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. N

    Finite difference method for even potential in QM

    Hello to everyone, while solving homework course Nanotechnology and Nanocomponents, I have encountered a problem in FD method that is applied in even potential. In my homework assignment it is explicitly said that it must be done only in x>0 part of the domain, where my problem starts with...
  2. K

    Finite Quantum Well: Wave Function when E>V{0}?

    Homework Statement If an electron is in a finite quantum well and it's E>V{0} what does the wave function look like? Homework Equations The Attempt at a Solution Wondering if anyone could help me out with this? I know that outside the well the electron will have the same...
  3. H

    Writing Finite Element Code for Structural Analysis

    Structural Analysis-Writing Finite Element Code, Dear all, I have written a code ( in fact it is a software) for 3D finite element structural analysis. While developing the code I found that assembling global stiffness matrix is quite complicated. The complication is even more when we...
  4. B

    Calculating magnetic field of finite solenoid

    Hey guys! New guy here so bear with me on my first post:) I'm trying to calculate the B field in the center of a finite solenoid for different outer radius sizes. I was able to find a formula online that gave the B field in the center of a solenoid given its length, inner radius, outer...
  5. C

    Can a positive integrand oscillate fast enough so that the integral is finite?

    Homework Statement If $$f(x)>0$$ is continuous for all $$x\ge0$$ and the improper integral $$\int_0^{\infty}f(x) dx$$ exists, then $$\lim_{x\rightarrow\infty}f(x)=0.$$ 2. Relevant I think this assertion is false. A counterexample can be constructed along the following lines of...
  6. I

    For separable extensions, why may we argue as if they're finite?

    I'm reading the following article by Maxwell Rosenlicht: http://www.jstor.org/stable/2318066 (The question should be clear without the article, but I present it here for reference.) In the beginning of the article he discusses differential fields (i.e. a field F with a map F\to F...
  7. B

    MHB Evaluate Finite Summation Expression

    How to evaluate the following expression? \sum_{i=0}^{N} \binom{N}{i} \left(-1\right)^{i}\left(\frac{1}{2+i}\right)^{k} regards, Bincy
  8. ShayanJ

    Field of a finite line of charge

    I tried to find the potential of a finite line of charge with length 2l and constant charge density \lambda .So I set up the coordinates somehow that the line is on the x-axis and the origin is at the center of the line.Then I did the following: \phi=\int_{-l}^l \frac{\lambda dx'}{4 \pi...
  9. A

    Is the universe finite or infinite?

    Does the universe has boundaries?, is it finite?
  10. M

    Yes or No? Injection into the Naturals finite?

    For any set S, the natural numbers N and function f, if f : S → N is injective but not surjective, is S finite?
  11. S

    Working with finite fields of form Z_p

    Homework Statement Let p be an odd prime. Then Char(Z_p) is nonzero. Prove: Not every element of Z_p is the square of some element in Z_p.Homework Equations The Attempt at a Solution I first did this, but i was informed by a peer that it was incorrect because I was treating the congruency as...
  12. B

    Conditional probability on a finite set

    T ≡ "two coins tossed 7 times by two people A and B giving outcomes [A^+B^+, A^-B^+, A^+B^-, A^-B^+, A^+B^+, A^-B^-, A^-B^+], where + = heads and - = tails" Calculate P(A^+B^+|T), P(A^+|T), P(B^+|T) and P(B^+|T,A^+) I asked this question elsewhere and there was a suggestion that the question...
  13. H

    Magnetic field by a finite section of wire?

    hey guys i have a question. i solved the problem but i don't understand how to do it. Two perpendicular straight wires join in the ends of a semicircular loop of radius a = 11 cm, as shown in the figure above. If the current I =6 A, what is the resultant field at the center of the circular...
  14. S

    Solve two eigenfunctins for a Finite Square Well

    Homework Statement Solve Explicitly the first two eigenfunctions ψ(x) for the finite square wave potential V=V0 for x<a/2 or x>a/2, and V=0 for -a/2<x<a/2, with 0<E<V0. Homework Equations See image The Attempt at a Solution See image. After modeling an in class example, my classmates and i...
  15. H

    Schrodinger's equation and the finite well(conceptual)

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  16. P

    Hausdorff Space and finite complement topology

    I want to come up with examples that finite complement topology of the reals R is not Hausdorff, because by definition, for each pair x1, x2 in R, x1 and x2 have some disjoint neighborhoods. My thinking is as follows: finite complement topology of the reals R is a set that contains open sets...
  17. Math Amateur

    Finite Reflection Groups in Two Dimensions - R2

    I am seeking to understand reflection groups and am reading Grove and Benson: Finite Reflection Groups On page 6 (see attachment - pages 5 -6 Grove and Benson) we find the following statement: "It is easy to verify (Exercise 2.1) that the vector x_1 = (cos \ \theta /2, sin \ \theta /2 )...
  18. H

    Dynamic analysis using finite element method- Help needed

    Dear all, I have written a code for dynamic analysis of a mechanical structure. My primary purpose is to find natural frequencies of the structure. When I test my code for a cantilever bar whose natural frequencies are known analytically, I found a big difference between the the first...
  19. G

    Question about calculating electric field made by finite point charges

    Homework Statement Hi! I have a question about calculating electric field made by finite point charges q_{1},q_{2},..., q_{n}. From the book "introduction to electrodynamics", you can see that the electric field E at a point P made by the finite point charges can be calculated by the below...
  20. M

    Show that the set is countable or finite.

    Hi, can someone please help me with this problem. Let A be an open subset of the interval [0; 1]. 1. Show that the set W = {C(x) : x is in A} is countable or finite. This is what I have... Suppose W is an infinite subset of N. Then we have f : W-> N, which is one-to-one. By the fact that...
  21. C

    Finite Dimensional Hausdorff Topological Space

    How do I prove that a Hausdorff topological space E is finite dimensional iff it admits a precompact neighborhood of zero?
  22. P

    How Deep Should a Finite Square Well Be for Two Electron Energy Levels?

    Homework Statement A finite square well 2.0fm wide contains one electron. How deep must the well be if there are only two allowed (bound) energy levels for the electron? Homework Equations (1) E = [ a^2 * hbar^2 ] / 2m (2) u = sqrt [2m(E+Vo)] / hbar The Attempt at a Solution Use...
  23. A

    What is the Limit of the Natural Logarithm of Infinity Minus One?

    \int^{\infty}_{1}\frac{1}{e^{t}-1}dt = -ln(e - 1) + 1 Not sure how to get the +1 part from infinity, seems like it should be infinity, i.e. ln(e^{\infty} -1) = ? Any help appreciated, thanks.
  24. H

    Stiffness matrix in finite element method

    Dear all, I have written a code for structural analysis using the finite element method. For some reason, I directly started with 3D elements ( hexahedron). I used to believe that the code was fine but recently i realized that the results ( deformation, natural frequency,..) strongly depend...
  25. S

    Prove all subsets of a finite set are finite

    Homework Statement Check the title Homework Equations Using the following definition of finite/infinite: A set X is infinite iff \exists f:X \rightarrow X that is injective but f(X) \not= X, i.e. f(X) \subset X. A set X is finite iff \forall f:X \stackrel{1-1}{\rightarrow} X it must follow...
  26. H

    Natural Frequency in Finite Element Method

    Hi all, A fixed-free bar has a single natural frequency. When we discretize such a bar in the finite element method, then the natural frequencies are the eigenvalues and an nχn matrix where n is the number of the degree of freedom which is usually large. Thus we obtain up to n natural...
  27. G

    Is the Universe Finite or Infinite in Space?

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  28. F

    Proof that e^z is not a finite polynomial

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  29. F

    What is finite elasticity talking about?

    Hi, dear all, recently study the solid mechanic continuity, keep reading about to solve large deformation of material, you will need so called "finite elasticity" What is this finite elasticity refer to ? "Finite elasticity is a theory of elastic materials capable of undergoing large...
  30. R

    Prob. for Difference of mean, single finite pop.

    Homework Statement Homework Equations The Attempt at a Solution
  31. H

    Dynamic Structural Analysis Using Finite Element Method

    Hi all, I need to do a dynamic structural analysis using finite element method and I have a question about the mass matrix. Question: I have the force per nodes and I need to calculate the displacement of each node at a given time. For this purpose, it seems that I need to distribute the...
  32. H

    Commutative finite ring and the Euler-Lagrange Theorem

    Homework Statement We are given the ring Z/1026Z with the ordinary addition and multiplication operations. We define G as the group of units of Z/1026Z. We are to show that g^{18}=1. Homework Equations The Euler-phi (totient) function, here denoted \varphi(n) The Attempt at a Solution...
  33. 6

    Finite and Countable union of countable sets

    Homework Statement Show the following sets are countable; i) A finite union of countable sets. ii) A countable union of countable sets. Homework Equations A set X, is countable if there exists a bijection f: X → Z The Attempt at a Solution Part i) Well I suppose you could start by considering...
  34. O

    How finite element analysis differs from mathematic derivation in beam bending?

    So I just started learning to use the finite element package abaqus for modelling beam tip deflection under different loading conditions. I think I understand the theory behind it but was wondering if some one could answer a few questions about it to further my understanding. Firstly, how do...
  35. Q

    Momentum space representation for finite lattices - continued

    I have been banned, maybe my nickname was not so kind. I let the topic continue here. I report my last comment: "Ok, I got the point. thanks for replying! It's just a change of basis that under boundary condition diagonalize the Hamiltonian. But then a subtle point: In order for...
  36. B

    Momentum space representation for finite lattices

    Hi all, I have a question. For sure the momentum representation used in solid state physics works for infinite lattices or periodic ones. But when it comes to finite lattice, i.e. 100 sites, can the momentum representation be used? What are the errors? Where does this fail? Thanks for...
  37. Math Amateur

    Representation Theory of Finite Groups - CH 18 Dummit and Foote

    I am reading Dummit and Foote on Representation Theory CH 18 I am struggling with the following text on page 843 - see attachment and need some help. The text I am referring to reads as follows - see attachment page 843 for details \phi ( g ) ( \alpha v + \beta w ) = g \cdot ( \alpha v +...
  38. F

    Infinite square well with finite potential energy inside

    Assume that you have a one dimension box with infinite energy outside, and zero energy from 0 to L. Then my understanding of the Schrodinger equation is that the equation inside will be: -h^2/2m*d2/dx2ψ = ihd/dtψ And the energy eigenstates are given by ψ(x,t) = e-iwt*sin(kx) where k = n*π/L...
  39. N

    Function bounded on [a,b] with finite discontinuities is Riemann integrable

    Homework Statement to prove that a function bounded on [a,b] with finite discontinuities is Riemann integrable on [a,b] Homework Equations if f is R-integrable on [a,b], then \forall \epsilon > 0 \exists a partition P of [a,b] such that U(P,f)-L(P,f)<\epsilon The Attempt at a...
  40. A

    MHB Proving Finite Domain Identity Element: Tips & Tricks

    How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?
  41. P

    Reversing a regular deterministic finite automata

    I have seen descriptions for an algorithm that can take a regular deterministic finite automata and create a non-deterministic finite automata that is guaranteed to generate the reverse of string accepted by the DFA. Does anyone know of a "formal" proof that shows this is true in all cases...
  42. W

    Span of a linearly independent subset of a hilbert space is a subspace iff finite

    Homework Statement Let S be a linearly independent subset of a Hilbert space. Prove that span(S) is a subspace, that is a linear manifold and a closed set, if and only if S is finite. Homework Equations The Attempt at a Solution Assuming S is finite means that S is a closed set...
  43. Math Amateur

    Linear Algebra Preliminaries in Finite Reflection Groups

    Linear Algebra Preliminaries in "Finite Reflection Groups In the Preliminaries to Grove and Benson "Finite Reflection Groups' On page 1 (see attachment) we find the following: "If \{ x_1 , x_2, ... x_n \} is a basis for V, let V_i be the subspace spanned by \{ x_1, ... , x_{i-1} ...
  44. Math Amateur

    Orthogonal Transformations _ Benson and Grove on Finite Reflection Groups

    I am reading Grove and Benson's book on Finite Reflection Groups and am struggling with some of the basic linear algebra. Some terminology from Grove and Benson: V is a real Euclidean vector space A transformation of V is understood to be a linear transformation The group...
  45. G

    Finite element analysis results interpretation

    Hello, I have been following this forum for some time now, but this is the first time I participate. I would appreciate if you could give me a hand in understanding the results of a finite element analysis of an automotive component we have designed. The analysis results indicate that the...
  46. J

    Finite abelian group into sequence of subgroups

    G finite abelian group WTS: There exist sequence of subgroups {e} = Hr c ... c H1 c G such that Hi/Hi+1 is cyclic of prime order for all i. My original thought was to create Hi+1 by reducing the power of one of the generators of Hi by a prime p. Then the order of Hi/Hi+1 would be p, but...
  47. T

    MATLAB Matlab program using implicit Finite Difference

    Hello, I need help writing a MATLAB program to solve a heat transfer problem implicitly. For some reason this is very confusing to me. The problem is stated below. Any help is greatly appriciated. Let me know if you need a little more info. I need to write a program to solve this...
  48. H

    Gaussian cylinder in the finite case

    Homework Statement Consider two long coaxial metal cylindrical tubes, with radii a and b and length L. (You may assume a,b<<L. Also a<b.) Suppose the inner cylinder is given a charge +Q and the outer cylinder a charge -Q. Using Gauss' Law, compute the electric field for all r between a and...
  49. S

    Finite square well potential question Constants

    I need to find B in terms of F in a finite square well potential I started with -Ae^(-i*K*a) - Be^(i*K*a) = Csin(k2*a) - Dcos(k2*a) and Ae^(-i*K*a) - Be^(i*K*a) = i*K*k2 [C*cos(k2*a) - D*sin(k2*a)] where C = [sin(k2*a) + i*(K/k2)cos(k2*a)]*Fe^(i*K*a) D = [cos(k2*a)-...
  50. A

    Finding the potential of a 1d finite square potential well

    Homework Statement The deuterium nucleus (a bound state of a proton and a neutron) has one bound state. The force acting between a proton and a neutron has a strong repulsive component of range 0.4 fm and an attractive component of range ~2.4 fm. The energy needed to separate the neutron from...
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