翻訳と辞書 Words near each other ・ Stenbolone ・ Stenborg ・ Stenborg Company ・ Stenborg Theatre ・ Stenbury Down ・ Stenbäck ・ Stench and Stenchibility ・ Stench kow ・ Stench Point ・ Stencil ・ Stencil (disambiguation) ・ Stencil (numerical analysis) ・ Stencil (typeface) ・ Stencil Art Prize ・ Stencil buffer ・ Stencil code ・ Stencil graffiti ・ Stencil House ・ Stencil jumping ・ Stencil lithography ・ Stencil Printing ・ Stencoose ・ Stencyl ・ Stendal ・ Stendal (district) ・ Stendal Nuclear Power Plant ・ Stendal station ・ Stendal Vorbahnhof station ・ Stendal, Indiana ・ Stendal-Stadtsee station Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stencil code ： ウィキペディア英語版 Stencil code Stencil codes are a class of iterative kernels〔 Roth, Gerald et al. (1997) Proceedings of SC'97: High Performance Networking and Computing. ''(Compiling Stencils in High Performance Fortran. )'' 〕 which update array elements according to some fixed pattern, called stencil.〔 Sloot, Peter M.A. et al. (May 28, 2002) ''(Computational Science – ICCS 2002: International Conference, Amsterdam, The Netherlands, April 21–24, 2002. Proceedings, Part I. )'' Page 843. Publisher: Springer. ISBN 3-540-43591-3. 〕 They are most commonly found in the codes of computer simulations, e.g. for computational fluid dynamics in the context of scientific and engineering applications. Other notable examples include solving partial differential equations,〔 the Jacobi kernel, the Gauss–Seidel method,〔 image processing〔 and cellular automata.〔 Fey, Dietmar et al. (2010) ''(Grid-Computing: Eine Basistechnologie für Computational Science )''. Page 439. Publisher: Springer. ISBN 3-540-79746-7〕 The regular structure of the arrays sets stencil codes apart from other modeling methods such as the Finite element method. Most finite difference codes which operate on regular grids can be formulated as stencil codes. ==Definition== Stencil codes perform a sequence of sweeps (called timesteps) through a given array.〔 Generally this is a 2- or 3-dimensional regular grid.〔 The elements of the arrays are often referred to as cells. In each timestep, the stencil code updates all array elements.〔 Using neighboring array elements in a fixed pattern (called the stencil), each cell's new value is computed. In most cases boundary values are left unchanged, but in some cases (e.g. LBM codes) those need to be adjusted during the course of the computation as well. Since the stencil is the same for each element, the pattern of data accesses is repeated.〔 Yang, Laurence T.; Guo, Minyi. (August 12, 2005) ''(High-Performance Computing : Paradigm and Infrastructure. )'' Page 221. Publisher: Wiley-Interscience. ISBN 0-471-65471-X 〕 More formally, we may define stencil codes as a 5-tuple $(I,\; S,\; S\_0,\; s,\; T)$ with the following meaning:〔 * $I\; =\; \backslash prod\_^k\; (\backslash ldots,\; n\_i)$ is the index set. It defines the topology of the array. * $S$ is the (not necessarily finite) set of states, one of which each cell may take on on any given timestep. * $S\_0\backslash colon\; \backslash Z^k\; \backslash to\; S$ defines the initial state of the system at time 0. * $s\; \backslash in\; \backslash prod\_^l\; \backslash Z^k$ is the stencil itself and describes the actual shape of the neighborhood. There are $l$ elements in the stencil. * $T\backslash colon\; S^l\; \backslash to\; S$ is the transition function which is used to determine a cell's new state, depending on its neighbors. Since ''I'' is a ''k''-dimensional integer interval, the array will always have the topology of a finite regular grid. The array is also called simulation space and individual cells are identified by their index $c\; \backslash in\; I$. The stencil is an ordered set of $l$ relative coordinates. We can now obtain for each cell $c$ the tuple of its neighbors indices $I\_c$ : $I\_c\; =\; \backslash \; \backslash ,$ Their states are given by mapping the tuple $I\_c$ to the corresponding tuple of states $N\_i(c)$, where $N\_i\backslash colon\; I\; \backslash to\; S^l$ is defined as follows: : $$ N_i(c) = (s_1, \ldots, s_l) \text s_j = S_i(I_c(j)) \, This is all we need to define the system's state for the following time steps $S\_\backslash colon\; \backslash Z^k\; \backslash to\; S$ with $i\; \backslash in\; \backslash N$: : $$ S_(c) = \beginT(N_i(c)), & c \in I\\ S_i(c), & c \in \Z^k \setminus I \end Note that $S\_i$ is defined on $\backslash Z^k$ and not just on $I$ since the boundary conditions need to be set, too. Sometimes the elements of $I\_c$ may be defined by a vector addition modulo the simulation space's dimension to realize toroidal topologies: : $$ I_c = \ This may be useful for implementing periodic boundary conditions, which simplifies certain physical models. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stencil code」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.