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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.

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how to compute the rate of deformation gradient in finite-element context?

I am implementing hyper visco-elastic material models similar to those from Pioletti et al. see here There, a viscous potential, e.g $W_v = \eta [I_1-3]J_2 \quad \text{with} \quad J_2 = \mathrm{tr}(\...
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Thermo Hydraulic Mechanical modeling of energy wall slab in camsol multiphysics

I am currently working on a complex simulation project involving an energy wall slab, and I need assistance in accurately modeling and validating it using COMSOL Multiphysics. Here are the details of ...
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Any FEM book recommendations that focus on stability and proofs on error bounds?

Everything from descrete stability proofs for steady state and time dependent problems. energy stability, stability of mixed methods, nonlinear problems, vector valued problems in fluid/structural/EM, ...
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Getting singular matrices for lid driven cavity problem

I was trying to solve the lid driven cavity problem using the galerkin method with SUPG stabilization. I was using GMRES method as my solver and I am also getting a solution. And the solution looks ...
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Lumped (diagonal) vs. consistent (non-diagonal, symmetric) mass matrix in Nastran

I've been tinkering with DMAP to explore the procedure followed by Nastran when solving a complex modes analysis. I've reached a passage I cannot understand: at some point Nastran formulated what it ...
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Immersed Boundary FEM reference recommendation

I want to do some Fluid-Structure Interaction using the Immersed Boundary FEM. Could you please recommend some books or lecture notes on it?
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What do diagonal (DOF-to-self) terms of stiffness matrix physically mean?

I am used to interpreting each entry of a solid mechanic system's stiffness matrix as a 1D (linear or angular) spring joining one DOF (column index) to another (row index). But this interpretation ...
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Can finite element exterior calculus be used for the proof of discrete stability?

I've heard about Finite Element Exterior Calculus (FEEC) and its applications in numerical simulations, but can FEEC be utilised to prove discrete stability in computational methods? If so, can the ...
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How to assemble K local matrix for a hexahedron cell in a piecewise linear fashion?

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How to constraint the tangential gradient on a boundary in FEniCS?

The problem I'm considering is a 2D scalar PDE. The domain $\Omega$ is a disk with two holes $\partial\Omega_1$ and $\partial\Omega_2$ and an external boundary $\partial\Omega_0$. The PDE and boundary ...
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How to expand the C matrix for three aditional degrees of freedom for rotational forces?

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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 ...
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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
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Formulation of K for tetrahedral elements for the Finite Element Method

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prusso's user avatar
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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 ...
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"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 ...
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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{...
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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), ...
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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
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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
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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
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1 answer
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Can domain decomposition methods also be applied to linear systems resulting from finite difference discretizations?

Question In general, do domain decomposition methods (DDMs) require a linear system of equations $Au = f$ to be formed by finite element discretization/method (FEM) of a PDE? Or could one simply use a ...
Jared Frazier's user avatar
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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
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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: $$\...
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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 $(\xi, \eta, \zeta)$ ...
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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
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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
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2 votes
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177 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
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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
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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 ...
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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
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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
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1 answer
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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
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4 answers
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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 ...
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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
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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
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2 answers
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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
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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
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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
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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
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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
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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
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1 answer
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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 ...
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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
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1 answer
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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
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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
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1 answer
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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
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1 vote
1 answer
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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
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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
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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 ...
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