Questions tagged [deal.ii]
For questions about applying the deal.II C++ Finite Element library to a computational problem.
31 questions
3
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1
answer
189
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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}(\...
1
vote
0
answers
105
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Matrix Free alternatives in dealii
I am implementing a Fast Multipole Method (FMM) in deal ii.
I do not want to store a dense matrix, but lower rank matrices and to use matrix free methods. By now, I store the elements of the low-rank ...
- 119
1
vote
1
answer
155
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c++ software packages to solve linear systems subject to constraints
I have a finite element project based on deal.II and cmake/make as build system.
I am aware of popular libraries such as deal.II, trilinos, petsc, mumps, superlu_dist,... to solve large sparse linear ...
3
votes
2
answers
214
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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 ...
1
vote
1
answer
135
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Adaptive mesh refinement with inter-element continuity
I am searching for a library that can perform adaptive mesh refinement (AMR) on large distributed unstructured meshes. For now, the cells are high-order quads/hexa.
I was looking into p4est, which is ...
- 832
4
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1
answer
395
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Under what circumstances is parallel scaling of the finite element method not "solved"?
I see things like this deal.II example, (ctrl + f for "superMUC") which seems to show some pretty impressive scaling (nearly twice as fast for twice as many CPU cores for a wide range of ...
- 155
2
votes
2
answers
275
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Errors imposing boundary conditions weakly with DG
I am using interior penalty discontinuous Galerkin to solve a simple Laplace problem:
\begin{align*}
\nabla u=0
\end{align*}
with prescribed 0 and 1 Dirichlet boundary conditions on opposite edges of ...
- 506
0
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0
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77
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deal.II and curved faces: how can I get the curved description
I'm not a deal.II expert, and while studying step-6 I was reading the documentation of the MappingQ1 class in the deal.II documentation. At some point in the description (https://www.dealii.org/...
- 435
1
vote
2
answers
325
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Find intersections between mesh and curve inside it
I have a simple square mesh, and a curve (discretised by another mesh) inside it. Here a picture worths thousand words. What I want to achieve is to find, for every cell $K$ of the circular (...
- 435
10
votes
2
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787
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FEM for vector valued problems: reference request
I'm a PhD working in a computational mechanics lab. I come from a Math department, and I have a good background for what concerns the basics of finite elements, like inf-sup conditions, DG, non-...
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3
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2
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509
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Nitsche's method for imposition of Dirichlet boundary conditions: implementation standpoint
I'm trying to understand how Nitsche's method works in practice. I understood the theoretical principle behind it, but what I can't understand is its implementation. More precisely, I'd like to solve ...
- 435
4
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0
answers
89
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Global reconstruction defined elementwise in a-posteriori error estimator
This question is a follow-up of this previous one. In "Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems" by Georgoulis et al., an error estimator is ...
- 435
0
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1
answer
112
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How is the integral of a projection over an element $T$ computed in practice? (deal.II related)
I'm studying an error estimator for the equation $\nabla\cdot(\beta u) + cu = f$ and it contains the following term $$||f - cU_h - \Pi(f-c U_h) ||_T$$
where :
$\Pi$ is the local orthogonal $L^2$ ...
- 435
2
votes
1
answer
374
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SIPG method for $-\nabla \cdot (\nu \nabla u)=f$
Consider the diffusion equation with a coefficient $\nu$: $$-\nabla \cdot (\nu \nabla u)=f$$ with Dirichlet boundary conditions $u = g_D$ in $\partial \Omega$.
If the coefficient would be constant, ...
- 435
3
votes
1
answer
265
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Time discretization Navier Stokes equation
This question is a follow-up of this one.
The weak form of Navier Stokes equation is (assuming $v,q$ test functions for the velocity and the pressure, respectively)
$$(\frac{du}{dt},v)_{\Omega} + (\...
- 309
2
votes
0
answers
160
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Confusion about preconditioner for incompressible Navier-Stokes equation with implicit-explicit method
Consider the time-dependent Navier-Stokes equation
$$u_t + (u \cdot \nabla) u - \Delta u + \nabla p = f$$
$$\operatorname{div}(u)=0$$
Looking at deal.ii tutorials, I've notice that there are ...
- 309
0
votes
1
answer
398
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deal.ii - ParaView "warp by scalar" of my output is not continuous
During our finite element course, we've solved the linear elasticity problem in 2D on a square (GridGenerator::hyper_cube) with $Q_1$ bilinear finite elements in ...
- 435
0
votes
1
answer
110
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Displacement field not correct?
Consider the elastic equation $$- \operatorname{div}(C \nabla \mathbf{u}) = \mathbf{f}$$ as presented in step-8. Here $\mathbf{u}$ is the displacement vector, let's consider the 2d case.
As you can ...
- 435
1
vote
1
answer
274
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Confusion about bilinear form for elasticity equation in deal.ii tutorial
I'm learning how to solve vector-valued problems with deal.II library. In particular, I'm looking at the following introduction from the official website https://www.dealii.org/current/doxygen/deal.II/...
- 435
2
votes
2
answers
192
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Manufactured solution for $-\operatorname{div}(a(x) \nabla{u}) = f$ when $\alpha(x)$ is discontinuous
I'm studying the dealii tutorial number 4,5 and I understand the workflow. I've also been able to find the EOC by using manufactured solution where $f$ is a smooth r.h.s. and $\alpha(x)$ smooth too.
...
- 435
1
vote
1
answer
144
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Step3 in deal.II - Convergence of the mean
I'm trying to understand the Convergence of the mean part of the Step-3 tutorial in deal.II. The authors say that $\frac{1}{|\Omega|}\int_{\Omega} u_h(x)dx$ converges with $\mathcal{O}(h^2)$, but I ...
- 435
2
votes
1
answer
374
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Gradient-jump penalty term in FEM
I am slightly confused regarding the meaning of the $i-th$ gradient-jump term $[\nabla \phi_i]$ in the context of finite element methods, used in the assembly of the stiffness matrix (an example with <...
- 155
1
vote
1
answer
1k
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Library for Discontinuous Galerkin method: FEniCS vs deal.ii
I am aware that both FEniCS and deal.ii are capable of solving problems with Discontinuous Galerkin (DG) method. I would like to specifically know if any of these two softwares can cater these ...
- 141
7
votes
3
answers
4k
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Spectral Element vs Finite Element
I am trying to understand the difference between SEM and FEM. If I go by this paper, spectral element methods are a subset of FEM methods and the only difference lies in the choice of basis functions. ...
- 73
1
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0
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85
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Radially symmetric system of PDEs in deal.II
I am trying to solve the radially symmetric polar form of the PDE with homogeneous Neumann BC in deal.II on a unit circle:
$$ u_t = \Delta u - \nabla \cdot (u \nabla h) $$
$$ h_t = \Delta h $$
I am ...
user27099
1
vote
0
answers
139
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computational tool for higher order Lagrangian interpolation for finite element
In finite element, I can calculate the Lagrangian interpolation shape functions for each degree of freedom in an element, from the the number of nodal degrees of freedom and the number of nodes ...
- 53
3
votes
2
answers
2k
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Developing a C++ solid mechanics program
I am a beginner in computational science and programming. I am doing research in non linear solid mechanics analysis and using C++ for coding. I have been exploring various finite element open source ...
- 53
2
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1
answer
261
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Boundary elements method -- calculation of solid angle
I am developing a BEM code based on a deal.ii tutorial. Consider the Poisson equation
$$
\Delta u=-f\,,
$$
and its Green's function $G\left(\mathbf{x},\mathbf{x}'\right)$ with the property
$$
\Delta ...
- 297
2
votes
1
answer
283
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Topics about the deal.II finite element library class "SparsityPattern"
When learning the deal.II FE library, I am a bit confused about the mechanism of its "SparsityPattern" class. Through reading the documentation, I only got to know that it uses the Compressed Row ...
- 699
7
votes
2
answers
369
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Comparing various implementations/software packages for large-scale finite element simulations
I currently use FEniCS and Deal.II to solve various FEM problems. I am also writing my own implementation of these problems by directly implementing the data structures, routines, and solvers within ...
- 791
5
votes
2
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252
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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 ...
- 849