• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.3
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• pp.331-340
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• 2010

The basic theory and application of new adaptive finite element algorithm have been proposed in this study including the adaptive hp-refinement strategy, and the effective method for constructing hp-approximation. The hp-adaptive finite element concept needs the integrals of Legendre shape function, nonuniform p-distribution, and suitable constraint of continuity in conjunction with irregular node connection. The continuity of hp-adaptive mesh is an important problem at the common boundary of element interface. To solve this problem, the constraint of continuity has been enforced at the common boundary using the connectivity mapping matrix. The effective method for constructing of the proposed algorithm has been developed by using hierarchical nature of the integrals of Legendre shape function. To verify the proposed algorithm, the problem of simple cantilever beam has been solved by the conventional h-refinement and p-refinement as well as the proposed hp-refinement. The result obtained by hp-refinement approach shows more rapid convergence rate than those by h-refinement and p-refinement schemes. It it noted that the proposed algorithm may be implemented efficiently in practice.

• Structural Engineering and Mechanics
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• v.11 no.5
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• pp.535-546
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• 2001

A new p-adaptive analysis scheme for hp-clouds method is presented. In the scheme, refined global equations are resolved into two parts, one of them being related to the newly appended dof's. The solution obtained in previous analysis step is reflected in the force vector. The size of the p-adaptive equation consisting of the newly appended dof's is much smaller than the original equation. Consequently, the computational cost is drastically decreased. Through numerical examples, the efficiency and efficacy of the method in comparison with the existing p-refinement scheme of the hp-clouds have been demonstrated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.10a
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• pp.39-44
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• 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
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• v.13 no.1
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• pp.118-127
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• 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.

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

• Economic and Environmental Geology
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• v.43 no.3
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• pp.259-267
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• 2010

Resistivity logging instruments were designed to measure electrical resistivity of formation, which can be directly interpreted to provide water-saturation profile. Short and long normal logging measurements are made under groundwater level. In some investigation sites, groundwater level reaches to a depth of a few meters. It has come to attention that the proximity of groundwater level might distort short and long normal logging readings, when the measurements are made near groundwater level, owing to the proximity of an insulating air. This study investigates the effects of the proximity of groundwater level (and also the proximity of earth surface) on the normal by simulating normal logging measurements near groundwater level. In the simulation, we consider all the details of real logging situation, i.e., the presence of wellbore, the tool mandrel with current and potential electrodes, and currentreturn and reference-potential electrodes. We also model the air to include the earth’'s surface in the simulation rather than the customary choice of imposing a boundary condition. To obtain apparent resistivity, we compute the voltage, i.e., potential difference between monitoring and reference electrodes. For the simulation, we use a twodimensional, goal-oriented and high-order self-adaptive hp finite element refinement strategy (h denotes the element size and p the polynomial order of approximation within each element) to obtain accurate simulation results. Numerical results indicate that distortion on the normal logging is greater when the reference potential electrode is closer to the borehole and distortions on long normal logging are larger than those on short normal logging.