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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Alternatives to Comsol Multiphysics

This might be a question better suited for the Software Recommendations side of S.E., however I do believe that people who frequent this part of S.E. are more likely to be able to answer this ...
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FEM for a nonlinear parabolic PDE

I'm looking to numerically compute the solution to $$ k(x,u) \partial_t u - \Delta u = f \quad\quad\text{ in } \Omega \times [0,T]$$ where $k$ is a continuous but nonlinear (in $u$) real-valued ...
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39 views

Tissue deformation Simulation using FEM [closed]

I need to simulate tissue deformation using FEM. Is it advisable to represent the object as a triangle mesh or a ...
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38 views

What is Mesh Independence Report?

I am performing analysis on chassis (Static Structural) and for optimization purpose i am asked to generate MESH-INDEPENDENCE REPORT,of which i have no idea. I have tried going through research papers ...
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72 views

Solve steady state reaction-diffusion/Helmholtz equation numerically

I am solving a problem of the form: $\frac{\partial u(x,y,t)}{\partial t} = \nabla^2 u(x,y,t) - f(x,y,t)u(x,y,t) - \kappa(x,y,t)$ At the moment, I am solving this at each time step by assuming a ...
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100 views

Solve diffusion equation with linear source term

I would like to solve numerically the diffusion equation, where the sink term depends linearly on the field, and there is field-independent sink: $\frac{\partial^2 u(x)}{\partial x^2} =f(x)u(x) - ...
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4answers
189 views

Motivation behind Galerkin method

I have a question about Galerkin method. I don't understand why the Galerkin method weights the residual by the shape functions and sets it equal to zero. I want to know what is reason of this. Why we ...
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123 views

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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167 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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114 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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199 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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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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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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82 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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107 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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223 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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47 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
32 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
127 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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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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107 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
83 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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200 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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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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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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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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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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129 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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62 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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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
92 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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96 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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140 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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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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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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120 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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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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214 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
148 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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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
354 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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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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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 ...
2
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1answer
86 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 ...
3
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1answer
110 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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72 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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55 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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3answers
461 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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227 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, ...