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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Recommendations for some new books about computational contact mechanics in solid mechanics
I want to simulate some frictional contact problems, but I'm not familiar with this field, could you please recommend some new books as introductions?thank you
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3D Quadrature schemes with points on boundary
In one dimension there are two types of quadrature schemes.
asymmetric rules like Newton-Cotes like formulas (Trapezodi, Simpson), and Clenshaw-Curtis place sampling points on boundary of the ...
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Why do we use hermite interpolation for finite element method in beams?
Why not just Lagrange polynomials basis functions
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Solving PDEs using FEM using cubic Hermite polynomials
everyone.
I am a beginner in Numerical mathematics, I have some idea of how to use Galerkin method to solve PDEs numerically, but so far I had no luck finding an example of how to solve a simple PDE ...
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eigenvalues of inhomogeneous Helmholtz equation violate superposition using FEM
I am trying to solve the in-homogeneous Helmholtz equation with damping and forcing using finite element method (FEM) with FEniCSx. The equation is;
$c^2\nabla^2p - c^2\omega i d \nabla^2p + \omega^2 ...
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references for optimization in the context of parameter identification with finite elements
i am performing parameter identification for a non-linear partial differential equation (elasticity) that I solve with finite elements.
My optimization problem is a non-linear least squares data-...
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A confusion about the bubble function in lumped mass FEM
I am studying knowledge related to lumped mass finite elements. As is well known, lumped mass finite element methods higher than 2nd order on simplex mesh require the construction of new function ...
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Is the weak form on this book about a level set FSI problem wrong?
I'm trying to repeat a level set FSI problem on the book <Level Set Methods for Fluid-Structure Interaction>, on the page 89, the provided freefem code define a weak form of the discretized ...
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Most promising reduced order modeling method
Many players in the field of engineering simulation software are investing on digital twinning and reduced order modeling techniques, meaning that the field bears potential.
I was wondering if among ...
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Confusion between standard finite element and mass-lumping finite element methods
Consider the following equation, subject to homogeneous Neumann boundary condition.
$$
u_t = \Delta u + f(u).
$$
The weak formulation is as follows:
$$
(u_t,w) = (\Delta u, w) + (f(u),w), \quad \...
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How to set Neumann BC for coupled transport problem in weak form?
Consider
$$\begin{aligned}
\partial_t v + b\cdot \nabla \phi &=0 \\
\partial_t \phi + b\cdot \nabla v &= 0
\end{aligned}$$
for $v:(x,y)\mapsto \mathbb{R}$, unknown and time-dependent ($...
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FEM for nonlinear first-order ODE
Currently I am trying to solve nonlinear Ricatti equation using FEM (Matlab language):
$$\frac{d r(z)}{dz} = i k(z) r(z) + \frac{i k(z)}{2}(\epsilon(z) - 1)(1 + r(z))^2$$
$z = [-h/2, h/2]$ and $r(-h/2)...
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FEM for a biphasic drying problem
I have the following PDE originating from a biphasic drying model, where $\xi \in [0,\Xi]$ is a radial coordinate attached to the dry skeleton of a wet cylindrical body:
$$
\frac{\partial u}{\partial ...
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Does the weighted residual method not use energy minimization in any form?
I've come across several texts/papers utilizing the concept of a minimum potential energy state corresponding to an equilibrium state, and I know that it is used in FEM formulations that are based on ...
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How to determine whether the symmetric stiffness matrix is positive definite or not? Is it related to the problem?
For two-dimensional or three-dimensional elliptic equations, when will the stiffness matrix be asymmetric and positive definite? This affected the solution efficiency so much that I had to choose an ...
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In FEM, why is the stiffness matrix positive definite?
In FEM classes, it's usually taken for granted that the stiffness matrix is positive definite, but I just can't understand why. Could anyone give some explanation?
For instance, we can consider the ...
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Defining the restriction operator in nested multigrid FEM
I'm new in the multigrid approach and I'm trying to implement an algorithm from this paper: https://www.researchgate.net/publication/242913687_A_Multigrid_Algorithm_for_the_p-Laplacian
I'm stuck with ...
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Why aren't mortar domain decomposition techniques used as much as schwarts type DD?
Schwartz type domain decomposition techniques require a transmission condition which can be hard to come by. Mortar type techniques enforce continuity with a Lagrange multiplier across domains. Are ...
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Determining the voxels between two boundary surfaces
Issue description
I am working on human brain tACS simulations where I have the models of the skin, skull, csf, brain and ventricles in STL format. The shape does not matter and there are no ...
CommunityBot
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Distributed Lagrange multiplier approach to impose constraint in Poisson equation
I'm trying to understand how Lagrange multipliers are applied in order to impose constraints in PDEs. Consider $B \subset \Omega$. For instance, a square inside another square domain $\Omega$. Let's ...
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Derivatives over a Finite Element mesh
I have a data extracted from Comsol on some node points and I know the coordinates of each node.
Does anyone know how Comsol calculate the partial derivative from the values at each node and also ...
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Does this second-order implicit Runge-Kutta method have a name?
I am studying the time-integration of the following paper,
Young, L. C. (1981). A finite-element method for reservoir simulation. Society of Petroleum Engineers Journal, 21(01), 115-128.
A copy (PDF)...
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Windows Fortran compiler for legacy Finite Element (1980) code?
The version of Fortran used comes from Montreal Ecole Polytechnique in 1980. I need a compiler for Fortran for Windows 7 or Windows 8.
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Galerkin Least-Squares stabilization for FEM solution advection (hyperbolic) equations
I am playing with Galerkin Least-Squares stabilization to solve advection diffusion problem in the context of the finite element method. This works very well for steady-state advection-diffusion ...
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How does the time needed for force propagation increase with the discretization (using symplectic Euler schemes)?
I am trying to model a physical system by (lets say the system is a long deformable object, on which I can apply forces). It can be described by Cosserat Rod theory and discretized, by modelling it ...
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recommendation on some papers/books about frontal solver used in FEM
I'm reading a program about computational plasticity, this program use frontal solver to solve the program, but I'm not familiar with frontal solver even after reading some papaers, so could you ...
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FEM 3D Solid with multiple materials
From Springer, Engineering Computation of Structures a mass matrix is defined from shape functions N based from the density tho of the material.
I expect to have to analyze a solid of multiple ...
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FE simulation of traction separation relations
I am trying to move completely open source. One of the things my research group does is cohesive zone modelling using traction separation laws, which I currently implement in ABAQUS. How easy would it ...
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In level set fluid structure interaction method why can we rewrite the elastic force in this form while there is no shear force?
when we consider a Immersed Membrane Without Shear, we can define a regularized elastic energy as $$\mathcal{E}(\varphi)=\int_{\Omega} E(|\nabla \varphi|) \frac{1}{\varepsilon} \zeta\left(\frac{\...
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Can a mixed boundary conditions in 1D Linear FE lead to non positive definite stiffness?
Consider the finite element discretisation of a general second order linear differential equation, with mixed boundary conditions at the end. The boundary conditions are given as $\alpha_0u'(0)+\...
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Dirichlet condition in finite element method
I'm trying to understand the approach described in these questions:
How to efficiently implement Dirichlet boundary conditions in global sparse finite element stiffnes matrices
How to apply non zero ...
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in Finite Element, which approximation requires less number of unknowns: B-splines vs Shape functions vs Spectral Elements
In Finite Element Analysis, one requires to approximate the solution in terms of basis functions. My questions is, which method in general is better? by 'better', I mean which involves less number of ...
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How can I validate my time integration scheme for my dynamic linear elasticity FEM code with a manufactured solution or similar?
I am solving for a dynamic linear elasticity problem:
\begin{equation}
\dfrac{\partial^2 u}{\partial^2 t} - \nabla \cdot \sigma = f
\end{equation}
where $ u \in R^2 $ with sufficient BCs and ...
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Quadrature over a triangle. Computing the dot products of the gradients
From the book "Understanding the Finite Element Method" by Mark S. Gockenbach (Chapter 7), there is stated an integral:
$$ \int_{T_k} \kappa \nabla \phi_i \cdot \nabla\phi_j. $$
for a ...
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Implementation of the roller constraint
What could be the best way to implement the roller constraint in finite element code, i.e. constraint of the type
$$\mathbf{u} \cdot \mathbf{n} = 0$$
I plan to enforce it in the weak sense by ...
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How to properly apply non-homogeneous Dirichlet boundary conditions with FEM?
In general, Dirichlet boundary conditions won't be satisfied exactly for FEM for non-homogeneous boundary conditions. The FEM codes I've seen set the degrees of freedom to interpolate the Dirichlet ...
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error estimate inequalities in finite elements
In finite element textbooks there are error estimate inequalities like
$e<~h^p$ or $e<~N^{-p/d}$, where h is the FE length scale, d the # of dimensions, p the FE order, N the # of DOFs. Are ...
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Appropriate space for weak solutions to an elliptical pde with mixed inhomogeneous boundary conditions
I'm working with the following mixed inhomogeneous boundary value problem:
$\nabla(\kappa\nabla u)=f$ in $\Omega$
with $\partial\Omega = \Omega_1 \bigcup\Omega_2$ such that
$u=g$ on $\partial\...
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Pressure boundary condition in lid driven cavity using finite element method
Thank you all
1.) I am trying to solve the lid-driven cavity problem for an incompressible Stokes and Navier Stokes equations using the general "Mixed" finite element method. Dirichlet ...
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Appropriate values for fluid-structure interaction model using finite element method in MATLAB
I'm having a program to compute the solution for a fluid-structure interaction model (blood and blood vessel walls) using FEM in MATLAB. The program is running fine but the function that I'm ...
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Solving systems of advection-diffusion-reaction equations with finite element methods
I have been doing a lot of self-study on numerically solving PDEs so that I can solve system of linear and nonlinear Advection-Diffusion-Reaction (ADR) systems on complex meshes.
I have been watching ...
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PhD in scientific computing to be a scientific programmer
Intro and disclaimer: this question concerns developing a career in Scientific Computing in industry, starting from an (applied) mathematics background, say an MSc. It definitely arises from my ...
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shape functions of interpolating a piecewise polynomial with continuous 0-th and 1-st derivatives
shape functions are the basis functions that interpolate a function in a subdomain using polynomials. linear interpolation is probably the most convenient approach which results in so-called "...
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No reasonable solution for cylindrical waveguide using FreeFEM++
I am using FreeFEM++ to simulate the cylindrical waveguide, but no reasonable solution is returned. Here I'm using the 94 GHz light ($\lambda$ = 3.17mm) as input, and radius of the waveguide is 1.27mm....
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PETSC: Solving a simpler PDE results in error while solving the original equation works in snes/tutorials/ex13.c
In snes/tutorials/ex13.c,
there is a function SetupPrimalProblem(),
which sets up the $f_0$ and $f_1$ in ...
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How to get damping matrix for structural model in FE analysis
I need to implement in C a method of obtaining transient solution of damped FE models based on modal results for a structural model (imported CAD geometry) defined with hysteretic (structural) damping....
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Continuous vs discontinuous space-time FEM
What are some reasons for approximating a (e.g. parabolic) PDE using the space-time method, with continuous finite elements in time, vs discontinuous finite elements in time?
Are there e.g. ...
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non zero dirichlet boundary condition entered in weak form
i am trying to write a julia code for linear elasticity in my case i dont have body force and traction but there is a nonzero drichlet bc(ubc) i want to engage the bc in weak form in linear part. is ...
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Equilibrium position finding with DSM
I've coded a framework that can be used to simulate the dynamic behavior of a system discretized by particles (nodes) that are connected by spring-damper elements. However, I want to compare it to a ...
