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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Finite Element integration with tensor notation

While I was studying discontinuous finite element methods I found an integration of a Navier Stokes equation using tensorial notation. The equation is the following: $\mathbf{\bar {u}}_{t} + ...
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129 views

Need a simple mesh format (for FEA) and a tool to generate the mesh

I want to write a 2D FEA code for my course project and I need to import a mesh (2d, simple quad/tri) on a simple geometry such as a L shaped plate or with a square/circular hole in it, something like ...
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1answer
107 views

Are additional penalty terms necessary to solve elliptic PDE's with DG-FEM?

After a cursory glance at several references to discontinuous galerkin finite element methods for the elliptic poisson PDE, i notice that all of them emphasize using penalty methods where an ...
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1answer
165 views

On the completeness of the Periodic Table of Finite Elements

In a recent SIAM News article, there is a long article describing a systematic organization of the finite elements, aptly dubbed the Periodic Table of Finite Elements. Its really quite fascinating to ...
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87 views

Poisson equation with pure Neumann boundary conditions (using FEM)

I am trying to derive the correct variational form for the Poisson equation with pure Neumann boundary conditions, and an additional contraint $\int_{\Omega} u \, {\rm d} x = 0$, as described in this ...
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87 views

Galerkin FEM: Handling Dirichlet boundary condition with quadratic basis function

Consider a simple BVP: $-u_{xx} = f$ with $u(1) = g$ and $-u_x(0) = H$. Following Hughes' notation for Galerkin FEM, the variational function space $V$ is defined first using basis $\{N_A(x)\}$, $A = ...
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81 views

Splitting Operator

I have a problem with this finite element formulation. After applied a Splitting Operator $Q=\hat{Q} + \tilde{Q}$ I do not know how to procede. I need to obtain the solution of the following finite ...
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1answer
86 views

When should a geometric stiffness matrix for truss elements include axial terms?

Bathe's Finite Element Procedures shows the "nonlinear strain stiffness matrix" for a 2D truss element as $$ \frac {^tP} {L_0 + \Delta L} \left[ \begin{array}{ccc} 1 & 0 & -1 & 0 \\ 0 ...
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187 views

Programming Finite Element Methods in C++

I am trying to develop a library for finite element methods in C++ and for that I am looking at the data structures for meshes. Based on what I've read up on fenics and deal.ii, the general ...
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46 views

Mixed DG for Poisson with mixed BC's

I am trying to find a good reference on a proper weak formulation for mixed DG (Raviart Thomas and DG) formulation for a Poisson equation with mixed boundary conditions. Can anyone suggest a good ...
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1answer
31 views

Transparent boundary conditions for finite element simulation of TDSE

I have implemented a version of Visscher's method for numerically solving the TDSE (A fast explicit algorithm for the time-dependent Schrödinger equation) (also described in Are there simple ways to ...
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2answers
121 views

Do I need to impose boundary conditions in the Jacobian matrix?

In the framework of Finite Element Method, when the Newton method is used, we solve $J(x^k) \delta x = -f(x^k)$, and the increment $\delta x$ would not change some entries from $x^k$ related to ...
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1answer
38 views

Modifying finite difference solution to Schrodinger eqn to account for fermion/boson effects

I have been playing with an implementation of Visscher's explicit method for solving the time dependent Schrodinger equation (Are there simple ways to numerically solve the time-dependent ...
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1answer
83 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 ...
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1answer
81 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 ...
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192 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 ...
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82 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; ...
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48 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: $\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$ ...
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171 views

How to use the Freefem++ (or Fenics) for solving 3D Helmholtz equations or Maxwell equations

I recently want to solve the three-dimensional Helmholtz equations with ABCs via the edge element method. But I am familiar with the program of C++/Python (-type) language, so I want to obtain some ...
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2answers
157 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 ...
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127 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.
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59 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 ...
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80 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 ...
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1answer
86 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 ...
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1answer
94 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 ...
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1answer
137 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 ...
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1answer
72 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) ...
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1answer
79 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 ...
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116 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, ...
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1answer
53 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
211 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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1answer
145 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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130 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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303 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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70 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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80 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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154 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 ...
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1answer
80 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
109 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
70 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
54 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 ...
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votes
3answers
369 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
220 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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18 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 ...
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1answer
474 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
249 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 ...
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2answers
112 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 ...
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2answers
104 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 ...
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1answer
71 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
88 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 ...