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Particle Method
Particle methods is a widely used class of numerical algorithms in scientific computing. Its application ranges from computational fluid dynamics (CFD) over molecular dynamics (MD) to discrete element methods. 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., Chen, H. Schreyer (1994). a Particle Method for History-Dependent Materials. ''Comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Fluid Dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid dynamics, fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by Boundary value problem#Boundary value conditions, boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulence, turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed Closed-form solution, analytical or Empirical research, empirical analysis of a particular problem can be used for compa ... [...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) *Cracker ... [...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 to find 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 like economics, 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 simulati ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stencil Code
Iterative Stencil Loops (ISLs) or Stencil computations 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. ... [...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 Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician Georg ..., the fluid equations are : \rho \left(\frac + \cdot\nabla\right) = -\nabla p + \mu\, \Delta u(x, ... [...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 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 Green's functions can be calculated. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mechanics deals with ''deformable bodies'', as opposed to rigid bodies. A continuum model assumes that the substance of the object completely fills the space it occupies. While ignoring the fact that matter is made of atoms, this provides a sufficiently accurate description of matter on length scales much greater than that of inter-atomic distances. The concept of a continuous medium allows for intuitive analysis of bulk matter by using differential equations that describe the behavior of such matter according to physical laws, such as mass conservation, momentum conservation, and energy conservation. Information about the specific material is expressed in constitutive relationships. Continuum mechanics treats the physical properties of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalizations of concatenation theory, also called string theory, string concatenation is a primitive notion. Syntax In many programming languages, string concatenation is a binary infix operator, and in some it is written without an operator. This is implemented in different ways: * Overloading the plus sign + Example from C#: "Hello, " + "World" has the value "Hello, World". * Dedicated operator, such as . in PHP, & in Visual Basic, and , , in SQL. This has the advantage over reusing + that it allows implicit type conversion to string. * string literal concatenation, which means that adjacent strings are concatenated without any operator. Example from C: "Hello, " "World" has the value "Hello, World". In many scientific publications or standards the con ... [...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'', a 2023 Japanese film directed by Takashi Shimizu * ''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 ba ... [...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 Cathy Davey from ''Tales of Silversleeve'', 2007 * "Moving", by Ed Sheeran from '' -'', 2023 * "Moving", by Suede from ''Suede'', 1993 * "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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the Motion (physics), physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamics (mechanics), dynamic "evolution" of the system. In the most common version, the trajectory, trajectories of atoms and molecules are determined by Numerical integration, numerically solving Newton's laws of motion, Newton's equations of motion for a system of interacting particles, where Force (physics), forces between the particles and their potential energy, potential energies are often calculated using interatomic potentials or molecular mechanics, molecular mechanical Force field (chemistry), force fields. The method is applied mostly in chemical physics, materials science, and biophysics. Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analyt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
