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Stencil Code
Iterative Stencil Loops (ISLs) are a class of numerical data processing solution 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 a 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. . They are most commonly found in 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. The regular structure of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Von Neumann Stencil Model
3-D, 3D, or 3d may refer to: Science, technology, and mathematics Relating to three-dimensionality * Three-dimensional space ** 3D computer graphics, computer graphics that use a three-dimensional representation of geometric data ** 3D film, a motion picture that gives the illusion of three-dimensional perception ** 3D modeling, developing a representation of any three-dimensional surface or object ** 3D printing, making a three-dimensional solid object of a shape from a digital model ** 3D display, a type of information display that conveys depth to the viewer ** 3D television, television that conveys depth perception to the viewer ** Stereoscopy, any technique capable of recording three-dimensional visual information or creating the illusion of depth in an image Other uses in science and technology or commercial products * 3D projection * 3D rendering * 3D scanning, making a digital representation of three-dimensional objects * 3D video game (other) * 3-D Secure, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Neighborhood
In cellular automata, the von Neumann neighborhood (or 4-neighborhood) is classically defined on a two-dimensional square lattice and is composed of a central cell and its four adjacent cells. The neighborhood is named after John von Neumann, who used it to define the von Neumann cellular automaton and the von Neumann universal constructor within it. It is one of the two most commonly used neighborhood types for two-dimensional cellular automata, the other one being the Moore neighborhood. This neighbourhood can be used to define the notion of 4-connected pixels in computer graphics.. The von Neumann neighbourhood of a cell is the cell itself and the cells at a Manhattan distance of 1. The concept can be extended to higher dimensions, for example forming a 6-cell octahedral neighborhood for a cubic cellular automaton in three dimensions. Von Neumann neighborhood of range ''r'' An extension of the simple von Neumann neighborhood described above is to take the set of poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stencil (numerical Analysis)
In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine. Stencils are the basis for many algorithms to numerically solve partial differential equations (PDE). Two examples of stencils are the five-point stencil and the Crank–Nicolson method stencil. Stencils are classified into two categories: compact and non-compact, the difference being the layers from the point of interest that are also used for calculation. In the notation used for one-dimensional stencils n-1, n, n+1 indicate the time steps where timestep n and n-1 have known solutions and time step n+1 is to be calculated. The spatial location of finite volumes used in the calculation are indicated by j-1, j and j+1. Etymology Graphical representations of node arrangements and their coefficients arose early in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stencil Jumping
Stencil jumping, at times called stencil walking, is an algorithm to locate the grid element enclosing a given point for any structured mesh. In simple words, given a point and a structured mesh, this algorithm will help locate the grid element that will enclose the given point. This algorithm finds extensive use in Computational Fluid Dynamics (CFD) in terms of holecutting and interpolation when two meshes lie one inside the other. The other variations of the problem would be something like this: Given a place, at which latitude and longitude does it lie? The brute force algorithm would find the distance of the point from every mesh point and see which is smallest. Another approach would be to use a binary search algorithm which would yield a result comparable in speed to the stencil jumping algorithm. A combination of both the binary search and the stencil jumping algorithm will yield an optimum result in the minimum possible time. The principle Consider one grid element of a 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Five-point Stencil
In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors". It is used to write finite difference approximations to derivatives at grid points. It is an example for numerical differentiation. In one dimension In one dimension, if the spacing between points in the grid is ''h'', then the five-point stencil of a point ''x'' in the grid is :\ \. 1D first derivative The first derivative of a function ƒ of a real variable at a point ''x'' can be approximated using a five-point stencil as: :f'(x) \approx \frac Notice that the center point ƒ(''x'') itself is not involved, only the four neighboring points. Derivation This formula can be obtained by writing out the four Taylor series of ƒ(''x'' ± ''h'') and ƒ(''x'' ± 2''h'') up to terms of ''h''3 (or up to terms of ''h''5 to get an error estimation as well) an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict. Computer simulations have become a useful tool for the mathematical modeling of many natural systems in physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering. Simulation of a system is represented as the running of the system's model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions. Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advanced Simulation Library
Advanced Simulation Library (ASL) is free and open-source hardware-accelerated multiphysics simulation platform. It enables users to write customized numerical solvers in C++ and deploy them on a variety of massively parallel architectures, ranging from inexpensive FPGAs, DSPs and GPUs up to heterogeneous clusters and supercomputers. Its internal computational engine is written in OpenCL and utilizes matrix-free solution techniques. ASL implements variety of modern numerical methods, i.a. level-set method, lattice Boltzmann, immersed Boundary. Mesh-free, immersed boundary approach allows users to move from CAD directly to simulation, reducing pre-processing efforts and number of potential errors. ASL can be used to model various coupled physical and chemical phenomena, especially in the field of computational fluid dynamics. It is distributed under the free GNU Affero General Public License with an optional commercial license (which is based on the permissive MIT License) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaprogramming
Metaprogramming is a programming technique in which computer programs have the ability to treat other programs as their data. It means that a program can be designed to read, generate, analyze or transform other programs, and even modify itself while running. In some cases, this allows programmers to minimize the number of lines of code to express a solution, in turn reducing development time. It also allows programs a greater flexibility to efficiently handle new situations without recompilation. Metaprogramming can be used to move computations from run-time to compile-time, to generate code using compile time computations, and to enable self-modifying code. The ability of a programming language to be its own metalanguage is called reflection. Reflection is a valuable language feature to facilitate metaprogramming. Metaprogramming was popular in the 1970s and 1980s using list processing languages such as LISP. LISP hardware machines were popular in the 1980s and enabled app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Template (programming)
Templates are a feature of the C++ programming language that allows functions and classes to operate with generic types. This allows a function or class to work on many different data types without being rewritten for each one. The C++ Standard Library provides many useful functions within a framework of connected templates. Major inspirations for C++ templates were the parameterized modules provided by CLU and the generics provided by Ada. Technical overview There are three kinds of templates: ''function templates'', ''class templates'' and, since C++14, ''variable templates''. Since C++11, templates may be either variadic or non-variadic; in earlier versions of C++ they are always non-variadic. Function templates A ''function template'' behaves like a function except that the template can have arguments of many different types (see example). In other words, a function template represents a family of functions. The format for declaring function templates with type para ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Application Checkpointing
Checkpointing is a technique that provides fault tolerance for computing systems. It basically consists of saving a snapshot of the application's state, so that applications can restart from that point in case of failure. This is particularly important for long running applications that are executed in failure-prone computing systems. Checkpointing in distributed systems In the distributed computing environment, checkpointing is a technique that helps tolerate failures that otherwise would force long-running application to restart from the beginning. The most basic way to implement checkpointing, is to stop the application, copy all the required data from the memory to reliable storage (e.g., parallel file system) and then continue with the execution. In case of failure, when the application restarts, it does not need to start from scratch. Rather, it will read the latest state ("the checkpoint") from the stable storage and execute from that. While there is ongoing debate on wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Steering
Computational steering is the practice of manually intervening with an otherwise autonomous computational process, to change its outcome. The term is commonly used within the numerical simulation community, where it more specifically refers to the practice of interactively guiding a computational experiment into some region of interest. Examples A simple, but contrived, example of computational steering is: * In a simulated chess match with two automated players: manually forcing a certain move at a particular time for one player, to change the evolution of the game. Some real examples of computational steering are: * In a population dynamics simulation: changing selection pressures exerted between hosts and parasites, to examine the effect on their coevolution. * In a fluid dynamics simulation: resetting the phase state of an immiscible fluid, to speed the search for its critical separation temperature. System design Computational steering systems are a manner of feedbac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GPGPU
General-purpose computing on graphics processing units (GPGPU, or less often GPGP) is the use of a graphics processing unit (GPU), which typically handles computation only for computer graphics, to perform computation in applications traditionally handled by the central processing unit (CPU). The use of multiple video cards in one computer, or large numbers of graphics chips, further parallelizes the already parallel nature of graphics processing. Essentially, a GPGPU pipeline is a kind of parallel processing between one or more GPUs and CPUs that analyzes data as if it were in image or other graphic form. While GPUs operate at lower frequencies, they typically have many times the number of cores. Thus, GPUs can process far more pictures and graphical data per second than a traditional CPU. Migrating data into graphical form and then using the GPU to scan and analyze it can create a large speedup. GPGPU pipelines were developed at the beginning of the 21st century for graphic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
