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Computational Mechanics
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a "third way" besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science. Overview Computational mechanics (CM) is interdisciplinary. Its three pillars are mechanics, mathematics, and computer science. Mechanics Computational fluid dynamics, computational thermodynamics, computational electromagnetics, computational solid mechanics are some of the many specializations within CM. Mathematics The areas of mathematics most related to computational mechanics are partial differential equations, linear algebra and numerical analysis. The most popular numerical methods used are the finite element, fini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Mechanics (journal)
''Computational Mechanics'' is a monthly scientific journal focused on computational mechanics. It is published by Springer and was founded in 1986. The journal reports original research in computational mechanics. It focuses on areas that involve the rational application of mechanics, mathematics, and numerical methods in the practice of modern engineering. Areas covered include solid and structural mechanics, multi-body system dynamics, constitutive modeling, inelastic and finite deformation response, and structural control. The journal also covers fluid mechanics and fluid-structure interactions, biomechanics, free-surface and two-fluid flows, aerodynamics, fracture mechanics and structural integrity, multi-scale mechanics, particle and meshfree methods, transport phenomena, and heat transfer. Lastly, the journal publishes modern variational methods in mechanics in general. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems Theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex systems, complex dynamical systems, usually by employing differential equations by nature of the ergodic theory, ergodicity of dynamic systems. When differential equations are employed, the theory is called continuous time, ''continuous dynamical systems''. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a Principle of least action, least action principle. When difference equations are employed, the theory is called discrete time, ''discrete dynamical systems''. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Computing
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science, and more specifically the Computer Sciences, which uses advanced computing capabilities to understand and solve complex physical problems. While this typically extends into computational specializations, this field of study includes: * Algorithms ( numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve sciences (e.g, physical, biological, and social), engineering, and humanities problems * Computer hardware that develops and optimizes the advanced system hardware, firmware, networking, and data management components needed to solve computationally demanding problems * The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and information science In practical use, it is typically the application of computer simu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reservoir Simulation
Reservoir simulation is an area of reservoir engineering in which computer models are used to predict the Fluid dynamics, flow of fluids (typically, oil, water, and gas) through porous media. The creation of models of oil fields and the implementation of calculations of field development on their basis is one of the main areas of activity of engineers and oil researchers. On the basis of geological and physical information about the properties of an oil, gas or gas condensate field, consideration of the capabilities of the systems and technologies for its development create quantitative ideas about the development of the field as a whole. A system of interrelated quantitative ideas about the development of a field is a model of its development, which consists of a reservoir model and a model of a field development process. Layer models and processes for extracting oil and gas from them are always clothed in a mathematical form, i.e. characterized by certain mathematical relations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crash Simulation
A crash simulation is a Virtuality, virtual recreation of a destructive crash test of a car or a highway Traffic barrier, guard rail system using a computer simulation in order to examine the level of safety of the car and its occupants. Crash simulations are used by automakers during computer-aided engineering (CAE) analysis for crashworthiness in the computer-aided design (CAD) process of modelling new cars. During a crash simulation, the kinetic energy, or energy of motion, that a vehicle has before the impact is transformed into Deformation (engineering), deformation energy, mostly by plastic deformation (Plasticity (physics), plasticity) of the car body material (Body in White), at the end of the impact. Data obtained from a crash simulation indicate the capability of the car body or guard rail structure to protect the vehicle occupants during a collision (and also pedestrians hit by a car) against injury. Important results are the deformations (for example, steering wheel int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed-form Expression
In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. Commonly, the basic functions that are allowed in closed forms are ''n''th root, exponential function, logarithm, and trigonometric functions. However, the set of basic functions depends on the context. For example, if one adds polynomial roots to the basic functions, the functions that have a closed form are called elementary functions. The ''closed-form problem'' arises when new ways are introduced for specifying mathematical objects, such as limits, series, and integrals: given an object specified with such tools, a natural problem is to find, if possible, a ''closed-form expression'' of this object; that is, an expression of this object in terms of previous ways of specifying it. Example: roots of polynomials The quadratic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Computing
Parallel computing is a type of computing, computation in which many calculations or Process (computing), processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different forms of parallel computing: Bit-level parallelism, bit-level, Instruction-level parallelism, instruction-level, Data parallelism, data, and task parallelism. Parallelism has long been employed in high-performance computing, but has gained broader interest due to the physical constraints preventing frequency scaling.S.V. Adve ''et al.'' (November 2008)"Parallel Computing Research at Illinois: The UPCRC Agenda" (PDF). Parallel@Illinois, University of Illinois at Urbana-Champaign. "The main techniques for these performance benefits—increased clock frequency and smarter but increasingly complex architectures—are now hitting the so-called power wall. The computer industry has accepted that future performance inc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supercomputer
A supercomputer is a type of computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2022, supercomputers have existed which can perform over 1018 FLOPS, so called Exascale computing, exascale supercomputers. For comparison, a desktop computer has performance in the range of hundreds of gigaFLOPS (1011) to tens of teraFLOPS (1013). Since November 2017, all of the TOP500, world's fastest 500 supercomputers run on Linux-based operating systems. Additional research is being conducted in the United States, the European Union, Taiwan, Japan, and China to build faster, more powerful and technologically superior exascale supercomputers. Supercomputers play an important role in the field of computational science, and are used for a wide range of computationally intensive tasks in various fields, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Method
In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an "iterate") is derived from the previous ones. A specific implementation with Algorithm#Termination, termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or Quasi-Newton method, quasi-Newton methods like Broyden–Fletcher–Goldfarb–Shanno algorithm, BFGS, is an algorithm of an iterative method or a method of successive approximation. An iterative method is called ''Convergent series, convergent'' if the corresponding sequence converges for given initial approximations. A mathematically rigorous convergence analysis of an iterative method is usually performed; however, heuristic-based iterative methods are also common. In contrast, direct methods attempt to solve the problem by a finit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Program
A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. It is one component of software, which also includes software documentation, documentation and other intangible components. A ''computer program'' in its human-readable form is called source code. Source code needs another computer program to Execution (computing), execute because computers can only execute their native machine instructions. Therefore, source code may be Translator (computing), translated to machine instructions using a compiler written for the language. (Assembly language programs are translated using an Assembler (computing), assembler.) The resulting file is called an executable. Alternatively, source code may execute within an interpreter (computing), interpreter written for the language. If the executable is requested for execution, then the operating system Loader (computing), loads it into Random-access memory, memory and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Equations
In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0, where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For example, x^5-3x+1=0 is an algebraic equation with integer coefficients and :y^4 + \frac - \frac + xy^2 + y^2 + \frac = 0 is a multivariate polynomial equation over the rationals. For many authors, the term ''algebraic equation'' refers only to the univariate case, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables (the ''multivariate'' case), in which case the term ''polynomial equation'' is usually preferred. Some but not all polynomial equations with rational coefficients have a solution that is an algebraic expression that can be found using a finite number of operations that involve only those same types of coefficients (that is, can be solved algebraically). This can be done for all such equati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
