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Questions tagged [deal.ii]

For questions about applying the deal.II C++ Finite Element library to a computational problem.

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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}(\...
Simon's user avatar
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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 ...
user90189's user avatar
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1 answer
131 views

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 ...
Simon's user avatar
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3 votes
2 answers
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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 ...
Simon's user avatar
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1 answer
114 views

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 ...
Zoltan Csati's user avatar
3 votes
1 answer
325 views

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 ...
Chessnerd321's user avatar
2 votes
2 answers
254 views

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 ...
CuteCompute's user avatar
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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/...
FEGirl's user avatar
  • 405
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2 answers
309 views

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 (...
FEGirl's user avatar
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10 votes
2 answers
709 views

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-...
bob_bill's user avatar
3 votes
2 answers
455 views

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 ...
FEGirl's user avatar
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4 votes
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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 ...
FEGirl's user avatar
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1 answer
109 views

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 $L^2$ ...
FEGirl's user avatar
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2 votes
1 answer
364 views

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, ...
FEGirl's user avatar
  • 405
3 votes
1 answer
248 views

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} + (\...
Vefhug's user avatar
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0 answers
148 views

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 ...
Vefhug's user avatar
  • 309
0 votes
1 answer
375 views

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 ...
FEGirl's user avatar
  • 405
0 votes
1 answer
109 views

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 ...
FEGirl's user avatar
  • 405
1 vote
1 answer
266 views

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/...
FEGirl's user avatar
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2 votes
2 answers
188 views

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. ...
FEGirl's user avatar
  • 405
1 vote
1 answer
143 views

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 ...
FEGirl's user avatar
  • 405
2 votes
1 answer
333 views

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 <...
ares's user avatar
  • 155
1 vote
1 answer
1k views

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 ...
Zxcvasdf's user avatar
  • 141
7 votes
3 answers
4k views

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. ...
efso's user avatar
  • 73
1 vote
0 answers
83 views

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 ...
user avatar
1 vote
0 answers
136 views

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 ...
user294664's user avatar
3 votes
2 answers
2k views

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 ...
user294664's user avatar
2 votes
1 answer
246 views

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 ...
sebastian_g's user avatar
2 votes
1 answer
278 views

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 ...
user123's user avatar
  • 689
7 votes
2 answers
363 views

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 ...
Justin's user avatar
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5 votes
2 answers
250 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 ...
Patrick Sanan's user avatar