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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1answer
41 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 ...
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2answers
346 views

Which SciPy nonlinear solver when Jacobian is analytically known and sparse?

I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ...
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1answer
2k views

Does the global stiffness matrix size depend on the number of joints or the number of elements?

When assembling all the stiffness matrices for each element together, is the final matrix size equal to the number of joints or elements?
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51 views

Zero error at nodes using FEM? [closed]

Reading the discussion at this link I got confused. I am solving, using Finite Element method, a simple Poisson problem, $$ -u''= f(x)\, ,$$ on a simple unit square domain where I have chosen ...
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1answer
104 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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2answers
60 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 ...
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47 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
41 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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1answer
65 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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9answers
36k views

Basic explanation of shape function

I just started studying FEM in a more structured basis compared to what I used to do during my undergraduate courses. I am doing this because, despite the fact that I can use the "FEM" in commercial (...
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1answer
49 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{...
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22 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 ...
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Lithium Ion Battery Model in Comsol

I'm new to Finite Element Analysis and am creating a Comsol model to get the temperature of a battery as it is cooled by cold plates with fluid flowing through them. I have broken the model into 3 ...
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2answers
76 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 ...
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1answer
95 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 $\...
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0answers
56 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 + \...
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2answers
372 views

Spectral Element vs Finite Element

I am trying to understand the difference between SEM and FEM. If I go by this paper, spectral element methods are a subset of FEM methods and the only difference lies in the choice of basis functions. ...
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1answer
130 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 ...
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1answer
5k views

Calculate Jacobian of triangular element given coordinates of vertices and displacements?

I am trying to determine quality of my mesh elements using the Jacobian determinant as the measure. My algorithm takes vertices of nodes in triangular mesh and moves them around so as to form ...
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0answers
62 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 ...
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1answer
129 views

seminorm of solutions of Laplace equation

If $u_1$ and $u_2$ are solutions of (weak-form) Laplace equation on a connected domain $\Omega$, with Dirichlet boundary values $u_{\partial\Omega, 1}$ and $u_{\partial\Omega, 2}$, respectively. If $$...
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0answers
49 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 ...
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1answer
403 views

What is the difference between Abaqus and Calculix contact input?

I would like to say first that am new at using Calculix. I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...
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1answer
70 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) ...
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2answers
179 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 ...
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1answer
95 views

(FEM) 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 ...
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48 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 ...
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1answer
129 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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1answer
70 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 ...
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1answer
180 views

Lower bound for bilinear form in FEM

I'm searching for lower bounds of bilinear forms arising in FEM for elliptic second order PDEs with mixed boundaries. I did some research and found: $$\max_{v_{h}\in\mathcal{V}_h(\mathcal{\Omega})}a(...
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2answers
336 views

Imposing total pressure over surface in FEM

I am trying to solve Stokes problem using Finite element method. My question is how to impose that total pressure over the surface is zero to remove the constant pressure mode?
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68 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 ...
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2answers
1k views

implementing higher order derivatives for finite element

I am implementing higher order derivatives for FEM. Example, to solve a Poisson problem, biharmonic or triharmonic PDE one needs first, second or third order derivatives respectively. As usually ...
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1answer
365 views

DG local equation, how to interpret mean-averaged test function

In the paper http://www.sciencedirect.com/science/article/pii/S0045782509003521, an HDG element-local equation is described on page 584 equation (4), with one of the equations taking the following ...
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55 views

References to solve system of differential equations which describe the evolution of sandpile surface using the finite element method

I want to solve the following nonlinear system in 1D \begin{cases} \dot{R} + v \frac{\partial R }{\partial x} - \frac{\partial }{\partial x}\left( D \frac{\partial R }{\partial x} \right) -\Gamma =...
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1answer
86 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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2answers
292 views

Boundary conditions for streamlines in enclosed flow

I am trying to solve Lid driven square cavity flow problem of Stokes equation using finite element method. I have boundary conditions for velocity as zeros on every boundary but u=1 on top boundary. ...
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1answer
191 views

Finite Element - Flux Calculation

I am solving an advection-diffusion equation using the FEM and am having trouble calculating my fluxes. I start with the equation, $$\frac{\partial n}{\partial t} = \frac{\partial j_{n}}{\partial x}\...
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1answer
545 views

Time discretization of the variational formulation of the Navier-Stokes equation

I've asked this question on mathoverflow too. Let $T>0$ $I:=(0,T]$ $d\in\mathbb N$ $\Lambda\subseteq\mathbb R^d$ be nonempty and open, $$\mathcal V:=\left\{\phi\in C_c^\infty(\Lambda,\mathbb R^d):...
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1answer
202 views

Proving solution existence and uniqueness of the Helmholtz equation with Robin boundary conditions with complex coefficients

I am trying to solve the Helmholtz equation with Robin boundary conditions with complex coefficients and the weak formulation $$ \iint_\limits\Omega\nabla p_0(x,y)\nabla\left(\overline{v(x,y)}\right)...
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0answers
96 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 ...
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3answers
621 views

Create mesh for complicated 3D object for finite element analysis

I see images of steel connections, concrete dams, and other complicated 3D objects in papers which finite element analysis has been performed on them. My questions are: How these objects are created ...
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2answers
67 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
34 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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1answer
516 views

Finite Element Analysis for Laminated Plates with Holes or Patches

As the title says, I am trying to code in FEM a plate structure that either has a hole in one of the layers or one of the layers is made of patches of plates, rather than one whole plate. However, ...
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1answer
33 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? ...
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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 ...
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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 ...
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1answer
77 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. $...
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0answers
102 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 "...

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