Finite Definition and 1000 Threads

The finite element method (FEM) is a widely used method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points.
The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain.
The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
Studying or analyzing a phenomenon with FEM is often referred to as finite element analysis (FEA).

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  1. R

    Poisson equation with finite difference method

    Hi guys , i am solving this equation by Finite difference method. (dt2/dx2 + dt2/dy2 )= -Q(x,y) i have developed a program on this to calculate the maximum temperature, when i change the mesh size the maximum temperature is also changing, Should the maximum temperature change with mesh...
  2. F

    Are there complex functions with finite, nonzero branch points?

    I just completed a brief introduction to branch points in complex analysis, and I find it difficult to imagine/come up with functions with nonzero branch points. My difficulty is this: for the point to be considered a branch point, f(r,θ) and f(r,θ+2π) must be different for ANY closed path...
  3. 1

    Finite group of even order has elements of order 2

    [The homework format does not appear on mobile] Problem: Show that a finite group of even order has elements of order 2 Attempt: The book gives a suggested approach that lead me to write the most round about, ugly proof I've ever written. Can't I just say: 1.) If G has even order, G/{1} has...
  4. T

    MATLAB Model a circle using finite difference equation in matlab

    hello. I have a MATLAB skeleton provided because i want to model a distribution with a circular geometry. all in all, i want the 3d graph of the code to be some type of cylinder. This is the code: % flat step condition for ii=1:nHi, for jj=1:nHj, if (X(ii)/R_P)<1 &...
  5. M

    Finite Difference method to solve diffusion equation

    Homework Statement Plot the transient conduction of a material with k = 210 w/m K, Cp = 350 J/kg K, ρ = 6530 kg/m3 Where the material is a cylinder, with constant cross sectional area and is well insulated. The boundary conditions for the cylinder: T(0,t) = 330K T(l,t) = 299K...
  6. A

    Finite state machine (summarizing)

    Hello, I have an FSM which has 1 serial input and 4 outputs. The FSM must react to the table attaced in file. I can see that if the input is(for example)4 the output is 7(+3). I have to draw a state diagram(mealy). I can't solve it. Need some help Thanks
  7. E

    How can I calculate the force between finite coil and metal plate?

    Hi, I would like to calculate the force between a finite coil and a nearby metal plate. A pulsed current is supposed to flow into the magnetic coil, which will generate a magnetic field near the coil. Due to this magnetic field, an Eddy current will be produced in a nearby metal plate and...
  8. J

    Conjugate Subgroups of a Finite Group

    Homework Statement Two subgroups of G, H and K are conjugate if an element a in G exists such that aHa^-1= {aha^-1|elements h in H}= K Prove that if G is finite, then the number of subgroups conjugate to H equals |G|/|A|. Homework Equations A={elements a in G|aHa^-1=H} The Attempt...
  9. J

    Finite Differences-Semi discretization method on Heat Equation

    Hi!, I'm working on a personal project: Solve the heat equation with the semi discretization method, using my own Mathematica's code, (W. Mathematica 9). The code: I'm having problems with the variable M (the number of steps). It works with M=1-5, but no further, I do not know what's going...
  10. N

    Number of ways to select M cohyperplanar points in finite space

    (I don't like the title, since it is a bit misleading. But, I couldn't think of a more descriptive title that fit in the length restrictions.) A recurring theme in a problem I am exploring is counting the number of subsets of size n in Z^{d}_{3} that have at least m mutually cohyperplanar...
  11. J

    Proving o(An) = o(a) for Finite Abelian Groups | G, N, a | Group Theory Homework

    Homework Statement Let G be a finite group with N , normal subgroup of G, and a, an element in G. Prove that if (a) intersect N = (e), then o(An) = o(a). Homework Equations The Attempt at a Solution (aN)^(o(a)) = a^(o(a)) * N = eN = N, but is the least power such that (aN)^m = N...
  12. Math Amateur

    MHB Finite Fields - F_4 - Galois Field of Order 2^2

    I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Section 6.5: Finite Fields, I need help with a statement of Beachy & Blair in Example 6.5.2 on page 298. Example 6.5.2 reads as follows:https://www.physicsforums.com/attachments/2858In the above...
  13. Math Amateur

    MHB Existence of Finite Fields with p^n Elements

    I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Theorem 6.5.7. I need help with the proof of the Theorem. Theorem 6.5.7 and its proof read as follows:In the above proof, Beachy and Blair write: By Lemma 6.5.4, the set of all roots of f(x) is a...
  14. Math Amateur

    MHB Why Are the Roots of xf(x) and xg(x) Distinct in Finite Fields?

    I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Proposition 6.5.5. I need help with the proof of the proposition. Proposition 6.5.5 and its proof read as follows: In the proof of Proposition 6.5.5 Beachy and Blair write: " ... ... Since F is the...
  15. Math Amateur

    MHB Finite Fields and Splitting Fields

    I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Theorem 6.5.2. I need help with the proof of the Theorem. Theorem 6.5.2 and its proof read as follows:In the conclusion of the proof, Beachy and Blair write the following: " ... ... Hence, since F...
  16. M

    Infinite universe but finite beginning?

    As far as i understand the current big bang theory, it started as a extremely dense object, finite in size. But we still think (or well it is very accepted to belive) that the universe is infinite. I know inflation should be though as an expansion everywhere at the same time rather than the ball...
  17. Greg Bernhardt

    Definition of Finite Field: Addition and Multiplication Groups

    Definition/Summary All finite fields are known; they are the Galois fields GF(p^n), where p is a prime. They have addition group Z(p)^n and multiplication group Z(p^n-1); their multiplication groups are cyclic. If p = 2, then addition and multiplication can be done very fast by typical...
  18. P

    How to Calculate the Magnetic Field at the Origin for a Finite Solenoid?

    Homework Statement A cylindrical shell of radius a and length 2L is aligned around the z-axis from z= -L ot z = +L. A current I is distributed uniformly on the cylinder and moves around the cylinder's z-axis. Find the magnitude of the magnetic field at the origin. Homework Equations...
  19. Math Amateur

    MHB Nature and character of Finite Fields of small order

    i am studying finite fields and trying to get an idea of the nature of finite fields. In order to achieve this understanding I am bring to determine the elements and the addition and multiplication tables of some finite fields of small order. For a start I am trying to determine the elements...
  20. U

    Infinite Square well with a Finite square well inside

    Ok here's a potential I invented and am trying to solve: V = -Vo in -b<x<b and 0 in -a<x<-b , b<x<a where b<a and ∞ everywhere elseI solved it twice and I got the same nonsensical transcendental equation for the allowed energies: \frac{-k}{\sqrt{z_0 - k^2}} \frac{e^{2kb} +...
  21. B

    Finite Square Well: Deriving Eq. (1)

    Hello everyone, I am reading about the Finite Square Well in Griffiths Quantum Mechanics Text. Right now, I am reading about the case in which the particle can be in bound states, implying that it has an energy E < 0. After some derivations, the author comes across the equation \tan z =...
  22. S

    What is the best book to start learning Finite Element Analysis?

    Hi guys, :smile: I am a mechanical engineer, and want to learn finite element analysis. I want to know what is the best book to start with. Assume I have no prior knowledge of the subject. :redface: Thanks, Sety.
  23. C

    MHB Is the Axiom of Choice Necessary to Well-Order Finite Sets?

    Hi, I want to show that there exists a well ordering for every finite set. (I know if you add axiom of choice you can prove this theorem for infinite sets too but I think the finite sets do not need axiom of choice to become well ordered)
  24. adoion

    Why does light have a finite speed?

    hy, there is nothing in Maxwells equations that would limit the speed of light. the only way one can get light speed, is to assume that em waves solve Maxwells equations and then one gets c as the square root of something out from Maxwells equations. the same goes for gravity waves, only...
  25. B

    Transition probabilities subject to Lloyd's finite information limit?

    This is a question about The Computational Capacity of the Universe by Seth Lloyd. It seems to me that arbitrary real numbers cannot be part of the state of the universe, since they carry an infinite amount of information. There are transition probabilities from the current state of the...
  26. A

    Couldn't the universe be finite if Omega =1?

    I am not a physicist or a cosmologist, just a science layman who has been doing a lot of reading and thinking. I have been reading a lot in popular literature that if Omega =1, then the universe must also be infinite. Do you think this is just an over-generalization intended for the general...
  27. F

    Difference of a function and a finite sum

    Hi everybody, I am looking for some help with a problem that has been nagging me for some time now. I'm going to give you the gist of it, but I can provide more details if needed. So, after some calculations I am left with a function of the following form $$ F_L(y) = f(y) -S_L(y)...
  28. DreamWeaver

    MHB Finite Binomial Sum: Proving 1 + 1/2 + 1/3 + ... + 1/n

    Show that \sum_{j=1}^{j=n}\binom{n}{j} \frac{(-1)^{j+1}}{j} = 1 +\frac{1}{2} +\frac{1}{3} + \cdots +\frac{1}{n}
  29. twistor

    Non-anthropic String Theory Landscape and Finite Universes

    What are you thoughts about Laura Mersini Haughton´s theory of the multiverse? She predicted a CMB cold spot, power suppression at low multipoles, preferred direction associated with the quadrupole octupole alignment, dark flow, and the deviation of the CMB amplitude. While dark flow remains...
  30. O

    MHB How can I find the kernel of a homomorphism of finite groups?

    i was given that Z8 to Z4 is given by f= 0 1 2 3 4 5 6 7 0 1 2 3 0 1 2 3 where f is homomorphism. how can i find the kernal K
  31. O

    MHB Understanding Finite Quotient Groups: G/H with G=Z6 and H=(0,3)

    G is a group and H is a normal subgroup of G. where G=Z6 and H=(0,3) i was told to list the elements of G/H I had: H= H+0={0,3} H+1={14} H+2={2,5} now they are saying H+3 is the same as H+0, how so?
  32. B

    Magnetic Field of a Finite Solenoid

    Homework Statement Find the magnetic field generated at the center of a coil of wire with N turns, a radius of r, and a current I running through it Relevant equations B=μ0nI, where n=N/L (L is the total length of the coil) The attempt at a solution B=μ0nI B=μ0I(N/L) L=2πrN B=(μ0NI)/(2πrN)...
  33. G

    Finite state machine (Digital) Sequence

    Hello, here is the problem that I have: Can you please tell me how to determine what is the sequence of the output. I can see it misses 101 and 010 and it repeats 000 and 100. I think both 101 and 010 are initial states. The answer I have for repeated sequence is 011, 111, 110, 100...
  34. F

    Does If f be a Measurable Function Imply Finite ∫|f|dm?

    If f be a measurable function. Assume that lim λm({x|f(x)>λ}) exists and is finite as λ tends to infinite Does this imply that ∫|f|dm is finite? Here m is the Lebesgue measure in R If not can anyone give me an example??
  35. V

    Supose that G is a finite abelian group that does not contain a subgro

    let us assume G is not cyclic. Let a be an element of G of maximal order. Since G is not cyclic we have <a>≠G. Let b be an element in G, but not in the cyclic subgroup generated by a. O(a) = m and O(b) = n where O() refers tothe orders. . then how can we use this to construct a subgroup of G...
  36. E

    If p is a covering map with B compact and fiber of b finite, E compact

    Homework Statement Let p: E \rightarrow B be a covering map. If B is compact andp^{-1}(b) is finite for each b in B, then E compact. Note: This is a problem from Munkres pg 341, question 6b in section 54. The Attempt at a Solution I begin with a cover of E denote it \{U_\alpha\}. I...
  37. R

    MHB Absolute stability of finite difference scheme

    The Finite difference scheme: \begin{equation} y_{n+3}-y_{n+1}= \frac {h}{3}(f_{n}-2f_{n+1}+7f_{n+2}) \end{equation} Deduce that the scheme is convergent and find its interval of absolute stability(if any) => the first characteristic polynomial is then \begin{equation} ρ(r)= r^3 -r...
  38. PsychonautQQ

    Finite well penetration depths dependence on Well Length

    So in the infinite well Energy is proportional to 1/L^2, so I'm assuming in the finite well there is some sort of similar relation. So as the L decreases, the energy increases, so the wavelength decreases. Decreasing the wavelength means more energy, so it should penetrate further, but also if...
  39. nomadreid

    Why not a flat but finite spatial universe?

    In the Wiki article on the FLRW metric, http://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric it says "the universe is nearly an isotropic and homogeneous FLRW spacetime". OK, so spacetime is globally flat, which implies that space is too. This...
  40. C

    Prove the diameter of a union of sets is finite

    Homework Statement Prove that the union of a collection of indexed sets has finite diameter if the intersection of the collection is non-empty, and every set in the collection is bounded by a constant A. The Attempt at a Solution The picture I have is if they all intersect (and assuming...
  41. F

    Finite element method and applied element method

    What are the advantages and disadvantages of both AEM and FEM and which on is easier. I am doing a project and I should use one of these two methods to solve for a truss system. P.S. computer programming shall be used. In the end which method is better for this case?
  42. M

    Measure defined on Borel sets that it is finite on compact sets

    The problem statement Let ##\mu## be a measure defined on the Borel sets of ##\mathbb R^n## such that ##\mu## is finite on the compact sets. Let ##\mathcal H## be the class of Borel sets ##E## such that: a)##\mu(E)=inf\{\mu(G), E \subset G\}##, where ##G## is open...
  43. hilbert2

    Eq. of motion of elastic 2D finite element

    A simple question about elasticity theory/finite element method: Suppose I have a tetragonal 2D piece of a linear isotropic elastic material, that has Young's modulus ##E## and Poisson's ratio ##\nu##. The vertices of the tetragon are at positions ##\textbf{x}_{1}##, ##\textbf{x}_{2}##...
  44. U

    Transcendental equation from a finite square well potential

    if I have a transcendental equation such as this one: tan(l a) = -l / sqrt (64/a^2 - l^2 ) Where l=sqrt(2m(E+V) /hbar^2 ) and 'a' is the width of a finite square well, how can I solve this equation in terms of both l and a. I have successfully graphed the two sides of the equation...
  45. J

    Proving the Inclusion of Elements of Finite Commutative p-Groups in A(p)

    Homework Statement Let A = A(p)\times A' where A(p) is a finite commutative p-group (i.e the group has order p^a for p prime and a>0) and A' is a finite commutative group whose order is not divisible by p. Prove that all elements of A of orders p^k, k\geq0 belong to A(p) The Attempt...
  46. M

    Finite Difference Solution to Poisson's Equation on Irregular Domain

    Hi, Are there any open source C or Fortran libraries for solving 3D Poisson'sequation on an irrefular domain? I'm having difficulty finding them. If not, is there any papers or recipes that would be useful so I could write my own? Speed is not a priority, I just need anything that works...
  47. W

    Electric Field of a Finite Cylinder

    Homework Statement Derive expressions for electric field produced along the axis of radial symmetry for an H km thick cylindrical slab of radius R with charge distributed around the volume. Then, give the electric field on the vertical axis for four of these cylindrical slabs.Homework Equations...
  48. gfd43tg

    Carnot Engine with finite reservoirs

    Homework Statement A Carnot engine operates between two finite heat reservoirs of total heat capacity CtH and CtC. a) Develop an expression relating TH to TC at any time. b) Determine an expression for the work obtained as a function of CtH ,CtC , TH and initial temperatures TH0 and TC0...
  49. M

    Why do infinitesimal rotations commute but finite rotations do not?

    In K&K's Intro to Mechanics, they kick off the topic of rotation by trying to turn rotations into vector quantities in analogy with position vectors. It's quickly shown, however, that rotations do not commute, making them rather poor vectors. They then show, however, that infinitesimal rotations...
  50. A

    Evaluating a Finite Sum to a Closed Form Expression

    I have a finite sum of the form: ∑n=1Nexp(an+b√(n)) Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.
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