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.
819
questions
2
votes
0answers
44 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
votes
0answers
45 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
62 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
44 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
168 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
61 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
97 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
59 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
82 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 ...
1
vote
0answers
76 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
33 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 ...
0
votes
0answers
38 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
32 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
99 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 ...
-1
votes
2answers
60 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.
...
1
vote
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
99 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
73 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
88 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 ...
2
votes
1answer
39 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
$$\frac{\partial^2p}{\partial{}x^2}+\...
1
vote
1answer
26 views
Four-noded rectangular element shape functions
I works on a project where I need to compute a modal analysis of an acoustic cavity. The cavity is rigid which translates the problem to the following equation
$$\frac{\partial^2p}{\partial{}x^2}+\...
2
votes
1answer
67 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
88 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
84 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
64 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
41 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 ...
0
votes
0answers
16 views
Efficient Alternatives to Operator Splitting in NLSE
Lately i've been trying to decide my thesis theme and i've become interested in adaptive finite elements and finite volumes algorithms. However, I need my thesis to fit into a physics related theme. ...
2
votes
0answers
85 views
Extracting FEM matrices in matlab pde toolbox
I am trying to follow the dynamic linear elasticity in Matlab, link here. My goal is to extract the FE Matrices using the function assembleFEMatrices in matlab and solve the resulting system of second-...
1
vote
0answers
28 views
Setting up diffusion with integral B.C. in Fenics
I'm trying to model diffusion through a cylindrical domain $D = \{ (x,y,z) : x^2 + y^2 \leq 1, \;\; 0 \leq z \leq 1\}$.
The is an initial concentration of the diffusant at the upper flat surface, ...
0
votes
0answers
34 views
Divergence issues when using intrinsic cohesive elements approach
When I model the strain localisation of a microscopic sample (or say RVE ) with cohesive elements approach, the convergence performance looks very terrible. I have to use extremely time increments (...
1
vote
1answer
94 views
Fenics: solving the same PDE multiple times
I am new to Fenics and just started reading the tutorial Solving PDEs in Python. For simplicity, we can refer to simplest example, page 17 (the linear poisson equation), despite not necessary.
My ...
1
vote
2answers
182 views
Lattice Boltzmann methods vs Navier stokes/ other eulerian methods for *water* simulation
Note, there is already a question here, however the answers don't answer the original question, let alone specific considerations when dealing with nearly in-compressible fluids (water). Another ...
1
vote
0answers
40 views
Finite element lemma proof
I was curious if anyone could help or provide a reference for the proof to the following lemma
Lemma:
Let $P_{1}$ be the set of polynomials of the first degree and let
$W = w(x) : w \in C([0,1]), ...
1
vote
2answers
59 views
Evaluation of slope at iteration ith - Newton-Raphson method
I'd like to know how Ansys computes the slope (=stiffness matrix) at point x1 in figure. I'm studying the way in which Ansys uses the Newton-Raphson method when there are nonlinearities.
In the slide ...
3
votes
1answer
57 views
Weighted QR Implementation
Say I want a QR decomposition of matrix $A$, where orthogonality of $Q$ is with respect to a generic non-degenerate positive-definite bilinear form $\phi$ (in my case, $\phi$ is "defined" by a finite-...
1
vote
0answers
25 views
Finite difference/element method : time step and spatial resolution close to a finite singularity
I'm using the finite element method (FEM), but my question is quite a global question. It's related to this question but it is not the same.
Let's assume we have this equation : $$\partial_t c - u\...
3
votes
0answers
84 views
numerical instabilities in Fluid Dynamics, Finite Element Method
I'm looking for references to understand where the numerical instabilities come from in hydrodynamics in general, and notably when the Péclet number: $Pe>1$. I'm using the finite element method.
...
1
vote
0answers
54 views
Derivatives over a Finite Element mesh
I have a data extracted from Comsol on some node points and I know the coordinates of each node.
Does anyone know how Comsol calculate the partial derivative from the values at each node and also ...
0
votes
0answers
45 views
FEniCS implementation of Maxwell equations for a dipole antenna
someone knows where I can find a FEniCS implementation of Maxwell equations for a dipole or other type of antenna? I mean a dipole antenna with an arbitrary geometry of every 'leg' in the dipole.
3
votes
1answer
140 views
Why do many people use FDM method to solve Stokes equations, i.e., saddle point matrix?
For numerical methods of the Stokes equations, with appropriate boundary:
$$-\nabla^{2} \vec{u}+\nabla p=\overrightarrow{0}$$
$$\nabla \cdot \vec{u}=0$$
one may use FDM (finite difference method) ...
0
votes
0answers
64 views
How to implement the following Finite Element method for Burgers' equation?
I am trying to replicate this result.
It involves using the Galerkin finite element approach onto the viscous Burgers' equation. However, my implementation (in R) seems to be giving me wrong results....
0
votes
1answer
56 views
Determination of Young's Modulus for a Finite Element Code
I am writing a finite element code for my final year project of BS Mechanical Engineering. The geometry is an integration of several parts composed of different materials. I don't have exact values of ...
0
votes
1answer
44 views
How to define $P0-$ Piecewise constant basis function in finite element method?
Suppose if we take $X_h(G)$ as finite element space then this space (space of piecewise constant basis function)is defined as
$$X_h=\{v: v|_{T}=c_{T}, T \in \mathbb{T}\},$$
where $\mathbb{T}$ is a ...
3
votes
1answer
90 views
Reference request: Riks method (Nonlinear FEM)
I'm struggling to find a good detailed reference explaining the Arc-length method or, more generally, Riks method and its derivations. I looked for the classical books in nonlinear mechanics (the ones ...
1
vote
1answer
86 views
Iterative solution of ill-conditioned matrix systems
I want to solve a matrix system of the form $Ax=b$ where $A$ is ill-conditioned. The matrix system comes from a structural simulation problem which was discretized using finite elements. I do not have ...
5
votes
1answer
103 views
Approximate $\|\Delta f\|^2_{L^2(\Omega)}$ in finite element context
I have minimization problem of the form
$$
G(f) + \|\Delta f\|^2_{L^2(\Omega)} \to \min
$$
over all $f\in C^2(\Omega)$, $\Omega$ being closed and bounded.
Let us forgot about $G$; I'm interested in ...
1
vote
0answers
16 views
Equi-order in pressure correction schme of Navier-Stokes equation
I am wondering if there is an stabilized equi-order scheme in pressure correction scheme in solving Navier-Stokes equation? Usually P2-P1 element combination is used to solve NS equation, and a PSPG ...
3
votes
1answer
76 views
Good reference on the implementation and limitations of SDIRK methods
For the solution of many PDE, implicit high-order time integration schemes are required. I am specifically interested in schemes that do not require a constant time step.
I am well acquainted with ...
0
votes
0answers
24 views
Automatic single point constraint
A lot of modern FE codes have an option called AUTOSPC. Examples are Nastran or Marc. I know that this option removes degrees of freedom to avoid a singular matrix system. But how to determine ...
2
votes
1answer
137 views
How to use Newton-Raphson method to handle nonlinear terms in coupled system of PDEs?
I'm trying to solve the Nonlinear Schrodinger's Equation (NLSE) in 2D using Finite Elements, but I don't know how to handle the nonlinear term. I suppose I have to apply the Newton-Raphson algortihm ...
