Skip to main content
Share Your Experience: Take the 2024 Developer Survey

Questions tagged [finite-element]

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 estimates.

Filter by
Sorted by
Tagged with
0 votes
0 answers
39 views

Gradient of field computed using FEM (L2 Projection)

From my understanding, in the finite element context, an L2 projection can be formulated as the following linear system: $$ M\ \phi = \beta $$ where $M$ is the mass matrix, $\phi$ the resulting ...
dlmpal's user avatar
  • 1
4 votes
0 answers
59 views

Computational efficiency of Galerkin projection in AMG

I have been using recently AMG as preconditioner for CG with several meshes for simple elliptic problems discretised with linear elements on "complicated" three dimensional geometries and I ...
FEGirl's user avatar
  • 405
0 votes
1 answer
65 views

Formulation of K for tetrahedral elements for the Finite Element Method

...
prusso's user avatar
  • 31
1 vote
1 answer
84 views

Computing Tangential Derivative using the Dirichlet value

Let $\Gamma$ be a smooth boundary of a domain $\Omega$. Let $u = g$ on $\Gamma$. How can I compute the tangential derivative of the function $u$ using the information that $u = g$ on $\Gamma$? Please ...
Bishnu Lamichhane's user avatar
0 votes
1 answer
120 views

"Cleanest, most professional" approach to implement a finite differences scheme in dimension greater than two

Coding a finite difference algorithm in 1D does not require a complex mesh. In higher dimensions, you would need a mesh and its connectivity graph to compute the differential operators. Finite ...
mle's user avatar
  • 125
2 votes
0 answers
49 views

Lowest order Raviart Thomas elements

I have questions regarding the implementation of Lowest order Raviart Thomas elements on quadrilaterals, some papers use the basis functions in this form: for example the right edge: $N = \left[\dfrac{...
Amr Ashraf Ibrahim Ibrahim's user avatar
2 votes
0 answers
62 views

Interpolation constant on triangles

There are quite a few references regarding the estimation for the interpolation error for the piece-wise affine finite elements. I find one particular estimate interesting (and useful in my case), ...
Beni Bogosel's user avatar
  • 1,057
0 votes
1 answer
38 views

How to ensure solution evolves forward in Modified Riks Method by Crisfield?

I am writing a Matlab based script for solving nonlinear FEA problems using Modified Riks method by Crisfield. As a starting point, I am solving $y = x^3 - 2 x^2 - x + 2$. Around the function minima ...
frustrated_engineer's user avatar
0 votes
1 answer
66 views

How to derive excitation equation used in Finite-Element-Method waveport-driven simulation?

I am working my way through getdp's linear waveguide example in 3D. It appears to me that the electric fields are excited by the waveports, as defined in the formulations file on lines 161-164: ...
Stuart Barth's user avatar
3 votes
0 answers
121 views

Galerkin Method - Why does integration-by-parts eliminate need to enforce Neumann boundaries?

I've posted this to MathStackexchange but I figured I'd also post here as well as I have yet to receive an answer on my original post, and that I would be more likely to encounter users of the ...
Timothy Leong's user avatar
0 votes
0 answers
73 views

Can domain decomposition methods also be applied to linear systems resulting from finite difference discretizations?

Question In general, do domain decomposition methods require a linear system of equations $Au = f$ to be formed by finite element discretization of a PDE? Or could one simply use a finite difference ...
Jared Frazier's user avatar
0 votes
0 answers
37 views

Transformation matrix for global displacements derivates to local ones

The derivatives of the displacements in the coordinate system $\bar{x} \bar{y} \bar{z}$ is given by \begin{equation} \begin{aligned} \{\bar{L}\} & = \begin{Bmatrix} ...
Riobaldo Tatarana's user avatar
1 vote
1 answer
123 views

How to refine $h$ and $\Delta t$ for convergence tests on evolution PDE

Setting I am solving for $u(x,y,t)$ the wave equation $\partial_{tt} u - \partial_{xx} u = f$ on $(x,y)\in\Omega=[0,1]\times \mathbb{R}$ by splitting it into an equivalent first order system: $$\...
user1313292's user avatar
0 votes
1 answer
99 views

Constructing metric terms for high order elements

Given 27 $(x,y,z)$ coordinates in 3D space which describe a generally curved quadratic hexahedron, which correspond to the HEXA_27 reference element figure with planar faces in $(\xi, \eta, \zeta)$ ...
Aurelius's user avatar
  • 2,365
0 votes
1 answer
68 views

Volume change of a deformable cylinder with a uniform spinning angular velocity

Consider a deformable cylinder without gravity with a uniform spinning angular velocity and the cylinder is not in contact with anything. In theory this cylinder shouldn't change its cross sectional ...
feynman's user avatar
  • 287
0 votes
0 answers
30 views

How to derive the deformation matrix $F$ of axisymmetric problem?

I am working on a 2D axisymmetric problem and am wondering how to derive the gradient operation matrix for an element and the deformation matrix, I have no clue how to do it and after searching on the ...
YuerWu's user avatar
  • 101
0 votes
0 answers
32 views

How to express the inner product of a tensor function using matrix Frobenius inner product

Let $\{ \phi_i(x)\}_{i=1}^{M}$ and $\{ \psi_j(y)\}_{i=1}^{N}$ be bases for the finite elements spaces for $x$- ($V_{x,h}$)and $y$- direction($V_{y,h}$), respectively. Given a function $w_h \in V_h = ...
Owen Jun's user avatar
  • 141
2 votes
1 answer
176 views

Galerkin projection in AMG

In the context of Classical AMG for elliptic problems discretised with finite elements (DG or CG), one has the (fine) matrix of the problem, say $A_0$, and the coarser operators of the hierarchy $\{...
FEGirl's user avatar
  • 405
1 vote
0 answers
38 views

Best way to find the meshing with lowest number of elements allowing a max error of 1%?

So, I have a reference simulation meshing that's 100% reliable but it's costly in terms of time so I'm looking for optimizing it by finding the minimum mesh allowing at most 1% of error with respect ...
Harold Morgan's user avatar
2 votes
0 answers
92 views

Iterative solvers for problems in solid and structural mechanics

I am looking for comprehensive literature (papers, books, reports etc..) on iterative solvers for solid and structural mechanics problems to understand the best iterative solvers and preconditioners ...
Chenna K's user avatar
  • 944
1 vote
2 answers
112 views

How to handle non bilinear weak form?

I solved the 2D heat equation using the finite element method. It all went well first with the adiabatic case, however problems occured when I introduced cooling with the enviroment. I modeled the ...
Boiler4562's user avatar
3 votes
1 answer
210 views

Iterative solver for high order DG methods (3D Laplace problem)

I have a 3D Laplace problem on quite a complicated geometry where I am using Discontinuous Galerkin method. My mesh is composed by hexas, hence I am employing classical tensor product basis functions $...
FEGirl's user avatar
  • 405
2 votes
1 answer
159 views

Jacobian for 6-noded triangle in 3D to calculate the area

I would like to calculate the surface area of a 6-noded triangle element, i.e., the face of a 10-noded tetrahedral element in 3D space. A typical solution is to calculate the surface integral of the ...
reox's user avatar
  • 125
4 votes
4 answers
205 views

FEM textbooks recommendation

I would really appreciate if you could recommend me some textbooks that explain FEM process well and have many exercises to solidify the knowledge. So far, Brenner and Zienkiewicz seem to be a bit ...
Nomad's user avatar
  • 65
0 votes
0 answers
27 views

maxwell and kelvin models via prony series in abaqus

abaqus documentation only shows generalized models and their formulae. What are the prony series in abaqus for the simplest maxwell and kelvin models?
feynman's user avatar
  • 287
2 votes
2 answers
34 views

How do we implement the balance of stress on interface in ALE FSI method?

""we aim for a consistent variational-monolithic coupling scheme in which we need all equations defined in the same domain; therefore, $\mathrm{ALE}_{f x}$ was introduced. In variational ...
吴yuer's user avatar
  • 193
1 vote
2 answers
109 views

How to compute overall inertia properties from FE mass matrix?

How should I evaluate the overall mass and moments of inertia (polar and transverse) of a finite elements model, having its mass matrix? Given that the global mass matrix is composed of symmetric mass ...
temporary_pigeon's user avatar
0 votes
1 answer
66 views

mesh size restriction of spatial discretization in FEMs and FDMs

Is there any mesh size restriction of spatial discretization in FEMs and FDMs (finite difference)? If a mesh is very coarse there is still perhaps nothing to stop the program from running and cause ...
feynman's user avatar
  • 287
0 votes
1 answer
78 views

how Petrov-Galerkin FEM different from others and advantages

How is the Petrov-Galerkin FEM different from more common FEMs? Could anyone give a layman description? What's the advantages of using the Petrov-Galerkin FEM?
feynman's user avatar
  • 287
1 vote
1 answer
141 views

Nodal functionals in finite element analysis

I have a quintic Hermite basis functions [-1,1] for FEM applications, I wanted to check if it's nodal functionals are proper. Could someone explain nodal functionals in details and give an example of ...
Nomad's user avatar
  • 65
1 vote
1 answer
165 views

Simple, easy to install and use Python FEM solver (and example) for 2D cylindrical Laplace equation

In my earlier question Interpolating the gradient of a cylindrically symmetric potential field expected obey the Laplace equation, especially near/across r=0 I give a simple example of a Jacobi ...
uhoh's user avatar
  • 1,048
0 votes
1 answer
51 views

How to implement the interface extension of fluid "displacement" in ALE?

In ALE, we first set a referenced space for fluid, then we extend the boundary fluid displacement to the whole fluid region, take harmonic extension as an example, we need $$\Delta \left ( \hat{u} \...
吴yuer's user avatar
  • 193
0 votes
1 answer
102 views

Keeping the surface flat for finite element analysis

I ran the FEM analysis for a simple supported beam problem using solid elements in plane strain condition, with linear kinematics and linear elastic material. I'm not happy with the solution since ...
kstn's user avatar
  • 241
0 votes
1 answer
73 views

Any code on ALE method for N-S equations or advection-diffusion equations?

I'm currently reading the book computational fluid-structure interaction, but the book doesn't provide any code, and I can't understand the ALE method, could you please provide some codes written in ...
吴yuer's user avatar
  • 193
1 vote
1 answer
91 views

Reference request: graph Laplacian approximation for domains/manifolds

Is there any reference on solving the heat equation on irregular geometries via creating a mesh and using the graph Laplacian instead of FEM techniques? (Convergence to real solution). That is to say, ...
Aner's user avatar
  • 151
0 votes
0 answers
39 views

Continuous Finite Element vs Space Frames

Finite Element allows one to divide a continuous medium into a mesh and compute structural properties of it. Instead of discretizing the continuous, why not start with a discrete method to begin with? ...
BBSysDyn's user avatar
  • 239
1 vote
1 answer
94 views

How to generate mesh for space-time FEM method in FEniCS?

suppose that I have a region called $\Omega $,suppose that this is a 2D or 3D region, how to generate the corresponding space-time mesh by using FEniCS? and how to extract the boundary and implement ...
吴yuer's user avatar
  • 193
1 vote
1 answer
58 views

Rolling friction settings in COMMERCIAL (Ansys) finite element software

Is there a standard way of implementing rolling friction in COMMERCIAL finite element software? There's no book about such a subject in COMMERCIAL FEM software though there are books on algorithms ...
feynman's user avatar
  • 287
0 votes
1 answer
146 views

Quintic Hermite shape functions

I am trying to use quintic Hermite basis functions for FEM applications, could someone please direct me to the general formula that would help me generate quintic Hermite shape functions? In natural ...
Nomad's user avatar
  • 65
0 votes
1 answer
50 views

FEA with order reduced for a large system with a very localized force application

I have a large structure with many DOFs. But the application of force is very localized say over one or two nodes. If I try to run FEA on this with Guyan Reduction, I think the efficiency of reduction ...
s6292_1997's user avatar
2 votes
1 answer
99 views

Why can the weak forms of the Stokes and continuity equations be combined into a single equation?

Consider this Stokes equations, $$ \left\{ \begin{array}{r} - \mu \Delta \vec{u} + \nabla P = \vec{f} \\ \nabla \cdot \vec{u} = 0 \end{array} \right. $$ Weak form I is: $$ \...
Hao's user avatar
  • 21
2 votes
1 answer
246 views

Solving of KU=F leads to numpy.linalg.LinAlgError: Singular matrix

Solver.py: ...
famatto's user avatar
  • 23
2 votes
1 answer
131 views

How to calculte the contributions of a lift operator in FEM?

This question is largely motivated by the famous paper "UNIFIED ANALYSIS OF DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS" The Bassi and Rebay biliniar DG form is given in page 11 in ...
CuteCompute's user avatar
1 vote
2 answers
189 views

Query about FE approximation of a Poisson equation with non-constant coefficients

Consider the standard weak form of the Poisson equation with coefficient $\alpha$: \begin{equation} \int_\Omega \dfrac{\partial v}{\partial x} \dfrac{ \partial \left( \alpha u \right) }{\partial x} = ...
CuteCompute's user avatar
0 votes
0 answers
35 views

How to embed linear elasticity/constrain solver in non-linear soft-body dynamics

I often do simulation of dynamics of mass points connected by strings (e.g. molecular dynamics, soft body dynamics etc.). Typically I do it simply by integration of equations of motion by e.g. verlet ...
Prokop Hapala's user avatar
0 votes
0 answers
54 views

How to get Gauss points for nodal force vector (surface integral) in tetrahedral elements in the isoparametric coordinate system $({\xi \eta \zeta})$?

I am aware of the following question Evaluating the surface integral in an FEM (Finite Elements Method) procedure. But they use the volumetric coordinates while I want to use the cartesian ...
Mr Thomas Anderson's user avatar
2 votes
0 answers
92 views

Why multigrid is inefficient?

I am trying to solve the Stokes equation containing viscosity nonlinearity using the open source finite element software underworld2 with nested PETSc. The resolution is 2000*200. The solution results ...
Darcy's user avatar
  • 21
1 vote
0 answers
83 views

Seeking open-source PDE Solver for inhomogeneous material properties

I'm currently in search of an open-source PDE solver (Finite Element Method is preferred) that can effectively handle the challenge of material properties coefficients associated with each element in ...
Sadjad Abedi's user avatar
3 votes
2 answers
182 views

what preconditioner for incompressible hyperelasticity in 3d (similar to stokes equation?)?

I am working on modeling incompressible elasticity at finite strains. $$ \mathrm{Div} \boldsymbol P = \boldsymbol 0, \quad \boldsymbol X \in \Omega_0 \subset \mathbb R^3, \\ J = 1, \qquad \boldsymbol ...
Simon's user avatar
  • 165
0 votes
0 answers
23 views

uniform refinement is not working in gmsh

I get 0 node and elements when I use -refine command line flag in gmsh. Explicitly writing RefineMesh; in the script produces the original mesh and not a refined one. Am I missing something while ...
Ashb's user avatar
  • 11

1
2 3 4 5
26