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151 relations: Absolute continuity, Aerospace engineering, Alexander Hrennikoff, Algebraic equation, Analysis, Antiderivative, Applied element method, Basis (linear algebra), Bessel function, Bilinear map, Boris Galerkin, Boundary element method, Boundary value problem, Bruce Irons (engineer), Calculus, Calculus of variations, Céa's lemma, Cholesky decomposition, Civil engineering, Closed-form expression, Complex system, Computational fluid dynamics, Computer, Computer experiment, Conjugate gradient method, Coordinate system, Cornell University, Cylinder, Differentiable manifold, Differential equation, Direct stiffness method, Dirichlet problem, Discontinuity layout optimization, Discrete element method, Discretization, Distribution (mathematics), DNV GL, Dot product, Eddy (fluid dynamics), Elasticity (physics), Electrical conductor, Electromagnet, Electromagnetic four-potential, Electromagnetic shielding, Electromagnetism, Elliptic boundary value problem, Elliptic curve, Elliptic operator, Engineering, Engineering analysis, ..., Ernest Hinton, Euler method, Euler–Bernoulli beam theory, Extended finite element method, Feng Kang, Finite difference method, Finite element machine, Finite element method in structural mechanics, Finite volume method, Finite volume method for unsteady flow, Fluid dynamics, Galerkin method, George Fix, Gilbert Strang, Gradient, Gradient discretisation method, Gramian matrix, Green's identities, Heat equation, Heat transfer, Hilbert space, Hp-FEM, Infinite element method, Initial value problem, Inner product space, Integral equation, Integration by parts, International Journal of Computational Methods, Interval finite element, Iron, Isogeometric analysis, John Argyris, John William Strutt, 3rd Baron Rayleigh, Lattice (group), Lattice Boltzmann methods, Linear algebra, Linear subspace, Linearity, List of finite element software packages, Loubignac iteration, Lp space, LU decomposition, Magnetism, Mass matrix, Mathematical physics, MATLAB, Mean value theorem, Mesh generation, Movable cellular automaton, Multidisciplinary design optimization, Multiphysics, Nastran, Navier–Stokes equations, Norm (mathematics), Numerical analysis, Numerical linear algebra, Numerical weather prediction, Olgierd Zienkiewicz, Ordinary differential equation, P-FEM, Partial differential equation, Partially ordered set, Partition of unity, Patch test (finite elements), Philippe G. Ciarlet, Physics, Pierre and Marie Curie University, Poisson's equation, Polygon, Polygon mesh, Polygon triangulation, Polynomial, Ray William Clough, Rayleigh–Ritz method, Richard Courant, Riesz representation theorem, Runge–Kutta methods, SESAM (FEM), Sobolev space, Software, Space mapping, Sparse matrix, Spectral element method, Spectral method, Steady state, Stiffness matrix, Structural analysis, Superconvergence, Support (mathematics), Swansea University, Torsion (mechanics), Transformation matrix, Transient state, Triangular function, Tropical cyclone, University of California, Berkeley, University of Stuttgart, Walther Ritz, Weak formulation, Weakened weak form, Weight function. Expand index (101 more) »
Absolute continuity
In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.
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Aerospace engineering
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft.
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Alexander Hrennikoff
Alexander Pavlovich Hrennikoff (Александр Павлович Хренников; 11 November 1896 — December 31, 1984) was a Russian-Canadian Structural Engineer, a founder of the Finite Element Method.
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Algebraic equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.
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Analysis
Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it.
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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Applied element method
The applied element method (AEM) is a numerical analysis used in predicting the continuum and discrete behavior of structures.
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Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
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Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.
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Bilinear map
In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments.
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Boris Galerkin
Boris Grigoryevich Galerkin (Бори́с Григо́рьевич Галёркин, surname more accurately romanized as Galyorkin; – 12 July 1945), born in Polotsk, Vitebsk Governorate, Russian Empire, was a Soviet mathematician and an engineer.
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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).
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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Bruce Irons (engineer)
Bruce Irons (1924 – 5 December 1983) was an engineer and mathematician, known for his fundamental contribution to the finite element method, including the patch test, the frontal solver and, along with Ian C. Taig, the isoparametric element concept.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Céa's lemma
Céa's lemma is a lemma in mathematics.
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Cholesky decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃ-/) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g. Monte Carlo simulations.
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Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works such as roads, bridges, canals, dams, airports, sewerage systems, pipelines, and railways.
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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Complex system
A complex system is a system composed of many components which may interact with each other.
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Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to solve and analyze problems that involve fluid flows.
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Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
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Computer experiment
A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system.
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Conjugate gradient method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite.
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Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
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Cornell University
Cornell University is a private and statutory Ivy League research university located in Ithaca, New York.
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Cylinder
A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Direct stiffness method
As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type.
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Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region.
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Discontinuity layout optimization
Discontinuity layout optimization (DLO) is an engineering analysis procedure which can be used to directly establish the amount of load that can be carried by a solid or structure prior to collapse.
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Discrete element method
A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of a large number of small particles.
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Discretization
In mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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DNV GL
DNV GL is an international accredited registrar and classification society headquartered in Høvik, Norway.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Eddy (fluid dynamics)
In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime.
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Elasticity (physics)
In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.
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Electrical conductor
In physics and electrical engineering, a conductor is an object or type of material that allows the flow of an electrical current in one or more directions.
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Electromagnet
An electromagnet is a type of magnet in which the magnetic field is produced by an electric current.
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Electromagnetic four-potential
An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived.
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Electromagnetic shielding
Electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials.
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Electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
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Elliptic boundary value problem
In mathematics, an elliptic boundary value problem is a special kind of boundary value problem which can be thought of as the stable state of an evolution problem.
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Elliptic curve
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.
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Elliptic operator
In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Engineering analysis
Engineering analysis involves the application of scientific analytic principles and processes to reveal the properties and state of a system, device or mechanism under study.
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Ernest Hinton
Ernest Hinton (16 March 1946 – 18 November 1999) was a British civil engineer and engineering professor.
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Euler method
In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
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Euler–Bernoulli beam theory
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory)Timoshenko, S., (1953), History of strength of materials, McGraw-Hill New York is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams.
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Extended finite element method
The extended finite element method (XFEM), is a numerical technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM).
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Feng Kang
Feng Kang (September 9, 1920 - August 17, 1993) was a Chinese mathematician and scientist.
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Finite difference method
In mathematics, finite-difference methods (FDM) are numerical methods for solving differential equations by approximating them with difference equations, in which finite differences approximate the derivatives.
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Finite element machine
The Finite Element Machine (FEM) was a late 1970s-early 1980s NASA project to build and evaluate the performance of a parallel computer for structural analysis.
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Finite element method in structural mechanics
The finite element method (FEM) is a powerful technique originally developed for numerical solution of complex problems in structural mechanics, and it remains the method of choice for complex systems.
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Finite volume method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.
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Finite volume method for unsteady flow
Unsteady flows are characterized as flows in which the properties of the fluid are time dependent.
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Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.
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Galerkin method
In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem (such as a differential equation) to a discrete problem.
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George Fix
George J. Fix (10 May 1939 – 10 March 2002) was an American mathematician who collaborated on several seminal papers and books in the field of finite element method.
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Gilbert Strang
William Gilbert Strang (born November 27, 1934), usually known as simply Gilbert Strang or Gil Strang, is an American mathematician, with contributions to finite element theory, the calculus of variations, wavelet analysis and linear algebra.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Gradient discretisation method
In numerical mathematics, the gradient discretisation method (GDM) is a framework which contains classical and recent numerical schemes for diffusion problems of various kinds: linear or non-linear, steady-state or time-dependent.
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Gramian matrix
In linear algebra, the Gram matrix (Gramian matrix or Gramian) of a set of vectors v_1,\dots, v_n in an inner product space is the Hermitian matrix of inner products, whose entries are given by G_.
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Green's identities
In mathematics, Green's identities are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act.
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Heat equation
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.
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Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Hp-FEM
hp-FEM is a general version of the finite element method (FEM), a numerical method for solving partial differential equations based on piecewise-polynomial approximations that employs elements of variable size (h) and polynomial degree (p).
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Infinite element method
The infinite element method is a numerical method for solving problems of engineering and mathematical physics.
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Initial value problem
In mathematics, the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.
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Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.
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International Journal of Computational Methods
The International Journal of Computational Methods has been published by World Scientific since 2004.
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Interval finite element
In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters.
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Iron
Iron is a chemical element with symbol Fe (from ferrum) and atomic number 26.
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Isogeometric analysis
Isogeometric analysis is a recently developed computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools.
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John Argyris
Johann Hadji Argyris FRS (Greek: Ιωάννης Χατζι Αργύρης; 19 August 1913 – 2 April 2004) was a Greek pioneer of computer applications in science and engineering,Hughes TJR, Oden JT, and Papadrakakis M (2011) John H Argyris, Memorial Tributes: National Academy of Engineering, 15, 24–31.
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John William Strutt, 3rd Baron Rayleigh
John William Strutt, 3rd Baron Rayleigh, (12 November 1842 – 30 June 1919) was a physicist who, with William Ramsay, discovered argon, an achievement for which he earned the Nobel Prize for Physics in 1904.
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Lattice (group)
In geometry and group theory, a lattice in \mathbbR^n is a subgroup of the additive group \mathbb^n which is isomorphic to the additive group \mathbbZ^n, and which spans the real vector space \mathbb^n.
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Lattice Boltzmann methods
Lattice Boltzmann methods (LBM) (or thermal Lattice Boltzmann methods (TLBM)) is a class of computational fluid dynamics (CFD) methods for fluid simulation.
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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List of finite element software packages
This is a list of software packages that implement the finite element method for solving partial differential equations.
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Loubignac iteration
In applied mathematics, Loubignac iteration is an iterative method in finite element methods.
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Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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LU decomposition
In numerical analysis and linear algebra, LU decomposition (where "LU" stands for "lower–upper", and also called LU factorization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix.
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Magnetism
Magnetism is a class of physical phenomena that are mediated by magnetic fields.
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Mass matrix
In analytical mechanics, the mass matrix is a symmetric matrix M that expresses the connection between the time derivative \dot q of the generalized coordinate vector q of a system and the kinetic energy T of that system, by the equation where \dot q^\mathrm denotes the transpose of the vector \dot q. This equation is analogous to the formula for the kinetic energy of a particle with mass m and velocity v, namely and can be derived from it, by expressing the position of each particle of the system in terms of q. In general, the mass matrix M depends on the state q, and therefore varies with time.
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Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
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MATLAB
MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.
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Mean value theorem
In mathematics, the mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
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Mesh generation
Mesh generation is the practice of generating a polygonal or polyhedral mesh that approximates a geometric domain.
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Movable cellular automaton
The Movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept.
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Multidisciplinary design optimization
Multi-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines.
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Multiphysics
Multiphysics is a computational discipline which treats simulations that involve multiple physical models or multiple simultaneous physical phenomena.
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Nastran
NASTRAN is a finite element analysis (FEA) program that was originally developed for NASA in the late 1960s under United States government funding for the aerospace industry.
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Navier–Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Numerical linear algebra
Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.
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Numerical weather prediction
Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions.
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Olgierd Zienkiewicz
Olgierd Cecil Zienkiewicz, CBE, FREng, FRS (18 May 1921 – 2 January 2009) was a British academic of Polish descent, mathematician, and civil engineer.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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P-FEM
p-FEM or the p-version of the finite element method is a numerical method for solving partial differential equations.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Partition of unity
In mathematics, a partition of unity of a topological space X is a set R of continuous functions from X to the unit interval such that for every point, x\in X,.
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Patch test (finite elements)
The patch test in the finite element method is a simple indicator of the quality of a finite element, developed by Bruce Irons.
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Philippe G. Ciarlet
Philippe G. Ciarlet (born 14 October 1938, Paris) is a French mathematician, known particularly for his work on mathematical analysis of the finite element method especially applied to elasticity.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Pierre and Marie Curie University
UPMC, formerly Pierre and Marie Curie University (Université Pierre-et-Marie-Curie) or also known as Paris VI, was a public research university in Paris, France from 1971 to 2017.
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Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics.
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Polygon
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
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Polygon mesh
A polygon mesh is a collection of, s and s that defines the shape of a polyhedral object in 3D computer graphics and solid modeling.
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Polygon triangulation
In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, Chapter 3: Polygon Triangulation: pp.45–61.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Ray William Clough
Ray William Clough, (July 23, 1920 – October 8, 2016), was Byron L. and Elvira E. Nishkian Professor of structural engineering in the department of civil engineering at the University of California, Berkeley and one of the founders of the finite element method (FEM).
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Rayleigh–Ritz method
The Rayleigh-Ritz method is a method of finding approximations to eigenvalue equations that cannot be solved easily (or at all) analytically.
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Richard Courant
Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician.
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Riesz representation theorem
There are several well-known theorems in functional analysis known as the Riesz representation theorem.
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Runge–Kutta methods
In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations.
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SESAM (FEM)
Sesam is a software suite for structural and hydrodynamic analysis of ships and offshore structures.
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Sobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function itself and its derivatives up to a given order.
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Software
Computer software, or simply software, is a generic term that refers to a collection of data or computer instructions that tell the computer how to work, in contrast to the physical hardware from which the system is built, that actually performs the work.
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Space mapping
The space mapping methodology for modeling and design optimization of engineering systems was first discovered by John Bandler in 1993.
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Sparse matrix
In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero.
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Spectral element method
In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high degree piecewise polynomials as basis functions.
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Spectral method
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the Fast Fourier Transform.
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Steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time.
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Stiffness matrix
In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation.
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Structural analysis
Structural analysis is the determination of the effects of loads on physical structures and their components.
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Superconvergence
In numerical analysis, a superconvergent or supraconvergent method is one which converges faster than generally expected (superconvergence or supraconvergence).
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Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.
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Swansea University
Swansea University (Prifysgol Abertawe) is a public research university located in Swansea, Wales, United Kingdom.
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Torsion (mechanics)
In the field of solid mechanics, torsion is the twisting of an object due to an applied torque.
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Transformation matrix
In linear algebra, linear transformations can be represented by matrices.
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Transient state
A system is said to be in a transient state when a process variable or variables have been changed and the system has not yet reached a steady state.The time taken for the circuit to change from one steady state to another steady state is called the transient time. Transient analysis KVL and KCL to circuits containing energy storage elements results in differential.
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Triangular function
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle.
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Tropical cyclone
A tropical cyclone is a rapidly rotating storm system characterized by a low-pressure center, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain.
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University of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public research university in Berkeley, California.
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University of Stuttgart
The University of Stuttgart (Universität Stuttgart) is a university located in Stuttgart, Germany.
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Walther Ritz
Walther Ritz (22 February 1878 – 7 July 1909) was a Swiss theoretical physicist.
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Weak formulation
Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations.
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Weakened weak form
Weakened weak form (or W2 form) is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings.
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Weight function
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.
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References
[1] https://en.wikipedia.org/wiki/Finite_element_method
