All Questions
1,333 questions
8
votes
2
answers
791
views
Method to quantify geometric difference of two dissimilar meshes
I am looking for a method or algorithm to produce a value that describes how different two meshes are geometrically but that have different topologies.
An example would be some CAD data that has had ...
- 83
2
votes
1
answer
179
views
Buckling reference using the FEM
I want to analyze buckling in a composite using the FEM. So far I have studied this references
Zdenek P Bazant, Luigi Cedolin. Stability of Structures: Elastic, Inelastic, Fracture and Damage ...
- 8,622
5
votes
4
answers
1k
views
Mesh generator that can do 2D & 3D elements combined?
I'm trying to analyze a circuit card assembly (CCA). The biggest problem is always trying to mesh the thin copper layers along with the thicker epoxy layers between. I'm making the approximation that ...
- 151
7
votes
1
answer
6k
views
What is numerical damping in the context of time-dependent FEM solvers?
Comsol Multiphysics (a popular FEM package) includes two time-stepping algorithms (IDA aka BDF, and Generalized-alpha), described in their documentation as follows (quoted here under Fair Use; ...
- 171
2
votes
0
answers
355
views
Treatment of Neumann (Traction) boundary conditions using projection methods
I am looking to solve the incompressible Navier-Stokes equations in 3D, using an inflow boundary condition specifying a velocity:
$\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$
...
- 21
5
votes
2
answers
460
views
Implementation of nonlinear term in FEM
Although there are similar questions, I am also struggling with the implementation of the following term in "my own code" by Finite Element Method, namely, $\nabla \phi \cdot \nabla \phi$. $\phi$ is ...
4
votes
2
answers
348
views
Analog of perfectly matched layers for finite element methods
Is there an analog of perfectly matched layers for finite element methods? References or small examples are much appreciated.
- 2,165
0
votes
1
answer
259
views
jump conditions for Poisson/Darcy equation in primal form versus mixed form
Consider the Darcy equation,
$$\mathbf{v} + \dfrac{k}{\mu_0}\nabla p = \mathbf{f} \\ \mathrm{div}\; \mathbf{v} = 0$$
If the coefficient $k$ is piecewise constant across an interface $\Gamma$ in the ...
- 445
5
votes
2
answers
655
views
Choice of spaces for mixed formulation for Poisson Equation Or Darcy equation
Consider the mixed formulation of the Poisson/Darcy system for a region $\Omega$:
$\alpha \mathbf{v} + \nabla p = f \\
\mathrm{div}[\mathbf{v}] = 0 $
with the boundary conditions
$\mathbf{v}\cdot ...
- 445
3
votes
1
answer
815
views
Jump condition for elliptic equation in standard finite element method
Consider the elliptic PDE
$ -\mathrm{div}(k(x)\nabla u) = f(x) \in \Omega$
and
$u = 0$ on $\partial \Omega$
If $k(x)$ is piecewise constant across an interface $\Gamma$ in the domain, then we ...
- 445
3
votes
1
answer
372
views
Books and references on implementing finite difference codes for PDEs
Are there any good books or references on implementing finite difference methods for PDEs? Specifically, I'm looking for something comparable to Gockenbach's book Understanding and Implementing the ...
- 767
6
votes
1
answer
552
views
Lagrange Multipliers in Multi-body Finite Element Code
I'm working on a Multibody dynamics code using the finite element method to simulate the behaviour of flexible beams (using this paper if anyone is interested/ it is relevant). I'd like to model ...
- 143
2
votes
1
answer
223
views
Optimal Discontinuous Galerkin (DG) solver on a parallel system
I am seeking the optimal method for implementing DG on a parallel system. For my research, I come across two types of problems.
For the first problem, I am solving a time-independent (steady-state) ...
4
votes
1
answer
144
views
Reconciling vector and scalar notation
I am trying to derive Galerkin type weak formulation for the Stokes equations. I'm having a bit of a problem reconciling the notation in the integration by parts. I know that the answer I'm looking ...
- 625
3
votes
0
answers
354
views
Efficient assembly of finite element matrix(coupled equations case)
I noticed this post, where spalloc and sparse are recommended for efficient assembly in Matlab. I personally use sparse ...
- 593
0
votes
1
answer
75
views
FEM with soil slope
I what to calculate displacements, stress and strain in a soil slope with a FEM script. The slope moves like a laminar flow.
Can you suggest me some bibliography on this problem?
I've already look on ...
- 103
6
votes
3
answers
3k
views
Books on mathematical foundation of finite element methods
After reading three books about finite element method, with two of them covering also finite volume and grid generation, I found myself lost when I have to discuss these topics with library developers ...
- 157
3
votes
1
answer
471
views
Finite Elements Weak Formulation generalization
I am struggling with an equation that represents the Weak form of Galerkin method:
$ \phi^{T}F(\textbf{u})\sim \int_{\Omega}^{ } \phi.f_{0}(\mathit{u},\nabla \mathit{u}) + \nabla\phi:f_{1}(\mathit{u},...
- 157
8
votes
1
answer
636
views
Finite element convergence rates for mixed problems
I've coded up a Stokes Flow problem using finite elements and am in the process of verifying that it works. I'm just not sure what convergence rate I should be expecting as I globally refine the mesh.
...
- 625
8
votes
4
answers
6k
views
How to efficiently assemble global stiffness matrix in sparse storage format (c++)
I am writing a finite element solver in C++. The main bottle neck is assembling the global stiffness matrix in sparse compressed row storage (so far I am only solving steady problems). Because I don't ...
- 1,929
1
vote
2
answers
454
views
Which type of meshing is more suited for simulation of electromagnetic metamaterial unit cells?
Electromagnetic metamaterials are resonant, periodic structures (repetition of a unit cell) involving both dielectric and conducting elements, and are used and simulated in frequency ranges from ...
- 111
1
vote
3
answers
427
views
Introductory Resources on FEM [duplicate]
I've currently begun studying Finite Element Method (FEM) and I'm finding it a little difficult to find resources that break it down into something comprehensible. All the resources I've found are ...
- 319
4
votes
3
answers
251
views
vector PDEs on manifolds
What are the subtleties involved in solving vector PDEs on manifolds? Can someone suggest a reference summarizing the problems involved?
Specifically I want to solve a vector Helmholtz equation with ...
- 176
2
votes
1
answer
776
views
Method of lines for inhomogeneous Dirichlet conditions
I understand how to set up the boundary conditions for a steady state problem discretized by Galerkin method, for a time dependent PDE below,
$$\frac{\partial}{\partial t} u = c\nabla^2 u + a\nabla u ...
- 593
3
votes
1
answer
236
views
Time Integration of a nonlinear reaction-diffusion system
I want to solve the following system of nonlinear reaction-diffusion equations (Schnakenberg Turing) using FEM methods (such as deal.ii):
$$ \partial_{t} u = \Delta u + \gamma\left(a-u+u²v\right)$$
$$...
- 31
1
vote
1
answer
257
views
Coupled PDE: a confusion in boundary condition setup
I have a coupled PDE problem(Poisson-Schrondinger system), i.e.
first I need to solve an eigenvalue problem (Schrodinger problem discretized by Galerkin method)
$$Ax=\lambda x, ~~~A=A(u)$$
the ...
- 593
0
votes
1
answer
104
views
Dynamic problem Finite Element
Hi guys! I am working on a dynamics problem that I am not really sure how to solve it. Can anyone help me? The professor gave as a hint that we should compute the stiffness matrix of a linear element ...
- 1
5
votes
5
answers
10k
views
scipy.sparse: Set row/column in sparse matrix to the identity without changing sparsity
I'm using the SciPy sparse.csr_matrix format for a finite element code. In applying the essential boundary conditions, I'm setting the desired value in the right ...
- 211
2
votes
3
answers
845
views
Help choose Finite Elements (FEM) software for elastic, multi body system!
I would appreciate help choosing a software for the Finite Elements Method (FEM).
I wish to model items like ropes, bull whips and fishing rods. (I intend to transfer the model into bio-mechanics, ...
- 261
13
votes
1
answer
3k
views
What are the relative benefits of using Adams-Moulton over Adams-Bashforth algorithm?
I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised ...
- 301
4
votes
1
answer
395
views
Finite differences vs. elements: Accuracy and implementation
I am trying to solve the 2D Poisson equation numerically:
$ \frac{\partial ^2 \phi}{\partial x^2} + \frac{\partial ^2 \phi}{\partial y^2} = 1 $
with the Dirichlet boundary condition $\phi = 0$.
I ...
- 41
2
votes
2
answers
277
views
Is there a bound on the number of edges, facets, and elements in a 3D simplicial mesh in terms of the number of mesh nodes?
I am currently working on a 2D finite element code with a mesh that contains duplicate nodes at certain interfaces where jumps occur. In order to set up the appropriate linear systems, I have to take ...
- 30.4k
3
votes
2
answers
272
views
Finite element: handle discontinuity/abrupt interface
I am using Galerkin's method to set up some pde solver for my problems(1D/2D) at hand.
Some abrupt material interfaces do exist, so far, what I did regarding this is simply:
1) no element across the ...
- 593
3
votes
1
answer
455
views
How to enforce the boundary conditions
I want to solve a poisson problem on two domains,(interface problem: Let $\Omega $ be a square, $\Omega=\Omega1 \cup \Omega2$ and let $\Omega1$ be a circle inside the square.
$\Gamma$ is the boundary ...
- 293
2
votes
2
answers
495
views
Computing element stiffness matrices with variable coefficients
I am trying to implement a simple FEM approach, using p1 triangular elements, for solving the diffusion equation with variable nodal diffusivities and I was wondering how to incorporate the variable ...
- 73
3
votes
0
answers
437
views
A Question About Weak Forms in Fenics
Is it possible to use test and trial functions from two different function spaces (defined over two different meshes) in a single weak form? Under what conditions can I do this (eg., each term in the ...
- 301
4
votes
1
answer
2k
views
Is there a mesh generator that will generate zero thickness elements for interfaces?
I have a geometry and a finite element method where there are a couple internal interfaces across which I want to enforce some fairly simple jump conditions.
One recommendation I've gotten has been ...
- 30.4k
4
votes
1
answer
3k
views
Comparison of Lattice Boltzmann Method vs Traditional Navier-Stokes based Methods
I have a choice of two options, analysing and implementing Lattice Boltzmann methods or traditional Navier Stokes based methods. I'm a CFD newbie and I have a rough idea (though not rigorous enough to ...
3
votes
2
answers
270
views
Does length unit in FEM affect numerical condition?
I try to solve a system of coupled PDEs using FEM. Unfortunately, the originating matrix has very poor condition. After days of double checking and thinking, I suspect the following reason:
Given a ...
- 1,463
5
votes
1
answer
408
views
How much measure theory should I know to understand the proofs in Brenner & Scott's FEM book?
I've been reading Larson and Bengzon's recent book on finite element methods, which has been good for getting an understanding of basic theory and computational procedures. The finite element book by ...
- 30.4k
2
votes
1
answer
284
views
Neumann / natural BCs in FEA
I'm trying to work out an as-general-as-possible 2D Laplace example for Finite Element Analysis. Starting from $\Delta u = 0$ for an unknown $u(x,y)$, I multiply both sides (well, in practice only the ...
- 123
10
votes
2
answers
488
views
Why do the shape of finite elements matter?
I have used FEA for a couple of years now, but using it and using it correctly are two different things, safety factor is not the solution to everything. I have the feeling I won't be using it right ...
- 203
5
votes
1
answer
4k
views
FEM: which is the correct way to impose Dirichlet B.C
I know the Neumann B.C. is implicit in FEM language. However, I have seen at least two ways to impose Dirichlet B.C.
e.g. for the following problem 1D,
$$\nabla^2 u + \nabla u= 0, u_{left}= 1, u_{...
- 593
1
vote
2
answers
3k
views
Help with basic Triangular Finite Elements, constructing stiffness/mass matrices
I am going through this example problem (picture below) and working it out myself. The problem is that I do not get the same mass matrix (M) as the example problem. I am able to get the same ...
- 11
3
votes
1
answer
246
views
High frequency noise at solving diffusion equation
I'm trying to simulate a simple diffusion based on Fick's 2nd law.
...
- 133
3
votes
0
answers
823
views
Beam finite element stiffness matrix from section constitutive matrix
I'm trying to construct the 12 x 12 beam element stiffness matrix from a section constitutive matrix (6 x 6 with shear stiffnesses, axial stiffness, bending stiffnesses and torsional stiffness on the ...
- 143
3
votes
1
answer
633
views
Recommendations on FEM software for implementing Nitsche's method on interfaces between matching meshes?
Suppose:
I have two domains, $\Omega_{1} = [0, 1/2] \times [0, 1]$ and $\Omega_{2} = [1/2, 1] \times [0, 1]$.
The domains share an interface $\Gamma = \{1/2\} \times [0, 1] = \partial\Omega_{1} \cap \...
- 30.4k
8
votes
5
answers
3k
views
Good Finite Element Library for a small project
I'm currently working on this project and I have a basic structural analyzer that uses the finite element method. Essentially, I turn each block into a set of trusses, construct a stiffness matrix ...
- 123
6
votes
1
answer
133
views
L1 functional setting for Navier-Stokes with finite elements
Typical finite element problems assume $L^2$ which is a Hilbert space, but I've heard that $L^1$ for Navier-Stokes results in less overshoots/undershoots, but $L^1$ is not Hilbert. The dual space for $...
- 542
5
votes
1
answer
1k
views
Which finite-element framework allows the easy implementation of HDG methods?
I have tinkered around with the implementation of hybridizable Discontinuous Galerkin (HDG) methods in DUNE-PDELab and DUNE-FEM for my PhD but since then I have not had the time to work on these codes ...
- 1,074