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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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 ...
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0answers
12 views

NASTRAN RBE3 element specify UM option

In NASTRAN model while creating RBE3 element, how do I specify UM option? I need to constrain certain degrees of freedom in using UM (m-set).
5
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1answer
98 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 ...
2
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1answer
54 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) ...
3
votes
1answer
67 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 ...
3
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0answers
86 views

Efficient assembly of finite element matrix(coupled equations case)

I noticed this post, where spalloc and sparse are recommanded for efficient assembly in Matlab. I personally use sparse assembling for simple cases. However, when it comes to the case of coupled PDE, ...
0
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1answer
48 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 ...
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3answers
174 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 ...
3
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1answer
121 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}) + ...
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110 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. ...
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3answers
141 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
58 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
68 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 ...
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3answers
147 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
65 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 ...
2
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1answer
89 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
56 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
52 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
votes
3answers
146 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
197 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
votes
1answer
417 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
votes
1answer
222 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
votes
2answers
104 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
96 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
67 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 ...
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2answers
75 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 ...
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0answers
137 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
votes
1answer
181 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
votes
1answer
167 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 ...
2
votes
2answers
118 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
13 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, ...
5
votes
1answer
109 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 ...
2
votes
1answer
99 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 ...
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2answers
274 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
votes
1answer
138 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
203 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
votes
1answer
127 views

High frequency noise at solving diffusion equation

I'm trying to simulate a simple diffusion based on Fick's 2nd law. ...
3
votes
0answers
137 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
votes
1answer
138 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 ...
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votes
2answers
216 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
votes
1answer
83 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
147 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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vote
3answers
133 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
199 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.
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5answers
223 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.
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60 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 ...
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1answer
124 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}} \\ ...
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2answers
230 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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66 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 $$ \phi_5(\xi,\eta)=\frac{1}{2}(1-\xi^2)(1-\eta) $$ ...