Questions tagged [finite-element]

A means of solving ordinary and partial differential equations. The domain of the problem is broken up into elements, and the solution in each element is expanded in a basis of functions. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error estimates.

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34 views

Is there a commercial program to compile a Finite Element Fortran program (1980)?

The fortran used come from Montreal Ecole polytechical in 1980 I need some thing that can read fortran and compile it in a Windows 7 or windows 8 operating system.
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57 views

Technique to find the CFL condition using the Galerkin method in space and finite-difference in time?

I am using the Galerkin method (Discontinuous to be precise) to discretize in space the scalar linear wave equation and the explicit second order centered finite difference scheme to discretize in ...
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Help in agglomerating a mesh with Metis?

I have got a mesh of triangles (for a finite element code) that I'd like to partition into polygons, much better if convex. I tried metis and it is very complicated but powerful if one knows about ...
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104 views

Solving PDEs in parallel

I have read different approaches on how to solve pdes in parallel which are discretized using finite element method. For example: Non-overlapping domain decomposition approach as mentioned in https://...
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36 views

Finite element analysis software for acoustic and electrostatic

I need to do a simulation for my thesis project involving some piezoelectric nanoparticles in a fluid beamed with ultrasounds. I'm looking for a software for such simulation and for now it seems me ...
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56 views

How to compute gradient of each node in finite element method?

I have a problem with computing gradient of each node in finite element method. I can get the value of each node. But how can I get the gradient? I know $u = \sum u_i \phi_i$ where $\phi_i$ are the ...
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58 views

Finite Element Analysis based on contractions of a subset of edges in enterior of mesh

I am modelling a problem that is "driven", not by typical boundary conditions but, by contractions in its interior. In a finite element analysis, I can specify the new lengths (not ...
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58 views

Transition from 2D to 3D finite element code, what are the inevitable modifications to be implemented?

Imagine we have a simple 2D FEM solver (we are dealing with solid mechanics) and we would like to develop it to a 3D FEM solver (let's say for the same solid mechanics problem) in this case what are ...
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67 views

Finite elements convergence issue with 2D elliptic equation

I deal with a system of coupled 2D Helmholtz-like equations solved via the P1 FEM on a given geometry. Let's consider, for instance, the following simplified coupled problem: for $i\in[-I,I]$ we have $...
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87 views

Problem with solving coupled ODE and DAE equations with mass matrix (Error using daeic12 (line 77) This DAE appears to be of index greater than 1)

I am trying to solve 6 ODE equations coupled with 1 DAE one. The ODE equations have been discritized in space domain and ode15s MATLAB solver is used to solve the equations in time domain. I have ...
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Electric Current Module in Comsol

I am trying to solve for the potential in the electric current module in Comsol. I have a wire with 2 current boundary conditions where the in equals the out. The model can be solved in stationary but ...
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161 views

Gauss-Lobatto quadrature and nodal points for FEM

By using the Legendre-Gauss-Lobatto (LGL) quadrature formula (QF) and LGL nodal points one achives a diagonal mass-matrix for finite element problems. (More specifically, the spectral element method.) ...
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187 views

FEM Python book

Is there any book or site available with Finite element Method for partial differential equations with python code apart from Fenics?
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inclined/general Dirichlet boundary conditions

For simpilcity, consider a single quad linear elasticity finite element in 2D. The Dirichlet boundary conditions on node 1 and node 2 are easy to implement and can be handled in the standard way. ...
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Learning the art/science of structural idealization

I am a mechanical engineer working in the field of aerospace structures. During the course of my studies, I have studied a course on structural analysis in which I learned 3D Euler-Bernoulli beam ...
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87 views

Which 2D PDE with an exact solution can I use to test/verify my FEM-PDE code?

I have created a program to solve 2D, time-dependent PDEs with the finite element method and get reasonable looking results for the 2D acoustic wave equation. Now I would like to go further and solve ...
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How can I improve the accuracy of the calculation of the magnetic field in Gmsh/GetDP?

I need to calculate the magnetic field along a straight line in proximity of an array of 6 magnets. I used the tutorial files "magnets" included in Gmsh and I slightly modified the file in ...
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Mesh transition between beam and shell element types

I am using NASTRAN solver & FEMAP as preprocessor for reduce modelling of wing using 1D and 2D finite elements. Beside transition of 1D & 2D elements to 3D, I had not found any method/solution ...
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60 views

How to compute the $L^{2}$ error of the gradient in the Finite Element Method

Let $\Omega\subset \mathbb{R}^{2}$ and $\tau_{h} = \{\Omega_{k}\}_{k=1}^{N}$ be a triangulation of $\Omega$. The $L^2$ error for a FEM approximation $u_{h}$ is given by: $ || u-u_{h} ||_{L^2} = \sqrt{ ...
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trilinear hex elements

Do the faces of tri-linear hex elements have to be planar? Three nodes define a plane. If the fourth node does not lie on the plane, then the nodes are not planar and the face is not plane. In general,...
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103 views

Create a sparse matrix

I am writing a FE program which calculates the displacements under a uniform load. I want to store the stiffness matrix in sparse form(COO) without using an external library.Assume an upper-bound for ...
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66 views

Construction of Prolongation and Restriction Operator for Geometric Multigrid (2D-FEM): Resulting in a Decreasing Solution

Consider the following problem, $$ -\Delta u(x) = f(x), \qquad x \in \Omega \\ u(x) = 0,\qquad x \in \partial \Omega$$ with $\Omega = [0,1]\times [0,1]$ being the domain and $\partial \Omega$ being ...
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Abaqus approach to simulate many flexible elements

I would premise that i am not an expert on the domain (i am a programmer that usally work with DB and data, not structural problem), but i have just see the work of a friend of mine and i am curious ...
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1answer
39 views

Symmetry in P1 basis elements on a reference triangle in 2D-FEM

I am trying to understand the finite element method and want to apply it to a 2D equation with a triangular mesh. I have chosen the reference element to be the triangle with vertices $(0, 0), (0, 1)\...
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How can the choice of coarsening factor affect Multigrid's convergence?

The linear system $Ax=b$ is coming from the discretization of an elliptic PDE. Multigrid method is used in order to solve it. Suppose $c_0$ is the coarsening factor on level 0 and $c_m$ the coarsening ...
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107 views

how to Implement linear tetrahedral elements for finite element computations?

I am trying to implement 3D tetrahedral elements in my finite element code (which works fine for linear triangles and quadrangles in 2D). But my simulations are crashing with tetrahedral elements. My ...
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164 views

Heat equation in non-dimensional form behaving differently than in usual format

Starting from $$ c_p \frac{\partial u }{\partial t} = k \nabla^2 u $$ in a one dimensional domain [0,1] where $c_p$ and $k$ are modeling two different materials: $$ k = \begin{cases} 1 ~\text{if} ~x &...
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Parallel In Time with Multigrid

I am trying to solve the linear finite element equation $M\ddot{u}+Ku=F(t)$, where $M$ is the mass matrix ,$K$ the stiffness matrix and $F(t)$ the external load vector, parallel in time using XBraid ...
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62 views

Solution predictors for accelerating convergence in nonlinear FEM

I am looking for the details of commonly-used predictors for accelerating the convergence of iterations using Newton-Raphson scheme for nonlinear problems in FEM. I am looking specifically for static ...
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55 views

How to use FEniCS to calculate the electric field of an isolated charged sphere

Initially I thought that this is the kind of question which ought to have already been answered in the form of an example online, but so far I haven't found one. I will admit that I am very new to ...
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79 views

Numerical integration in time for finite elements

I am trying to solve $M\ddot{u}=-Ku+F_\text{ext}$ for a 2D linear elastic model with $M$ be the mass matrix,$K$ the stiffness matrix and $F_\text{ext}$ the external load vector coming from a uniformly ...
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63 views

Convergence of Conjugate Gradient Algorithm

I am trying to solve a linear elasticity model using finite element discretization in a rectangle domain [0,1]x[0,1]. For the solution of the the linear system $Ku=F$ I am using the CG algorithm. ...
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101 views

How to apply Dirichlet boundary conditions to time-dependent PDEs?

Assume the time-dependent linear elasticity equation. Using a finite element discretization we obtain $$M\ddot{u}=Ku+F_\text{ext}$$ where $M$ is the mass matrix,$K$ is the stiffness matrix, and $F_\...
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65 views

Ill-conditioned stiffness matrix

I am writting a Fem code in c++ for a 2d plane stress model. My question is regarding the assembly stiffness matrix.I noticed that some elements of the matrix are not exactly zero but insted a number ...
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Finite elements algorith for a fluid in a tube with an elastic obstacle (Fluid-Solid coupling)

I want to solve the model of a tube with an elastic obstacle, something like a simple model of an vessel with a valve. The fluid is given by an evolutionary incompressible Navier--Stokes equations, ...
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152 views

Finite element (1D) for steady state non-linear problem

I need to solve with linear finite elements the equation $$\frac{\partial }{\partial x}\Bigl(\text{sgn}(x) u \Big) +\frac{\partial}{\partial x} \Bigl[ \sqrt{u} \frac{\partial u}{\partial x} \Bigr] =0$...
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41 views

FEM solution becoming wider as number of nodes increase

My FEM scheme uses a 4-node quadrilateral element with bilinear shape functions. The simple problem I'm solving is. $\nabla ^2 f = 5$ But as I increase the number of nodes, the plot of the solution ...
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154 views

FEM does not match exact solution

I am trying to solve : $$-u''(x) + u(x) = \sin(2\pi x)\, ,\quad 0<x<1\, ,$$ $t>0$, with $u(0) = u(1) = 0$. That has as exact solution $$u(x) = \frac{\sin(2\pi x)}{1 + 4\pi^2}\, .$$ But the ...
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115 views

Non-Linear advection diffusion with nondifferetiable advection term

I'm looking at Murray's book: Mathematical biology: an introduction , first volume, pag. 404 In particular, I'm interested to solve the following PDE: $$\partial_t u = \partial_x (\text{sign}(x) u) + \...
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Split of complex parts in weak form

I am working on a numerical model to simulate the acoustic and elastic wave propagation in frequency domain via the Finite Element Method. Basically, the problem is to solve the Helmholtz equation in ...
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160 views

1D FEM for nonlinear diffusion coefficient

I want to solve with linear finite elements the equation $$\partial_t u = \partial_{x}(a(u)\partial_xu)$$ in the domain $t \in [0,1]$ and $x \in [-L,L]$. Here $a(u)$ is just a function of $u$. ...
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Hi I am trying to model a 2D Lug angle using Gmsh 4.6. How can I combine transfinite quad and regular full quad meshes in the following geo file?

I need transfinite mesh a small section of the bolt hole to insert a crack. However, The transfinite mesh and regular full quad mesh seem being incompatible and throwing errors. How can I combine ...
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1answer
62 views

Imposing pressure variation instead of Dirichlet boundary conditions on Finite Element Method

I always see Finite Element codes solving PDE with Dirichlet or Neumann boundary conditions. But, I have a problem now consisting of a straight cylinder with a circular base (a simple 3D tube), with ...
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125 views

Global stiffness matrix from element stiffness matrices for a thin rectangular plate (Kirchhoff plate)

I have the element stiffness matrix for a thin "kirchhoff" plate. The plate is 3 [m] x 5 [m] and is simply supported on all edges. It's thickness is 0,2 [m]. On the plate there acts a ...
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228 views

FEM shape functions on triangular elements: transition from 2D to 3D

I'm writing a code for solving PDEs through the finite element method. In particular, I'm facing with 3D problems, in which I don't know how to calculate shape functions derivatives on the boundaries (...
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1answer
113 views

Weak formulation for advection diffusion reaction

I need a check on the following exercise about weak formulations and finite elements. Consider the advection diffusion system $$ \begin{cases} -(\mu u')' + \beta u' + \gamma u = f \\ u(a)=0 \\ u(b) = ...
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65 views

How to calculate the interior value of triangular element in edge (vector) finite element?

I was using an edge (vector) finite element to solve electromagnetic diffusion (two-dimensional cases). The element that I used was a triangular element. I have got the result of the finite element in ...
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336 views

Finite-difference software for solving custom equations

Are there any good, easy to use, software for simulating the evolution of systems of generic differential equations? I know there are custom programs for various specific circumstances (such as ...
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108 views

Parallelisation strategies for mixed FE formulations

Mixed FE formulations with LBB-stable elements require two different meshes for the primary and the constraint variables, for example, displacement and pressure. With continuous approximation for the ...
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1answer
64 views

Going From Blender Structure defined by triangles to full 3D mesh (Using GMSH?)

I currently have created a model airplane in Blender by drawing a closed volume with triangular planes. I want to do a FEM calculation on this object, meaning I need a fine 3D tetrahedral mesh of this ...

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