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.
875
questions
2
votes
2answers
89 views
Weak form of the Navier-Cauchy equation
I am trying to obtain the weak form of the Navier-Cauchy equation, which is
$$- \rho \omega ^2 \textbf{U} - \mu \nabla ^2 \textbf{U} - (\mu + \lambda) \nabla (\nabla \cdot \textbf{U}) = \textbf{F}$$
...
2
votes
0answers
32 views
FEM with elastic inhomogeneous properties leads to mesh-induced anisotropy
I'm solving an elastic homogenization problem and I'm having problems with mesh artifacts.
I would like to first give a brief summary of what I do: I have a system with inhomogeneous (but isotropic) ...
1
vote
1answer
80 views
$P0$ elements for $H1$
Are there $P0$ (zero degree/constant element) nonconforming methods for approximating solutions in $H1$? More specifically, I have the equation:
$$u-f - T\Delta u = 0$$
Which can be interpreted as ...
0
votes
2answers
156 views
Integration by parts with cross derivatives to obtain the weak form [duplicate]
I’m trying to write the weak form of the Navier-Cauchy equation in the component form, where $u_1$ and $u_2$ are the displacement components:
$$-(2 \mu +\lambda) \frac{\partial ^2 u_1}{\partial x_1 ^2}...
1
vote
0answers
33 views
Cell-centered DG extension to the two-point flux approximation scheme
A current problem that I am working on requires me to compute the solution from the heat diffusion evolution on a discontinuous function. More precisely - I have a Delaunay triangulation and within ...
3
votes
0answers
42 views
Some formulations of domain coupling lead to saddle point problems. Is this merely an artifact?
Background I wanted to learn how to couple FEM and BEM (for the Poisson equation), because I wanted to better understand how open boundary conditions look like. Therefore I worked through the relevant ...
1
vote
1answer
56 views
Simple reference problems for time harmonic Maxwell equations
For Navier-Stokes problems we can often choose a relatively simple verification problem such as the lid driven cavity, flow over a cylinder, or flow over a backward facing step to verify our ...
4
votes
3answers
81 views
I wrote a 2D Finite Element program for Axial Loaded Plates, but the results are unexpected
TLDR: I used Python to write a 2D Finite Element program using 'Constant Strain Triangles' and my beam keeps pointing slightly upwards instead of straight sideways (like the force). I'm new to FEA and ...
0
votes
0answers
18 views
At what l/d ratio will a frame element start to behave as a shell element?
I'm working in ETABS. There are few columns of dimension 300mmx1400mm. The height of building is 36.6 meter above ground level and the dimension of building is 26mx68m. I'm getting the time period of ...
3
votes
0answers
49 views
How to construct a Fortin Operator for Crouzeix-Raviart Element?
I want to prove the LBB condition for the Stokes Equations discretised by the Crouzeix-Raviart element.
The continuous Stokes Equation in the weak formulation is
Find $u \in H_0^1(\Omega, \mathbb{R}^...
3
votes
1answer
64 views
Why does smoothed aggregation multigrid method used as preconditioner in conjugate gradient slows down the solution time?
I'm solving a system of linear equations obtained from the FEM discretization of a simple linear elasticity problem on a cube with zero displacements at one plane and a load on the opposite one. The ...
2
votes
1answer
61 views
Fast way to build stiffness directly as CSC matrix
I have been working on finite element code in Fortran 2008, and have implemented my own sparse matrix types. I have found that mapping local stiffness matrices (real type) to a global COO sparse type ...
1
vote
1answer
76 views
Methodology Suggestion for Wave-propagation Problem using Finite Elements
I want to simulate the propagation of a sinusoidal plane wave in a rectangular domain using Finite Elements Method. First, the wave should propagate through a fluid medium, then it will encounter a ...
1
vote
2answers
61 views
Solution of symmeric/non-symmetric linear system
I would like to understand what happens in the following:
I have a really simple Poisson problem, in 1D, with $u_0 = u_N = 0$. I assembled the stiffness matrix and the right-hand side, and I applied ...
1
vote
1answer
93 views
Partial differential equation FEM application
I have a PDE which looks like Helmholtz wave equation on one dimensional domain.
$$\dfrac{d^2u(x)}{dx^2}+\pi^2u(x)=f(x)$$
where $-\infty <x<\infty $
Also, $f(x)= 1$ for $-0.25<x<0.25$, I ...
0
votes
0answers
18 views
COMSOL Circularl polarization
I'm having some problems trying to implement circularly polarized light in COMSOL Muliphysics.
For a isotropic homogenous media, I've obtained without problems the TE and TM reflectance curves. ...
0
votes
0answers
23 views
Determining the voxels between two boundary surfaces
I am working on human brain tACS simulations where I have the models of the skin, skull, csf, brain and ventricles in STL format. The shape does not matter and there are no intersections. I want to ...
2
votes
0answers
53 views
Solve 1D saturation equation using FEM
I want to solve the following 1D equation to model the time evolution of saturation in a porous medium using finite elements (I'm a beginner).
The permeability $K$ and the pressure $p$ depend on the ...
0
votes
0answers
18 views
Adding a boundary surface on a STL model in Gmsh
Background info
I want to run brain simulations with models from the PHM repository (not relevant to the problem but suits the narrative) which are shipped in STL format. The meshes of the STL have ...
1
vote
0answers
90 views
Stokes problem with imposed acceleration on boundaries (projection scheme)
I am trying to solve FSI problems with finite elements and using a projection scheme (I am taking as reference the review of Guermond:
Guermond, J. L.; Minev, P.; Shen, Jie, An overview of ...
0
votes
1answer
59 views
FDM on nonlinear PDEs
I'm working with a 2D Navier Stokes PDE in the unstabilized version - the equation is a linear equation of the type $\frac{∂u}{∂t} = F(u,t)$.
In order to perform time discretization with FDM (finite ...
1
vote
0answers
39 views
Add orthogonality constraint to PDE over entire domain finite element
I have a nonlinear differential equation for $u:\mathbb{R}^2\rightarrow\mathbb{R}^3$ that I can express in the form:
$ \nabla (g(u)_{ij} \nabla(u)^j) = 0 $
which is similar to the "Nonlinear Poisson" ...
1
vote
0answers
20 views
Finding isocontour lines, populating points on said lines (in MATLAB)
I'm trying to extract data from a potential field. I have an example code of a potential field, using meshgrid in MATLAB. I've pasted the code below.
What I'd like to do next is 'convert' this field ...
0
votes
0answers
38 views
Spurious eigenvalues in a finite element eigenvalue problem
This post is closely related to this one and uses the exact same setup: a mix of quadratic and cubic basis functions in a finite element approach, where variables $u_1$ and $u_2$ are quadratic and $...
2
votes
1answer
61 views
Mesh partition quality
I am working on static FE mesh partitioning and in order to achieve a good quality partitioning I want to know how to drecrease interprocessor communication by increasing the connectivity of elements ...
0
votes
0answers
63 views
Open Boundary Conditions for Solving Navier Stokes in moving ALE domain
I'm trying to solve the problem of a body freely rising in a fluid due to gravity, the density of the body is just slightly less than that of the fluid.
The body is rigid, so I have to solve a ...
2
votes
1answer
132 views
Boundary conditions in a finite element eigenvalue problem
I've been reading multiple papers and related posts for a while now, but I can't seem to find a specific answer to the issues I'm having so I hope someone can clarify things here.
I'll provide some ...
0
votes
0answers
61 views
Applying boundary Conditions on FEM
I have a partial differential equatons as shown below.
$$\dfrac{d}{dx}((1+x)\dfrac{du(x)}{dx})=0$$
With the following boundary conditions.
$$u(0)=0, u(3)=10$$
To solve it using FEM, I multiplied the ...
1
vote
1answer
71 views
Galerkin method for heat equation
I'm working out the Galerkin method for the heat equation $$\frac{\partial u}{\partial t} - \frac{\partial^2 u}{\partial x^2} = 0$$ subject to $u(0,t)=0,u_x(1,t)=v(t)$.
I want to use a Fourier basis ...
0
votes
1answer
28 views
Norm of operator in finite element discretization of Heat equation
I am solving the heat equation discretized spatially via FEM and temporally via backward Euler.
I get the system
$$M \dot{u} = K u +f$$ where $u$ is a vector representing the solution at spatial ...
3
votes
1answer
94 views
Difference between MoM and FEM
Method of Moments and Finite Element Methods are two of the most used methods in computational electromagnetics to solve electromagnetic equations.
As it is known, in FEM sparse matrixes are used ...
1
vote
1answer
38 views
Adaptive Lagrangian-Eulerian methods and practical benchmark results
Does anyone know of any published study that talks about the practical aspects of running Adaptive Lagrangian-Eulerian techniques for solid and/or fluid mechanics problems?
I'm looking for things ...
2
votes
0answers
36 views
Implementation of Z^2 error estimator in Abaqus for adaptive mesh refinement
Currently, I am working on a remeshing routine for my simulations (Abaqus 6.14-1) using python scripts. The simulation deals with the Brinell indentation test and as the remeshing software I use Gmsh ...
1
vote
2answers
79 views
Practical way to build element stiffness matrix for 3D FEM simulations
The element stiffness matrix in 3D FEM problems is build as follows:
$$ K = \int\limits_{[-1,1]^3} B^T C B\, |J| \mathrm{d}r\, \mathrm{d}s\, \mathrm{d}t$$
The integral can be solved using e.g. Gauss ...
1
vote
0answers
37 views
Lattice spring models vs. finite element models
I am a beginning graduate student in the field of continuum mechanics. It is my understanding that most problems in this field are numerically solved via finite element methods (FEM). However, I have ...
0
votes
1answer
58 views
Parallel mesh partitioning
When a mesh partitioning takes place and every process works on a part of the mesh is any way to rename the global numbering of nodes(on each process) into a local numbering?Is there any software that ...
0
votes
0answers
50 views
How to solve odd-order differential equations in FEM? Petrov-Galerkin?
I've recently learned about using weighted residuals with the Galerkin method to numerically approximate even-order differential equations (for linear elements, I'm still a beginner). It seems for odd-...
0
votes
1answer
93 views
Normalized legendre and quadrature basis for discontinous Galerkin method
I've successfully implemented a 1D DG code with non-normalized Legendre basis and I've now moved onto developing a 2D code using tensor products. For my 2D code I've chosen to have normalized ...
1
vote
1answer
57 views
How long should the hyperelastic equations be solved before updating the mesh?
How long should the hyperelastic equations be solved before updating the mesh? To be specific, I'm interested in the hyperelastic model with a neo-Hookean solid:
$$
\nabla\cdot\sigma + f = \rho\ddot{...
1
vote
0answers
68 views
Compute mass matrix in vibrations problem by using finite element method
I have to compute the mass matrix of a Hexahedral mesh.
There are 3 methods to compute mass matrix. I'm interested in one method which consists of dividing the mass of the element by the number of ...
0
votes
0answers
54 views
Stress during unloading in FEM simulation of an elasto-plastic truss element
I am simulating the behaviour of a single bar composed of two node points by fixing one point and applying a force on the oder node with $F_x = 1$ and fixing $u_y=0$. I am assuming the material to ...
1
vote
1answer
77 views
Full approximation scheme - smoothers - literature recomendation
I would like to use full approximation scheme(FAS) for solving nonlinear PDE. I am looking into practical implementation of FAS in parallel(MPI) settings. I noticed the most common/effective smoother ...
1
vote
1answer
68 views
FEM diffusion: inaccurate results small time steps
I wrote some FEM code and found some strange results when using a very small time step. So, I decided to analyze the discrete equations.
Consider the following linear diffusion problem in 1 dimension:...
0
votes
0answers
73 views
Solving a nonlinear problem with a very small components with finite element method
In solving nonlinear hyperelastic solid mechanics problems, to converge to the correct solution we need to do step-by-step loading which makes the deformation at each step very small (for my ...
1
vote
3answers
149 views
What numerical methods are used to model deformations in elastic physics?
What numerical methods are used to model deformations in elastic physics? For example, here's an example of a hyperelastic deformation in Ansys:
Perhaps more simply than hyperelasticity, for linear ...
5
votes
1answer
94 views
Non-conforming bi-linear finite element
The four-noded bi-linear rectangle element, which sometimes goes under the name Melosh element, is non-conforming unless the element sides are aligned.
Out of curiosity I have implemented this element ...
2
votes
1answer
70 views
Computation of equivalent thermal resistance and thermal capacitance from FE model
I need to compute the equivalent thermal resistance and thermal capacitance of a structure used for heat transfer. For illustration purpose let’s say it’s the 2D problem of the following figure. In ...
1
vote
3answers
193 views
Morley element implementation reference
I am looking for a detailed reference on the implementation of the Morley element for FEM, specifically for the biharmonic equation. By detailed, I mean that it should discuss the problems associated ...
2
votes
1answer
122 views
Gradient-jump penalty term in FEM
I am slightly confused regarding the meaning of the $i-th$ gradient-jump term $[\nabla \phi_i]$ in the context of finite element methods, used in the assembly of the stiffness matrix (an example with <...
1
vote
2answers
79 views
What are the alternatives for ABAQUS in generating an *.inp file from a CAD model
ABAQUS gives a .inp file (in pre-processing stage) where the information with regard to the preprocessed model is defined, information such as geometry, mesh type, number of elements, boundary ...
