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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35 views

Solving Linear Systems in Julia

To give you some context, I am currently implementing a simple finite element solver in Julia. I am getting run-times that are 70% of a Matlab code. (Both codes are essential equivalent in ...
-2
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0answers
9 views

NASTRAN : MODAL ANALYSIS SOL 103 of an assembly of a superelement and a finite element model [on hold]

I need to do a modal analysis of an assembly of a superelelment with a finite element model on Msc Nastran. This is what I have in the f06 file : SYSTEM FATAL MESSAGE 6144 (MERGE1PR) *THE SIZES OF ...
1
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1answer
42 views

How to update velocity to include pressure when using P2/P1 elements

I am in the process of writing a finite element code to solve the Navier-Stokes equations using the theta method for time stepping (basically Crank-Nicholson for diffusion and forward Euler for ...
3
votes
2answers
117 views

What's the difference between C0 penalty methods and Discontinuous Galerkin methods?

I am trying to understand the DG FEM methods, but I got lost in their definitions. In some papers I read that the "C0 penalty method" is one example of the DG method, but sometimes they are separated ...
3
votes
2answers
84 views

How to calculate efficiently mesh edges midpoints?

I have a 2D mesh of triangles used in Finite Element method to discretize the domain. I want to calculate the midpoints of all the edges because I want to use $\mathbb{P}^2$ elements. I am using ...
3
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0answers
39 views

Stability analysis for explicit time discretization in the Finite Element Method

I have been looking for stability analysis of general reaction-diffusion problems, of the form $\frac{\partial u}{\partial t}=\nabla\cdot D\nabla u-k\,u$ , to be solved using the standard Finite ...
0
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0answers
22 views

Converting a labelled pixel grid to an isoregion geometry file

I am working with ASCII text files that each contain a grid of integer labels. The grid can be interpreted like the pixels of an indexed raster image. e.g. $\begin{pmatrix} 1& 1& 1& ...
6
votes
1answer
97 views

What exactly causes mesh locking in thin plate bending problems?

In thin plate bending problems, it would be very nice if we could model a thin rectangular plate with a mesh of many elements in the transverse directions, but only a single element in the ...
1
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2answers
89 views

How to correctly normalize modulus and phase of an eigenvector?

I am solving a linear stability problem using finite element discretization. Then, I have a generalised eigenvalue problem: $$ \lambda M x = J x.$$ I obtain complex eigenvalue and eigenvectors from ...
4
votes
1answer
122 views

What is the general idea of Nitsche's method in numerical analysis?

I know that the Nitsche's method is a very attractive methods since it allows to take into account Dirichlet type boundary conditions or contact with friction boundary conditions in a weak way without ...
3
votes
1answer
70 views

P2/P0 and P2/(P1+P0) finite elements for stokes and darcy equations

Typically I have seen P2/P1 elements used for Stokes equation, but I want to use P2/(P1+P0) and P2/P0 elements because I want to ensure local mass conservation. When I say P2/(P1+P0), I simply mean ...
0
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0answers
12 views

Resonant interactions, instability of nonlinear waves- which numerical method:HOSE or FNPT-based?

I am studying non linear interactions for water waves. Resonant interations type problems or instability of waveforms are the kinds of problems of interest. Resonant interactions and related ...
0
votes
2answers
105 views

Relationship between FEM solutions of PDE with different spatial resolutions

I use FEM to simulate deformations of elastic objects for animation applications in computer graphics. The governing equation is generally with the form: $$ \mathbf{M}\ddot{\mathbf{u}} ...
0
votes
1answer
46 views

How does the animation work in eigenvalue problem of FEM

I have used free vibration analysis in FEM. After analysis, we can usually use animation to see the motion of each eigenmode (In Abaqus or Comsol, I would choose either half harmonic or full ...
1
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1answer
79 views

openfoam - Programming customized PDEs

I am looking for a method to automatically solve custom PDEs on a custom control volume. Specifically I would like to solve equations similar (but not exactly alike) to: $$\frac{\partial y}{\partial ...
1
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0answers
60 views

Arpack and Matlab give different values for eigenvalues

I am solving a generalized eigenvalues problem with inversed complex shift: $$(M-\sigma J)^{-1}J \boldsymbol{x} = \boldsymbol{x} \nu \enspace .$$ My matrices are obtained from a finite element ...
1
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0answers
27 views

Integro-differential eigenvalue problem, COMSOL

In my research I encounter an eigenvalue integro-differential equation of the form: $$f_n(x,y)=\lambda_n\iint_D\frac{\nabla'\cdot\big\lbrace ...
2
votes
0answers
45 views

Selecting a Finite Element discretization for subsurface flows

Are there guidelines to follow in selecting the right FE discretization. Specifically, for subsurface flow models like Darcy's equation (both single and multi-phase), Richard's equation, etc. I know ...
4
votes
1answer
141 views

How to formulate lumped mass matrix in FEM

When solving time dependent PDE's using the finite element method, for example say the heat equation, if we use explicit time stepping then we have to solve a linear system because of the mass matrix. ...
1
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2answers
93 views

How to deal with nonlinear term in Navier Stokes equations (finite element code)

I am trying to solve the Navier Stokes equations using the finite element method. I plan on using the pressure correction method to deal with the pressure and an implicit time stepping scheme for ...
2
votes
1answer
110 views

Is my matrix symmetric?

I obtained a mass matrix through Finite Elements discretization. Now, I want to check if it is symmetric. To do that I subtract to my matrix $M$ its transposed $M^T$. The result is another matrix of ...
3
votes
1answer
87 views

Meshless Methods and the Kronecker Delta Property

In texts I often read that meshless methods, as opposed to the FEM, do not exhibit the Kronecker Delta Property [1]: $N_I(x_J)\neq\delta_{IJ} = \begin{cases}1 &\mbox{if } I=J \\0 ...
0
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0answers
35 views

Gauss Integration over Zero Order Element

I'm working with the Boundary Element Method and want to integrate an expression over a triangular region. I would like to use Gauss Integration to do this, but I'm having trouble since the triangular ...
0
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0answers
52 views

Proof of convergence for Newton method in finite element analysis

The Newton method in FEA is to solve for a non-linear equation where stiffness matrix is a function of displacement: And to assemble the stiffness matrix from constitutive laws, we need the tangent ...
3
votes
2answers
112 views

Is “tangent stiffness matrix” the same as “stiffness matrix”?

I'm trying to implement nonzero Displacement Boundary Conditions in VegaFEM on a non-linear model, using the method outlined in §3.6.2 of University of Colorado's intro to FEM (modify $f = Ku$: set ...
2
votes
2answers
161 views

The meaning of conservative discretization in Galerkin FEM and Discontinuous Galerkin

I do understand the meanning of "conservative discretization" within the FVM/FDM framework, indeed it is well explained in this post. Now, according to the table in this slide (pp.4), it concludes: ...
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1answer
65 views

Finite element method for odd order DE

What are theoretical hurdles in applying Galerikin method on, say, first order time dependent ODE? Is there no way we can form an inner product??
4
votes
1answer
80 views

Shell vs frame element model stiffness differences

I have a model of a tall, slender structure that I am investigating using both shell and 3D frame elements. The shell elements are type MITC4, 4-node membrane elements. The frame elements are the ...
2
votes
1answer
107 views

Inverse isoparametric mappings for quadrilateral finite elements

I have an isoparametric mapping $F_{E}: \hat{E} \to E$ where $\hat{E}$ is a reference quadrilateral (square) and $E$ is some quadrilateral in the domain $\Omega$. If $E$ is a parallelogram, then the ...
3
votes
1answer
144 views

Boundary conditions in conforming Galerkin method for biharmonic equation

I am trying to solve simple scalar biharmonic equation using bubnov-galerkin finite element method. I am using $H^2$ conforming basis functions. I was wondering that if anyone can give me some ...
4
votes
1answer
96 views

Find the direction of the gradient on a finite element mesh

Suppose we have a triangular mesh of a two dimensional shape $\Omega$, and on this mesh we define a P1 finite element structure. I know that given $u,v$ by their values at the vertices of the ...
0
votes
0answers
45 views

Best way to average surface data or function data in 2d grid

I have pressure data on a 2D triangular surface. I can compute average(data). What is the best way to average the surface data?
4
votes
1answer
45 views

Estimating the local compression/expansion ratio for a transformation on a point cloud

Let's say we have an unorganized point cloud P1 with N points, each with coordinates {x,y,z}. We apply non-rigid transformation to P1 (translation + rotation + warping), to obtain point cloud P2. ...
0
votes
1answer
97 views

FEM - Shape function of a HEX20 - plot in MATLAB

I have a FE model of a simple plate with hole (tension load) with HEX20 mesh. I need to obtain the Shape Function of one of the elements (the one with highest stress) and plot it (with MATLAB). After ...
0
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0answers
62 views

Conditions for always positive gradient of heat field in evolutionary thermo-elastic system

I am investigating stability and convergence of series of approximations for coupled thermoelasticity problem yielded by one-step recurrent time-integration scheme. I've managed to show that the ...
0
votes
2answers
86 views

Finite element programming tutorial [closed]

I am new to this site and it might therefore not be the best place for this question. I have been using finite element programs (CFD mainly) for some time and I want to learn more about the basics. ...
6
votes
1answer
144 views

How to project a vector into the H(div) space (in the context of finite elements)?

Say I have a simple elliptic PDE: $$ -\nabla\cdot(K\nabla p) = f \;\;\;\text{in}\;\Omega $$ with the appropriate boundary conditions. I solve for $p$ using a FEM (a discontinuous Galerkin method to ...
6
votes
1answer
80 views

Space-time finite element discretization for time-dependent PDEs

In FEM literature, semi-variational methods are typically used in the solution of time-dependent PDEs. I have not seen a fully-variational approach i.e. where space and time are discretised by FEM, ...
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0answers
96 views

Determining Youngs Modulus of defined material in FEA (ABAQUS)

I am quite new to FEA but need to determine if I am performing my simulations correctly. I have a cube of material with defined elastic properties (Youngs Modulus and poison ratio). I perform a ...
6
votes
1answer
123 views

How to avoid negative values of numerical solution of transport equation using FEM scheme?

The transport equation is actually an advection-diffussion-reaction equation, which has the form as $$\frac{\partial C}{\partial t} + v_1 \frac{\partial C}{\partial x} + v_2 \frac{\partial ...
1
vote
1answer
52 views

Reaction-Diffusion problem A->B, solving for B

I need to solve a Reaction-Diffusion using Finite Elements, piecewise linear elements. In this problem, a reaction $A \rightarrow B$, with rate law $ r_A = - k_A \cdot u_A $, takes part, where $u_i$ ...
1
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0answers
43 views

Can variational formulations be solved using series solutions?

What I specifically mean is, given some functional $F\left[\mathbf{x}\right]$ which is stationary with respect to $\dot{\mathbf{x}}=f(\mathbf{x})$ and some boundary or initial conditions, can one ...
3
votes
1answer
72 views

Solving pure Neumann problem enforcing B.C. with Lagrange Multiplier

I want to solve the Laplace Equation with pure Neumann B.C. using Finite Element Method: $- \Delta u = f \ $ in $ \ \Omega $ $- \partial u/\partial n = g \ $ on $ \ \Gamma = \partial \Omega$ With ...
2
votes
1answer
89 views

Best preconditioner for mixed-poisson problem (RT0 elements)

For a very large mixed-poisson problem with lowest order Raviart-Thomas elements (RT0), I plan on using an iterative solver. However, this kind of problem is not positive-definite (saddle point ...
5
votes
2answers
149 views

How do hexahedral FEM meshes improve approximation quality per degree of freedom, compared to tetrahredal meshes?

From the deal.II FAQ : ...quadrilaterals and hexahedra typically provide a significantly better approximation quality than triangular meshes with the same number of degrees of freedom; you ...
1
vote
1answer
141 views

Step-wise finite element formulations: can this be done?

Given the functional: $$ F[\mathbf{x}]=\frac{1}{2}[\mathbf{x}^{\text{T}} * D(\mathbf{x})]-\frac{1}{2}[\mathbf{x}^{\text{T}} * \mathbf{Ax}]-\frac{1}{2}\mathbf{x}^{\text{T}}(0)\mathbf{x}(t) $$ Where ...
9
votes
3answers
173 views

Finite elements on manifold

I'd like to solve some PDEs on manifolds, say for example an elliptic equation on a sphere. Where do I start? I'd like to find something that use preexisting code/libraries in 2d , nothing so fancy ...
4
votes
1answer
168 views

Why are functional representations of systems important in numerical applications?

I tried asking a similar question in SE.Physics, and I got some information regarding the abstract side of this, but I figured I should post here to get more complete information about the numerical ...
3
votes
0answers
51 views

Creating FEM mesh for image region — what is the most suitable shape function?

I wish to create a FEM mesh to solve an inverse elasticity problem, for an irregular domain. This domain is given by a medical image, so it is discretised and each square on the grid has one scalar ...
0
votes
0answers
30 views

Resources for viscous behavior in simple FEM

I am working on a simple explicit-integration lumped-mass elastic FEM code which implements CST+DKT triangles (plate+shell) and constant-strain tetrahedra ...