the analytical domain has to be refined automatically to obtain an acceptable level of accuracy by increasing the p-level non-uniformly or selectively. To verify the performance of the modified S.P.R. method, the new error estimator based on limit value has been proposed. The validity of the proposed approach has been tested with the help of some benchmark problems of linear elastic fracture mechanics such as a centrally cracked panel, a single edged crack, and a double edged crack.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.26 no.4A
• /
• pp.677-687
• /
• 2006

Kriging interpolation is one of the generally used interpolation techniques in Geostatistics field. This technique includes the experimental and theoretical variograms and the formulation of kriging interpolation. In contrast to the conventional least square method for stress recovery, kriging interpolation is based on the weighted least square method to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by variogram modeling for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In addition to this, the p-level is increased non-uniformly or selectively through a posteriori error estimation based on SPR (superconvergent patch recovery) technique, proposed by Zienkiewicz and Zhu, by auto mesh p-refinement. The cut-out plate problem under tension has been tested to validate this approach. It also provides validity of kriging interpolation through comparing to existing least square method.

• Journal of computational fluids engineering
• /
• v.11 no.4 s.35
• /
• pp.39-47
• /
• 2006

In this paper, the authors developed a multidimensional interpolation method inside a finite volume cell in the computation of high-order accurate numerical flux such as the fifth order WEND (weighted essentially non-oscillatory) scheme. This numerical method starts from a simple Taylor series expansion in a proper spatial order of accuracy, and the WEND filter is used for the reconstruction of sharp nonlinear waves like shocks in the compressible flow. Two kinds of interpolations are developed: one is for the cell-averaged values of conservative variables divided in one mother cell (Type 1), and the other is for the vertex values in the individual cells (Type 2). The result of the present study can be directly used to the cell refinement as well as the convective flux between finer and coarser cells in the Cartesian adaptive grid system (Type 1) and to the post-processing as well as the viscous flux in the Navier-Stokes equations on any types of structured and unstructured grids (Type 2).

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1992.10a
• /
• pp.39-44
• /
• 1992

This paper is concerned with formulations of the hierarchical $C^{o}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method we proposed to verify the superior convergence and algorithmic efficiency with the help of the clamped L-shaped plate problems.s.

• Geophysics and Geophysical Exploration
• /
• v.13 no.1
• /
• pp.118-127
• /
• 2010

Resistivity logging instruments are designed to measure the electrical resistivity of a formation, and this can be directly interpreted to provide a water-saturation profile. However, resistivity logs are sensitive to borehole and shoulder-bed effects, which often result in misinterpretation of the results. These effects are emphasised more in the presence of tool eccentricity. For precise interpretation of short- and long-normal logging measurements in the presence of tool eccentricity, we simulate and analyse eccentricity effects by combining the use of a Fourier series expansion in a new system of coordinates with a 2D goal-oriented high-order self-adaptive hp finite-element refinement strategy, where h denotes the element size and p the polynomial order of approximation within each element. The algorithm automatically performs local mesh refinement to construct an optimal grid for the problem under consideration. In addition, the proper combination of h and p refinements produces highly accurate simulations even in the presence of high electrical resistivity contrasts. Numerical results demonstrate that our algorithm provides highly accurate and reliable simulation results. Eccentricity effects are more noticeable when the borehole is large or resistive, or when the formation is highly conductive.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.3
• /
• pp.139-170
• /
• 2013

We extend a p-hierarchical decomposition of the second degree finite element space of N$\acute{e}$d$\acute{e}$lec for tetrahedral meshes in three dimensions given in [1] to meshes with hexahedral elements, and derive p-hierarchical decompositions of the second degree finite element space of Raviart-Thomas in two dimensions for triangular and quadrilateral meshes. After having proved stability of these subspace decompositions and requiring certain saturation assumptions to hold, we construct a local a posteriori error estimator for fem and bem coupling of a time-harmonic electromagnetic eddy current problem in $\mathbb{R}^3$. We perform some numerical tests to underline reliability and efficiency of the estimator and test its usefulness in an adaptive refinement scheme.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.13 no.2
• /
• pp.151-160
• /
• 1993

This paper is concerned with formulations of the hierarchical $C^{\circ}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element based on Integrals of Legendre shape functions is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method are proposed to verify the superior convergence and algorithmic efficiency with the help of the simply supported L-shaped plate problems.

• Computational Structural Engineering
• /
• v.10 no.4
• /
• pp.217-228
• /
• 1997

The high precision analysis by the p-version of the finite element method are fairly well established as highly efficient method for linear elastic problems, especially in the presence of stress singularity. It has been noted that the merits of the p-version are accuracy, modeling simplicity, robustness, and savings in user's and CPU time. However, little has been done to exploit their benefits in elasto-plastic analysis. In this paper, the p-version finite element model is proposed for the materially nonlinear analysis that is based on the incremental theory of plasticity using the constitutive equation for work-hardening materials, and the associated flow rule. To obtain the solution of nonlinear equation, the Newton-Raphson method and initial stiffness method, etc are used. Several numerical examples are tested with the help of the square plates with cutout, the thick-walled cylinder under internal pressure, and the circular plate with uniformly distributed load. Those results are compared with the theoretical solutions and the numerical solutions of ADINA