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Project
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
Finite_element_machine
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Mathematical model of computation
computer science, a finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical
Finite-state_machine
Finite element exterior calculus (FEEC) is a mathematical framework that formulates finite element methods using chain complexes. Its main application
Finite element exterior calculus
Finite_element_exterior_calculus
Finite-state machine
deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state
Deterministic finite automaton
Deterministic_finite_automaton
In numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be
Interval_finite_element
Machine whose output is determined by its state and inputs
In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs
Mealy_machine
Finite-state machine whose output values are determined only by its current state
Moore machine is a finite-state machine whose current output values are determined only by its current state. This is in contrast to a Mealy machine, whose
Moore_machine
Topics referred to by the same term
investigate molecular surface structures Finite element machine, a parallel computer project by NASA Finite element method, a numerical technique for partial
FEM
American computer scientist
successfully develop one of NASA's first parallel computers, the finite element machine, & developed rapid matrix equation algorithms tailored for high-performance
Olaf_Storaasli
A virtual finite-state machine (VFSM) is a finite-state machine (FSM) defined in a virtual environment. The VFSM concept provides a software specification
Virtual_finite-state_machine
Computation model defining an abstract machine
algorithm. The machine operates on an infinite memory tape divided into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols
Turing_machine
Numerical method used in structural mechanics
The finite element method (FEM) is a powerful technique originally developed for the numerical solution of complex problems in structural mechanics, and
Finite element method in structural mechanics
Finite_element_method_in_structural_mechanics
Virtual recreation of a destructive car crash
of analysis called the Finite Element Method. The complex problems are solved by dividing a surface into a large but still finite number of elements and
Crash_simulation
In computer science, a communicating finite-state machine is a finite-state machine labeled with "receive" and "send" operations over some alphabet of
Communicating finite-state machine
Communicating_finite-state_machine
Theoretical object in mathematics
the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could
Field_with_one_element
in business. 1979 – September: Hurricane David occurred. 1982 – Finite element machine was invented at NASA Langley Research Center (approximate date)
Timeline_of_Hampton,_Virginia
Any one of the distinct objects that make up a set in set theory
In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing
Element_of_a_set
Finite element analysis software
NASTRAN is a finite element analysis (FEA) program that was originally developed for NASA in the late 1960s under United States government funding for
Nastran
Nonlinear finite element analysis software
Archived 2015-01-19 at the Wayback Machine "Marc | Hexagon". Hexagon AB. Retrieved 2025-03-06. Nonlinear Finite Element Analysis of Elastomers Archived 2015-01-19
MSC_Marc
Family of computer-aided design apps
feature solid modeling, 3D direct modeling, 2D orthographic views, Finite Element Analysis and simulation, schematic design, technical illustrations,
PTC_Creo
computer security, machine learning Michael Stonebraker – relational database practice and theory Olaf Storaasli – finite element machine, linear algebra
List_of_computer_scientists
Analysis and solving of problems that involve fluid flows
Computational magnetohydrodynamics Discrete element method Fictitious domain method Finite element method Finite volume method for unsteady flow Fluid animation
Computational_fluid_dynamics
Axiom of set theory
II-finite, III-finite, IV-finite, V-finite, VI-finite and VII-finite. I-finiteness is the same as normal finiteness. IV-finiteness is the same as Dedekind-finiteness
Axiom_of_choice
Quantum analog of probabilistic automata
In quantum computing, quantum finite automata (QFA) or quantum state machines are a quantum analog of probabilistic automata or a Markov decision process
Quantum_finite_automaton
Finite collection of distinct objects
-maximal element. III-finite. The power set ℘ ( S ) {\displaystyle \wp (S)} is Dedekind finite. IV-finite. S {\displaystyle S} is Dedekind finite. V-finite. |
Finite_set
Strand7 is a Finite Element Analysis (FEA) software product developed by the company with the same name. The Strand computer software was first developed
STRAND7
Study of abstract machines and automata
finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine,
Automata_theory
German engineer
mechanics. Bathe is considered to be one of the pioneers in the field of finite element analysis and its applications. He was born in Berlin as a second child
Klaus-Jürgen_Bathe
Type of differential equation
generalized finite element method (GFEM), extended finite element method (XFEM), spectral finite element method (SFEM), meshfree finite element method, discontinuous
Partial_differential_equation
Branch of physics
inversion to calculate the weights of basis functions (when modeled by finite element methods); matrix products (when using transfer matrix methods); calculating
Computational electromagnetics
Computational_electromagnetics
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either
Classification of finite simple groups
Classification_of_finite_simple_groups
Ability to solve a problem by an effective procedure
is to compute, given an element u in U, the corresponding element f(u) in V. For example, U and V may be the set of all finite binary strings, and f may
Computability
Set of elements in any of some sets
else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C. A finite union is the union of a finite number of sets; the
Union_(set_theory)
Automaton which either accepts or rejects infinite inputs
non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata
Büchi_automaton
Use of software for engineering design and analysis
to engineering analysis. Computer-aided engineering (CAE) includes finite element method or analysis (FEA), computational fluid dynamics (CFD), multibody
Computer-aided_engineering
Collection of mathematical objects
because the former has one element (namely, ∅ {\displaystyle \emptyset } ) and the latter has no elements at all. A set is finite if there exists a natural
Set_(mathematics)
Major events in the history of the Commonwealth of Virginia
Catholic elected to a statewide office in Virginia history. 1982 Finite element machine is invented at NASA Langley Research Center (approximate date).
Timeline_of_Virginia_history
nonstationary partial differential equations (PDEs) based on hp-FEM (adaptive finite element method of higher order of accuracy). Both parts of the code are written
Agros2D
One-to-one correspondence
function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Given
Bijection
Computer-aided design approach
a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. Currently
Isogeometric_analysis
Branch of logic
interpretations (semantics). Finite model theory is a restriction of model theory to interpretations on finite structures, which have a finite universe. Since many
Finite_model_theory
Sequence of characters, data type
\Sigma ^{*}} itself is countably infinite, each element of Σ ∗ {\displaystyle \Sigma ^{*}} is a string of finite length. A set of strings over Σ {\displaystyle
String_(computer_science)
Open source software for computational fluid dynamics
TELEMAC is short for the open TELEMAC-MASCARET system, or a suite of finite element computer program owned by the Laboratoire National d'Hydraulique et
TELEMAC
Finite or infinite ordered list of elements
that is infinite in one direction, and finite in the other; such a sequence has a first element, but no final element, and are called singly infinite sequence
Sequence
FEBio(Finite Elements for Biomechanics) is a software package for finite element analysis and was specifically designed for applications in biomechanics
FEBio
Mathematical set that can be enumerated
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently
Countable_set
notable for our purposes are: finite difference methods, finite volume methods, finite element methods, and spectral methods. Finite difference replace the infinitesimal
Numerical methods in fluid mechanics
Numerical_methods_in_fluid_mechanics
Canonical Richard Stallman, founder of GNU Olaf Storaasli, NASA Finite element machine Bjarne Stroustrup, founder of C++ Ken Thompson, Unix and Plan 9
List_of_computing_people
Generalization of finite element method
hp-FEM is a generalization of the finite element method (FEM) for solving partial differential equations numerically based on piecewise-polynomial approximations
Hp-FEM
Algebraic structure with an associative operation and an identity element
Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for process
Monoid
Size of a possibly infinite set
(bijection) between the elements of the two sets. The cardinality of a finite set can be identified with a natural number, which can be found simply by
Cardinal_number
Finite element method solver for electromagnetic structures
FEM Element is a commercial finite element method solver for electromagnetic structures from EEsof. FEM Element can perform electromagnetic simulation
FEM_Element
Set whose elements all belong to another set
} suppose that a is a particular but arbitrarily chosen element of A show that a is an element of B. The validity of this technique can be seen as a consequence
Subset
Numerical simulation on electromagnets
Ansys HFSS (high-frequency structure simulator) is a commercial finite element method solver for electromagnetic (EM) structures from Ansys. Engineers
Ansys_HFSS
Function that preserves distinctness
{\displaystyle f} is a function with finite domain it is sufficient to look through the list of images of each domain element and check that no image occurs
Injective_function
Engineering analysis program
Femap (Finite Element Modeling And Postprocessing) is an engineering analysis program sold by Siemens Digital Industries Software that is used to build
Femap
Mathematical set containing no elements
modelled by the empty set. When speaking of the sum of the elements of a finite set, one is inevitably led to the convention that the sum of the elements
Empty_set
Type of automaton
about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below). Deterministic
Pushdown_automaton
Set that is not a finite set
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence
Infinite_set
Packaging machine that forms cartons
score, etc. Some board factors can be simulated; others might need a finite element analysis or an experimental process capability study. Folding carton
Cartoning_machine
CAD software package for electric motors and generators
permanent magnet dc machines, switched reluctance motors, synchronous machines and claw pole machines. An integrated ultra fast finite element module (EMag)
Motor-CAD
Group whose operation is composition of permutations
permutation of each of its elements. A general property of finite groups implies that a finite nonempty subset of a symmetric group is a permutation group
Permutation_group
Method in mathematical logic
} of all finite linear orderings, for which the Fraïssé limit is a dense linear order without endpoints (i.e. no smallest nor largest element). By Cantor's
Fraïssé_limit
Computer-aided design software
thermal, using the finite element method; and fluid, using the finite volume method). Manufacturing finished design by using included machining modules. NX is
Siemens_NX
Mathematical function that can be computed by a program
include every element of B. Because each finitary relation on the natural numbers can be identified with a corresponding set of finite sequences of natural
Computable_function
Concept in geometry
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the
Coxeter_element
Mathematical proposition equivalent to the axiom of choice
{\displaystyle C} has the finite intersection property; so, the union is in P {\displaystyle P} . Thus, by Zorn's lemma, there is a maximal element M {\displaystyle
Zorn's_lemma
Mathematical term in group theory
Grigorchuk group is a finitely generated group constructed by Rostislav Grigorchuk that provided the first example of a finitely generated group of intermediate
Grigorchuk_group
Engineering discipline
September 2018. "Accelerated Finite Element Analysis". FiniteNow. 29 July 2025. Retrieved 6 August 2025. "Accelerating Finite‑Element Structural Elastic Dynamic
Mechanical_engineering
Theorem in mathematical logic
states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory
Compactness_theorem
Analog of the continuous Laplace operator
Approximations of the Laplacian, obtained by the finite-difference method or by the finite-element method, can also be called discrete Laplacians. For
Discrete_Laplace_operator
with one element Empty semigroup Andreas Distler, Classification and enumeration of finite semigroups Archived 2015-04-02 at the Wayback Machine, PhD thesis
Semigroup_with_three_elements
Ordered listing of items in collection
enumeration: All (non empty) finite sets are enumerable. Let S be a finite set with n > 0 elements and let K = {1,2,...,n}. Select any element s in S and assign
Enumeration
Mathematical set of all subsets of a set
S is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}. If S is a finite set with the cardinality |S| = n (i.e., the number of all elements in the
Power_set
Mathematical group based upon a finite number of elements
In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical
Finite_group
Finite-state machine where edges carry weights
weighted finite-state machine is a generalization of a finite-state machine in which the edges have weights, for example real numbers or integers. Finite-state
Weighted_automaton
Finite-element mesh generator
Gmsh is a finite-element mesh generator developed by Christophe Geuzaine and Jean-François Remacle. Released under the GNU General Public License, Gmsh
Gmsh
Study of discrete mathematical structures
can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deal with finite sets, particularly
Discrete_mathematics
Method of exchanging cryptographic keys
protocol: Alice and Bob agree on a natural number n and a generating element g in the finite cyclic group G of order n. (This is usually done long before the
Diffie–Hellman_key_exchange
Remembered information in a computer system
access. Since each binary memory element, such as a flip-flop, has only two possible states, one or zero, and there is a finite number of memory elements, a
State_(computer_science)
Z88 is a software package for the finite element method (FEM) and topology optimization. A team led by Frank Rieg at the University of Bayreuth started
Z88_FEM_software
Sequence of operations for a task
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve
Algorithm
Impossible task in computing
whether a given first-order sentence is a logical consequence of a given finite set of sentences, but validity in first-order theories with infinitely many
Entscheidungsproblem
Sequence of words formed by specific rules
expression; those strings accepted by some automaton, such as a Turing machine or finite-state automaton; those strings for which some decision procedure (an
Formal_language
Template that specifies one or more axioms
is an instance of the schema. Axiom schemata are commonly used to give finite descriptions of theories whose axioms include infinitely many formulas.
Axiom_schema
OOFEM is a free and open-source multi-physics finite element code with object oriented architecture. The aim of this project is to provide efficient and
OOFEM
Mathematical function such that every output has at least one input
tuː/) is a function f such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x)
Surjective_function
Set-theoretic concept
is an element of U {\displaystyle U} and if y {\displaystyle y} is an element of x {\displaystyle x} , then y {\displaystyle y} is also an element of U
Grothendieck_universe
Algebraic structure
generates T. A single element x of S generates the subsemigroup { xn | n ∈ Z+ }. If this is finite, then x is said to be of finite order, otherwise it is
Semigroup
Finite field of two elements
Field with one element GF is the initialism of Galois field, another name for finite fields. Lidl, Rudolf; Niederreiter, Harald (1997). Finite fields. Encyclopedia
GF(2)
Area of mathematical logic
Sn(T) is finite. For every natural number n, the number of formulas φ(x1, ..., xn) in n free variables, up to equivalence modulo T, is finite. The theory
Model_theory
consistent with the constraints See also: Interval boundary element method, Interval finite element Loss of significance Numerical error Numerical stability
List of numerical analysis topics
List_of_numerical_analysis_topics
British academic of Polish descent, mathematician and civil engineer
born in Caterham, England. He was one of the early pioneers of the finite element method. Since his first paper in 1947 dealing with numerical approximation
Olgierd_Zienkiewicz
Every set is smaller than its power set
has a strictly greater cardinality than A {\displaystyle A} itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the
Cantor's_theorem
Czech-American mathematician (1926–2023)
finite element method and the proof of the Babuška–Lax–Milgram theorem in partial differential equations. One of the celebrated results in the finite
Ivo_Babuška
American technology company
cycle. Ansys Mechanical finite element analysis software uses computer models to simulate structures, electronics, or machine components to evaluate the
Ansys
mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states
Semiautomaton
Infinitely many tasks in finite time
countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations
Supertask
Structure dual to a unital associative algebra
those functions from S to K that map all but finitely many elements of S to zero; identify the element s of S with the function that maps s to 1 and
Coalgebra
FINITE ELEMENT-MACHINE
FINITE ELEMENT-MACHINE
Male
Italian
 Italian, Portuguese and Spanish form of Latin Clementius, CLEMENTE means "gentle and merciful."
Boy/Male
African, American, Australian, British, Chinese, Christian, Danish, English, French, German, Greek, Indian, Jamaican, Latin, Swedish, Swiss
Merciful; Mild; Gentle; Giving Mercy; Merciful in French
Male
English
Variant spelling of English Finnian, FINIAN means "little white one."
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
English American Danish
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Surname or Lastname
English
English : patronymic from the personal name Clement. As an American family name, this form has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Boy/Male
English American Biblical Latin
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Girl/Female
Indian
Infinite, Divine
Surname or Lastname
English, French, and Dutch
English, French, and Dutch : from the Latin personal name Clemens meaning ‘merciful’ (genitive Clementis). This achieved popularity firstly through having been borne by an early saint who was a disciple of St. Paul, and later because it was selected as a symbolic name by a number of early popes. There has also been some confusion with the personal name Clemence (Latin Clementia, meaning ‘mercy’, an abstract noun derived from the adjective; in part a masculine name from Latin Clementius, a later derivative of Clemens). As an American family name, Clement has absorbed cognates in other continental European languages. (For forms, see Hanks and Hodges 1988.)
Boy/Male
English
Gentle. Famous Bearer: Clement Moore, writer of 'Twas the Night Before Christmas'.
Boy/Male
Czechoslovakian, Danish, German, Greek, Latin, Polish
Giving Mercy; Mild; Merciful
Male
Portuguese
Portuguese form of Latin Philippus, FILIPE means "lover of horses."
Male
English
English surname transferred to forename use, derived from Latin Clemens or Clement, CLEMENTS means "gentle and merciful."
Male
Polish
 Danish, German, Polish and Swedish form of Greek Klementos, KLEMENS means "gentle and merciful."
Male
English
Short form of Latin Clementius, CLEMENT means "gentle and merciful." meaning "gentle and merciful." In the bible, this is the name of a companion of Paul.
Boy/Male
Australian, British, Danish, Dutch, English, Finnish, French, German, Irish, Latin, Swedish
Gentle; Merciful; Mild; Form of Clement
Male
Russian
(Климент) Russian form of Greek Klementos, KLIMENT means "gentle and merciful."
Surname or Lastname
English
English : patronymic from the personal name Clement.German, Dutch, and Danish : from the personal name Clemens (see Clement).Samuel Langhorne Clemens, better known by his pen name, Mark Twain, was descended from VA stock on his father’s side, from a Robert Clemens, who was born in Warwickshire, England, in 1634.
Male
Slovene
Slovene form of Greek Klementos, KLEMEN means "gentle and merciful."
Male
Hungarian
Hungarian form of Greek Klementos, KELEMEN means "gentle and merciful."
FINITE ELEMENT-MACHINE
FINITE ELEMENT-MACHINE
Girl/Female
Muslim/Islamic
Knowledge
Boy/Male
Tamil
Jagat Prakash | ஜகதபà¯à®°à®•ாஷ
Light of the world
Boy/Male
American, Australian, British, English, French, German, Swiss
Will Helmet; Resolute Protector; Will; Son of William
Girl/Female
Irish
From Ireland.
Girl/Female
Muslim/Islamic
Frail Delicate
Girl/Female
Arabic, Muslim
Heaven
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Devote Flower to God; Flower Offering
Girl/Female
Gujarati, Hindu, Indian
Full Moon; God
Girl/Female
American, Australian, British, Christian, Danish, Dutch, English, French, German, Latin, Swedish
Full of Life; Alive; Lively; Variant of Vivien; The Lady of the Lake in Malory's Mort Darthur; Life
Boy/Male
Hindu
Stars
FINITE ELEMENT-MACHINE
FINITE ELEMENT-MACHINE
FINITE ELEMENT-MACHINE
FINITE ELEMENT-MACHINE
FINITE ELEMENT-MACHINE
n.
One of the ultimate parts which are variously combined in anything; as, letters are the elements of written language; hence, also, a simple portion of that which is complex, as a shaft, lever, wheel, or any simple part in a machine; one of the essential ingredients of any mixture; a constituent part; as, quartz, feldspar, and mica are the elements of granite.
n.
See Yenite.
a.
Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; as, the infinite wisdom and goodness of God; -- opposed to finite.
a.
Having a limit; limited in quantity, degree, or capacity; bounded; -- opposed to infinite; as, finite number; finite existence; a finite being; a finite mind; finite duration.
v. t.
To constitute; to make up with elements.
n.
An infinitesimal part of anything of the same nature as the entire magnitude considered; as, in a solid an element may be the infinitesimal portion between any two planes that are separated an indefinitely small distance. In the calculus, element is sometimes used as synonymous with differential.
n.
One out of several parts combined in a system of aggregation, when each is of the nature of the whole; as, a single cell is an element of the honeycomb.
n.
See Conite.
n.
To unite or cause to adhere by means of a cement.
n.
One of the necessary data or values upon which a system of calculations depends, or general conclusions are based; as, the elements of a planet's orbit.
a.
Acting with great force; furious; violent; impetuous; forcible; mighty; as, vehement wind; a vehement torrent; a vehement fire or heat.
v. t.
To compound of elements or first principles.
n.
The four elements were, air, earth, water, and fire
n.
Any outline or sketch, regarded as containing the fundamental ideas or features of the thing in question; as, the elements of a plan.
n.
The simplest or fundamental principles of any system in philosophy, science, or art; rudiments; as, the elements of geometry, or of music.
adv.
In a finite manner or degree.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
n.
The elements of the alchemists were salt, sulphur, and mercury.
n.
Sometimes a curve, or surface, or volume is considered as described by a moving point, or curve, or surface, the latter being at any instant called an element of the former.
a.
Constituting one of eleven parts into which a thing is divided; as, the eleventh part of a thing.