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 ...

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138 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 ...
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0answers
31 views

How to create rotating obstacle [closed]

I want to create mesh for channel flow with a rotating cylinder can any one give me the idea? how to do it... I am using fenics FEM solver...
3
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1answer
100 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}) + ...
7
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1answer
94 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. ...
2
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3answers
112 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 ...
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2answers
57 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 ...
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3answers
61 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 ...
4
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3answers
143 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 ...
2
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1answer
63 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 ...
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1answer
69 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): $$ \partial_{t} u = \Delta u + \gamma\left(a-u+u²v\right)$$ ...
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1answer
52 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 ...
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1answer
49 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 ...
3
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3answers
104 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 ...
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2answers
191 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, ...
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0answers
17 views

Model actuators in non-linear beam element structure

I have written a non-linear finite element code using beam elements, and I'd like to represent hydraulic actuators in the model. In real terms, this would mean that the distance between two nodes at a ...
9
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1answer
409 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 ...
4
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1answer
210 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 ...
2
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2answers
103 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 ...
2
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2answers
93 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 ...
3
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1answer
62 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 ...
2
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2answers
71 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 ...
3
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0answers
131 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 ...
3
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1answer
167 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 ...
3
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1answer
155 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 ...
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2answers
116 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 ...
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0answers
12 views

dynamics of bending of flexible kvazi-1D object simulated using smooth basiset

Do you know a about method which use smooth basiset (like spline, $\sin, \cos$ ) rather than finite element method for simulation of bending of some flexible 1D object ( canteliver, bow, stiff rope, ...
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1answer
97 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 ...
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2answers
97 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 ...
7
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2answers
270 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 ...
2
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1answer
136 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, ...
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2answers
188 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 ...
3
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1answer
121 views

High frequency noise at solving diffusion equation

I'm trying to simulate a simple diffusion based on Fick's 2nd law. ...
3
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0answers
120 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 ...
3
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1answer
131 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 ...
2
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2answers
203 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 ...
6
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1answer
82 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 ...
4
votes
1answer
141 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 ...
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3answers
126 views

How to find the smallest positive eigenvalue of a large general system if they are all in +/- pairs of real eigenvalues

I used MKL Lapack SBGVX because it can solve for "selected" eigenvalues/modes (both positive and negative), thinking it would be efficient, but it is extremely slow when compared with Bathe's subspace ...
3
votes
1answer
181 views

Crouzeix-Raviart Finite Element

Can anybody recommend me a good introduction to Crouzeix-Raviart Finite Elements? Their motivation is not obvious and the body of literature is hard to overlook.
6
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5answers
214 views

Is discontinuous Galerkin really any more parallelizable than continuous Galerkin?

I've always heard that easy parallelization was one of the advantages of DG methods, but I don't really see why any of those reasons don't also apply to continuous Galerkin.
2
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0answers
59 views

Modal analysis of structure with aerodynamic damping

I'm using modal decomposition to predict the steady state response of a beam structure to harmonic loading. The structure itself is very lightly damped, but we know from experiments that the ...
0
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1answer
107 views

How does Abaqus calculate Hill's function for non-rectangular coordinate systems?

Within the manual, the effective/von Mises stress or Hill's potential for anisotropic bodies is calculated in Abaqus in cartesian rectangular coordinates as $\sigma_{eff}=\sqrt{I_{1}^{2}-3I_{2}} \\ ...
7
votes
2answers
227 views

Which novel data structures are used in adaptive FEM?

A lot of adaptive FEM libraries use more advanced mesh data structures to handle adding/removing nodes, edges, triangles, tetrahedra, etc. For example, the p4est library uses octree data structures ...
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0answers
64 views

The shape function of the corner point from a serendity element (Q8)

For a serendipity element, the shape function of a middle pt on a edge can be formed using the tensor product in each direction e.g. pt 5 on Quad8 $$ \phi_5(\xi,\eta)=\frac{1}{2}(1-\xi^2)(1-\eta) $$ ...
2
votes
2answers
138 views

In what regime do the continuous and discontinuous Galerkin method become unstable for advection-diffusion systems?

I know that the finite volume method (based around a central different stencil) is unstable for advection dominated advection-diffusion problems. This leads to different adaptive schemes to can be ...
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0answers
57 views

Locally conservative method for differential generalized eigenvalue problem

I have to approximate the smallest eigenvalue of the following generalized eigenvalue problem $$ - \nabla \cdot D(x) \nabla p(x) + \alpha(x) p(x) = \lambda \beta(x) p(x) $$ over a domain like ...
2
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1answer
71 views

Extended finite element method vs $P_k$-bubble element

Can you show me the main differences between 2 methods? I find out 2 reasons but I don't know they are right or not. XFEM is constructed base on enrichment functions whereas P1-bubble is constructed ...
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2answers
150 views

The effect of decoupling a coupled system of PDEs

I asked a somewhat similar question previously but perhaps it might have been too specific for anyone to really answer. Here is a bit more general of a question that I am struggling with. Consider the ...
8
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3answers
608 views

Finite Element Method vs Extended Finite Element Method (FEM vs XFEM)

What are main differences between FEM and XFEM? When should we (not) use XFEM intead of FEM and vice versa? In other words, when I meet a new problem, how I can know to use which one of them?
3
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2answers
168 views

Consumer GPUs for sparse matrices (e.g. FEA)

Are consumer grade GPUs (like the NVidia Geforce series) used for solving sparse linear equations systems in a professional setting? For example, by engineers performing finite element analysis? ...