• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.1-6
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• 1997

We will construct the generalized law of cosines in a tetrahedron, in a natural way, which gives three dimensional Pythagoras' theorem and enables us to calculate the volume of an arbitrary tetrahedron.

• 대한기계학회논문집
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• 제18권12호
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• pp.3159-3174
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• 1994

A simple octree encoding algorithm based on a tetrahedron root has been developed to be used for fully automatic generation of three dimensional finite element meshes. This algorithm starts octree decomposition from a tetrahedron root node instead of a hexahedron root node so that the terminal mode has the same topology as the final tetrahedral mesh. As a result, the terminal octant can be used as a tetrahedral finite element without transforming its topology. In this part(I) of the thesis, an efficient algorithm for the tetrahedron-based octree is proposed. For this development, the following problems have been solved, : (1) an efficient data structure for storing the octree and finite elements, (2) an encoding scheme of a tetrahedral octree, (3) a neighbor finding technique for the tetrahedron-based octree.

• 호남수학학술지
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• 제35권1호
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• pp.17-27
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• 2013

We survey and study several volume formulas of a Euclidean tetrahedron.

• 대한수학회지
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• 제50권6호
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• pp.1223-1256
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• 2013

We give a geometric proof of the analyticity of the volume of a tetrahedron in extended hyperbolic space, when vertices of the tetrahedron move continuously from inside to outside of a hyperbolic space keeping every face of the tetrahedron intersecting the hyperbolic space. Then we find a geometric and analytic interpretation of a truncated orthoscheme and Lambert cube in the hyperbolic space from the viewpoint of a tetrahedron in the extended hyperbolic space.

• 전자공학회논문지D
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• 제34D권7호
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• pp.37-44
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• 1997

A dadaptive refinement tetrahedron mesh has been presented for using in full band GaAs monte carlo simulation. A uniform tetrahedron mesh is used without regard to energy values and energy variety in case of the past full band simulation. For the uniform tetrahedron mesh, a fine tetrahedron is demanded for keeping up accuracy of calculation in the low energy region such as .GAMMA.-valley, but calculation time is vast due to usin gthe same tetrahedron in the high energy region. The mesh of this study, thererfore, is consisted of the fine mesh in the low energy and large variable energy region and rough mesh n the high energy. The density of states (DOS) calculated with this mesh is compared with the one of the uniform mesh. The DOS of this mesh is improved th efive times or so in root mean square error and the ten times in the correlation coefficient than the one of a uniform mesh. This refinement mesh, therefore, can be used a sthe basic mesh for the full band GaAs monte carlo simulation.

• Nuclear Engineering and Technology
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• 제48권1호
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• pp.43-54
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• 2016

In the present paper, development of the three-dimensional (3D) computational code based on Galerkin finite element method (GFEM) for solving the multigroup forward/adjoint diffusion equation in both rectangular and hexagonal geometries is reported. Linear approximation of shape functions in the GFEM with unstructured tetrahedron elements is used in the calculation. Both criticality and fixed source calculations may be performed using the developed GFEM-3D computational code. An acceptable level of accuracy at a low computational cost is the main advantage of applying the unstructured tetrahedron elements. The unstructured tetrahedron elements generated with Gambit software are used in the GFEM-3D computational code through a developed interface. The forward/adjoint multiplication factor, forward/adjoint flux distribution, and power distribution in the reactor core are calculated using the power iteration method. Criticality calculations are benchmarked against the valid solution of the neutron diffusion equation for International Atomic Energy Agency (IAEA)-3D and Water-Water Energetic Reactor (VVER)-1000 reactor cores. In addition, validation of the calculations against the $P_1$ approximation of the transport theory is investigated in relation to the liquid metal fast breeder reactor benchmark problem. The neutron fixed source calculations are benchmarked through a comparison with the results obtained from similar computational codes. Finally, an analysis of the sensitivity of calculations to the number of elements is performed.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권3호
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• pp.303-314
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• 2007

In this paper we try to study a method of constructing plane sections of regular tetrahedron and regular hexahedron. In order to construct plane sections of regular tetrahedron and regular hexahedron first of all, we extract some base problems that are used for construction. And we describe construction process using base problems in detail.

• 대한수학회지
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• 제49권4호
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• pp.765-778
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• 2012

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

• 대한의용생체공학회:학술대회논문집
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• 대한의용생체공학회 1998년도 추계학술대회
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• pp.273-274
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• 1998

We construct a volume whose boundary is a tetrahedron with triangular faces intersecting the cutting planes along the given contours. This volume is obtained by calculating the Delaunay triangulation slice by slice, mapping 2D to 3D as tetrahedron. Also, eliminate extra-voronoi skeleton and non-solid tetrahedron. In this paper, we propose new method to eliminate non-solid tetrahedron based on the modified extra-voronoi skeleton path. This method enable us to do a compact tetrahedrisation and to reconstruct complex shapes.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제21권3호
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• pp.385-406
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• 2007

본 연구에서는 삼각형의 방접원 및 사면체의 방접구에 관련된 다양한 성질을 증명하기 위해 바탕문제들을 추출하고, 바탕문제를 중심으로 삼각형의 방접원에 관련된 성질들을 체계화하고 증명하며, 삼각형의 방접원의 다양한 성질을 사면체로 유추하여 방접구의 성질을 추측, 증명하였다.