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Particle Method
In the field of numerical analysis, particle methods discretize fluid into particles. Particle methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. Some of particle methods are meshfree methods and vice versa. History One of the earliest particle methods is smoothed particle hydrodynamics, presented in 1977. Libersky ''et al.'' were the first to apply SPH in solid mechanics. The main drawbacks of SPH are inaccurate results near boundaries and tension instability that was first investigated by Swegle. In the 1990s a new class of particle methods emerged. The reproducing kernel particle method (RKPM) emerged, the approximation motivated in part to correct the kernel estimate in SPH: to give accuracy near boundaries, in non-uniform discretizations, and higher-order accuracy in general. Notably, in a parallel development, the Material point methods were developed around the same timeD. Sulsky, Z., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cracking Particles Method
Cracking may refer to: * Cracking, the formation of a fracture or partial fracture in a solid material studied as fracture mechanics ** Performing a sternotomy * Fluid catalytic cracking, a catalytic process widely used in oil refineries for cracking large hydrocarbon molecules into smaller molecules * Cracking (chemistry), the decomposition of complex organic molecules into smaller ones * Cracking joints, the practice of manipulating one's bone joints to make a sharp sound * Cracking codes, see cryptanalysis * Whip cracking * Safe cracking * ''Crackin, band featuring Lester Abrams * Packing and cracking, a method of creating voting districts to give a political party an advantage In computing: * Another name for security hacking; the practice of defeating computer security. * Password cracking, the process of discovering the plaintext of an encrypted computer password. * Software cracking, the defeating of software copy protection. See also *Crack (other) *Cracke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meshfree Methods
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field. Motivation Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes of data points. In such a mesh, each point has a fixed number of predefined neighbors, and this connectivity between neighbors can be used to define mathematical operators like the derivative. These operators are t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Immersed Boundary Method
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations (the elastic boundary changes the flow of the fluid and the fluid moves the elastic boundary simultaneously). In the immersed boundary method the fluid is represented in an Eulerian coordinate system and the structure is represented in Lagrangian coordinates. For Newtonian fluids governed by the Navier–Stokes equations, the fluid equations are : \rho \left(\frac + \cdot\nabla\right) = -\nabla p + \mu\, \Delta u(x,t) + f(x,t) and if the flow is incompressible, we have the further condition that : \nabla \cdot u = 0. \, The immersed structures are typically represented as a collection of one-dimensional fibers, denoted by \Gamma . Each fiber can be viewed as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Element Method
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in ''boundary integral'' form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as Method of moments (electromagnetics), method of moments or abbreviated as MoM), fracture mechanics, and contact mechanics. Mathematical basis The integral equation may be regarded as an exact solution of the governing partial differential equation. The boundary element method attempts to use the given boundary conditions to fit boundary values into the integral equation, rather than values throughout the space defined by a partial differential equation. Once this is done, in the post-processing stage, the integral equation can then be used again to calculate numerically the solution directly at any desired point in the interior of the solution domain. BEM is applicable to problems for which G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Immersed Particle Method
Immersion may refer to: The arts * "Immersion", a 2012 story by Aliette de Bodard * ''Immersion'', a French comic book series by Léo Quievreux * ''Immersion'' (album), the third album by Australian group Pendulum * ''Immersion'' (film), a 2021 Chilean thriller film * Immersion (series), a webseries which test the concepts of video games in real life, created by Rooster Teeth Productions * Immersion journalism, a style of journalism Science and technology * Immersion lithography or immersion microscopy, optical techniques in which liquid is between the objective and image plane in order to raise numerical aperture * Immersion (mathematics), a smooth map whose differential is everywhere injective, related to the mathematical concept of an embedding * Immersion (virtual reality), the perception of being physically present in a non-physical world, created by using VR Other uses * Immersion baptism, a type of baptism whereby the subject is immersed in water * Immersion Corporation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moving Particle Finite Element Method
Moving or Movin' may refer to: Moving of goods * Relocation (personal), the process of leaving one dwelling and settling in another * Relocation of professional sports teams * Relocation (computer science) * Structure relocation Music Albums * ''Moving'' (Peter, Paul and Mary album), 1963 * ''Moving'' (The Raincoats album), 1983 * ''Movin (Herman van Doorn album), 2001 * ''Movin (Jennifer Rush album), 1985 Songs * "Moving" (Kate Bush song), 1978 * "Moving" (Supergrass song), 1999 * "Moving" (Travis song), 2013 * "Moving", by Suede from ''Suede'', 1993 * "Moving", by Cathy Davey from ''Tales of Silversleeve'', 2007 * "Movin (Brass Construction song), 1976 * "Movin (Mohombi song), 2014 * "Movin, by Skin from '' Fake Chemical State'', 2006 Other uses * ''Moving'' (1988 film), a comedy starring Richard Pryor * ''Moving'' (1993 film), a Japanese film * ''Moving'' (British TV series), a British sitcom starring Penelope Keith *Moving (South Korean TV series), an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meshfree Methods
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field. Motivation Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes of data points. In such a mesh, each point has a fixed number of predefined neighbors, and this connectivity between neighbors can be used to define mathematical operators like the derivative. These operators are t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle-in-cell
In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points. PIC methods were already in use as early as 1955, even before the first Fortran compilers were available. The method gained popularity for plasma simulation in the late 1950s and early 1960s by Buneman, Dawson, Hockney, Birdsall, Morse and others. In plasma physics applications, the method amounts to following the trajectories of charged particles in self-consistent electromagnetic (or electrostatic) fields computed on a fixed mesh. Technical aspects For many types of problems, the classical PIC method invented by Buneman, Dawson, Hockney, Birdsall, Morse and others is relatively intuitiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
