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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questions
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22 views
Homogeneous vs Inhomogeneous B.C. Clarification
I'm creating a FEM simulation based off of the Thermal Diffusion Equation: https://en.wikipedia.org/wiki/Heat_equation
I allow users to select and set the initial temperature of elements (cells) ...
0
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0answers
56 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
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1answer
50 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{...
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0answers
59 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
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0answers
52 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
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1answer
72 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
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1answer
67 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:...
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71 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 ...
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What are the inputs of the function addCurveLoops() in gmsh-API?
In gmsh-API i got the function addCurveLoops(), i understand what it does, but i do not understand the inputs, the documentation says:
Add a curve loop (a ...
1
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3answers
131 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
91 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 ...
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0answers
41 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 ...
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2answers
136 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
114 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
73 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 ...
6
votes
1answer
128 views
Why lattice Boltzmann despite its huge number of mesh points still has worse accuracy in comparison to FEM for calculating wall shear stress?
I'm just doing a very simple experiment. I'm calculating wall shear stress based on Poiseuille flow for a pipe by using lattice Boltzmann method (LBM) and FEM to compare their values with the ...
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0answers
42 views
Unsteady diffusion equation with spatial finite elements and Forward Euler in time
I have solved the unsteady diffusion equation using piece-wise linear Finite elements(triangles) for spatial discretisation and Forward Euler for temporal discretisation. I have the following mesh ...
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0answers
50 views
When does reduced integration lead to artificial zero energy modes in stiffness matrix?
This question relates to the topic of locking free finite element development.
In the case of application of reduced integration to global stiffness matrix for the Timoshenko beam element with ...
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0answers
24 views
Normalized Coordinate system, Hermitian Cubic Shape function
How can I convert a local shape function given in terms of normalized/natural coordinates to global shape function in terms of x and y coordinate system in Hermitian cubic shape function.
Please ...
1
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1answer
71 views
What is the relationship between shape functions, interpolation functions, and degrees of freedom?
I am a newbie in FEM. I would like to get clarity regarding a few questions on shape functions in this post (please use as simple language as possible).
What is the relation between Shape function ...
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1answer
53 views
Stability condition for explicit time FEM for parabolic pdes
If we discretize a parabolic pde to obtain the system of ODE's
$\frac{\boldsymbol{B}}{\Delta t} \boldsymbol{u}_k = (\boldsymbol{K} + \frac{\boldsymbol{B}}{\Delta t}) \boldsymbol{u}_{k-1} + \boldsymbol{...
2
votes
2answers
78 views
How to find out the difference between a structured and unstructured mesh using the file containing the mesh information?
I have two different mesh files (both are .inp files obtained from Abaqus) that represent the exact same geometries with the same boundary conditions, etc. The only difference is that one of them is ...
2
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0answers
59 views
Defining appropriate test function spaces for the finite element solution of Euler's fluid equations
I have the following coupled equations for the conservation of mass and momentum of a compressible fluid :
\begin{equation}
\rho_t + (\rho u)_z = 0,
\end{equation}
$$
(\rho u)_t + (\rho u^2)_z + \...
0
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1answer
50 views
Global to local transformation matrix in 2D frame structures
In section 3.2 of this paper [1], where 2D planar frame structures are being analyzed, the authors mentioned a transformation matrix to be used in extracting the element displacement vector from the ...
2
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0answers
64 views
Correct approach for thermal finite element simulation of layered assembly
I would like to optimise the heat transfer on a PCB. Several dies are on the top and cooling air is going through the fins in heat sink on the bottom. The assembly consists of several layers like ...
3
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0answers
53 views
Solving saddle point problem having non-invertible top-left block with a PETSc nested matrix
My system is a symmetric FE problem with lagrange multipliers:
$Z=\begin{pmatrix}A & C^T \\ C & 0\end{pmatrix}$
The matrix $A$ is positive semi-definite, non-invertible. The whole matrix is ...
4
votes
1answer
71 views
Why the solid FEM problem can not be solved after constraining 3 degrees of freedom?
I write a simple MATLAB code for solving solid FEM problem.
The problem looks like that
(1) (2)
x-------x
| / |
| / |
| / |
x-------x
(3) (4)
...
0
votes
0answers
60 views
Heat diffusion simulation in a 3D piston using FENICS
I'm trying to simulate the heat diffusion in a 3D piston. I marked the boundaries on GMSH.
I have used a Dirichlet BC of 300 on the top face of piston. But the results look abnormal. There is a ...
0
votes
2answers
180 views
What are the most important theorems in computational science? [closed]
I was reading the book: The Finite Element Method: Theory, Implementation, and Applications by Mats Larson and Fredrik Bengzon, in page 140 of this book they say this:
"The Lax-Milgram Lemma is one ...
0
votes
1answer
98 views
Singularity in gradient caused by Dirichlet boundary condition
I am looking for a mathematical explanation for the singularity caused by a Dirichlet boundary condition partially imposed at a boundary.
For instance
$$
\nabla^2u=0 ~ \text{in}~\Omega
$$
where $\...
4
votes
1answer
136 views
What is the difference between Methods of Weighted Residuals and Spectral Methods?
Methods of Weighted Residuals (MWR) [1] usually include Galerkin, collocation, method of moments, least-squares and subdomain methods.
Spectral methods [2] usually include Galerkin, tau and ...
2
votes
0answers
70 views
Nodal and Element Equilibrium in FEM Solution
I am learning FEM from KJ Bathe's textbook and it is mentioned that for a general FEM solution, nodal and element equilibrium is satisfied. The explanation takes steps that I don't understand.
At ...
0
votes
1answer
87 views
Solution of thermal analysis using finite element
I want to solve a thermal analysis using finite elements. The governing equation is $$C \frac{dT}{dt}+K T = Q$$.
When using backward differencing for time, the resulting equation is quite straight ...
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0answers
116 views
Immersed boundary method in FEniCS?
I have looked at the FEniCS tutorials and documentation but I cannot find any mention to the possibility of implementing an immersed boundary method (IBM) for fluid dynamics.
In particular, I want ...
2
votes
0answers
35 views
Necessary information that a toplogical optimisation solver needs to collecte from a pre-processed CAD model
I am developing a solver that gets a CAD model as entry and does the topological optimisation calculation on it. My solver is inspired by the open source codes presented in literature.
Since it is ...
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0answers
39 views
Fast algorithm for computing lower mode shapes and natural frequencies in MATLAB using sparse stiffness and mass matrices
I am looking for a fast algorithm for computing eigenvalues and eigenvectors from sparse stiffness and mass matrices in MATLAB. The eig(K, M) doesn't work with ...
0
votes
1answer
34 views
Produce vertex displacements from volumetric shrinkage data on unstructured meshes
I was wondering what would be an efficient way to produce compatible displacements for mesh nodes/vertices if the computed data is volume shrinkage of each element/cell in the unstructured mesh?
...
0
votes
1answer
156 views
Multi-domain 3D Geometries for MATLAB PDE Toolbox
In principle the PDE Toolbox in MATLAB can handle multi-domain 3D geometries as noted here.
This feature and the associated function geometryfromMesh were introduced in MATLAB R2018a. The associated ...
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votes
2answers
80 views
How to use natural logarithm inside Expression on FENICS
I'm trying to evaluate the exact solution of heat diffusion in circular plate.
I'm not able to use the natural logarithm inside expression.
...
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0answers
29 views
What kind of problem or matrices are suitable for multigrid method?
For Poisson or Convection-diffusion equation as follows:
$$
-\Delta u=f,\qquad u|_\Omega = g.
$$
or
$$
-\Delta u +\vec{w}.\nabla u=f,\qquad u|_\Omega = g.
$$
using FDM or FEM discretization, we can ...
6
votes
0answers
112 views
How to check if my stiffness matrix is correct
I built the stiffness matrix for the Poisson equation on a 2-dimensional domain with the shape of "almost" an octagon, using pyramid basis functions. I used almost to intend the fact that I have an "...
2
votes
1answer
83 views
Lumped matrices in thermal analysis using finite elements
The governing equation of the transient heat transfer problem is
$$C \frac{dT}{dt}+K T = Q$$
$C$ is the heat capacity matrix. $K$ is the thermal conductivity matrix. $T$ is the temperature vector. $...
1
vote
1answer
129 views
Efficient CRS vectors evaluation using elements connectivities
What is an efficient way of evaluating the column (col_ind) and the row (row_ptr) vectors for the CRS (Compressed Row Storage) storage format using the Connectivity Array? The Connectivity Array is a ...
2
votes
1answer
42 views
Four-noded rectangular element shape matrices
I works on a project where I need to compute a modal analysis of an acoustic cavity. The cavity is rigid which translates the problem to the following equation
$$\frac{\partial^2p}{\partial{}x^2}+\...
1
vote
1answer
27 views
Four-noded rectangular element shape functions
I works on a project where I need to compute a modal analysis of an acoustic cavity. The cavity is rigid which translates the problem to the following equation
$$\frac{\partial^2p}{\partial{}x^2}+\...
2
votes
1answer
75 views
Defining Current Density in a FEM model (MATLAB)
I'm attempting to solve the Poisson equation in 3D for a magnetic vector potential in the presence of a current source. To validate my code, I'm initially looking to reproduce the model described in ...
7
votes
1answer
90 views
Understanding the Eisenstat-Walker method for choosing the tolerance of a linear solver when solving a non-linear PDE
We are working on the solution of large non-linear PDE (say the Navier-Stokes equation) which we solve using Newton's method with an analytical formulation of the jacobian. For very large systems, we ...
3
votes
1answer
88 views
Calculating the jacobian of norm and square root terms in the Finite Element Method
In the code that my group is writing (Lethe) we use a stabilized approach to solve the Navier-Stokes equation. The GLS stabilized method we use has a stabilisation term which contains a stabilization ...
2
votes
0answers
68 views
What is appropriate boundary condition for Poisson pressure equation?
I'm doing CFD simulations in unstructured grids. Well, it's a bit different from conventional unstructured grids that are used mainly in FEM or FVM as tetrahedral meshes. Mine is a voxelized mesh of ...
0
votes
1answer
43 views
Can we use interpolation function of different order to represent different degrees of freedom in a FEM element?
Consider a line element in FEM. Let each node have 3 DOF. They are x and y translation DOF and temperature. Can we use interpolation functions of different orders for the translation DOFs and ...
