All Questions
1,333 questions
3
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Rigid Body Elements
I am currently developing structural FEM solver in FORTRAN. My question is about Rigid Body Elements (Multi Point Constraints).
In NASTRAN there is RBE2 element defined by one independent and one or ...
2
votes
0
answers
3k
views
COMSOL - Implementing Perfectly Matched Layers (3D)
If there are any COMSOL gurus here, I want to simulate a 3D RF system infinite in 1 direction. I realize I need to use PML's, but am unsure how to configure them. it seems that simply scaling them by ...
- 21
2
votes
0
answers
78
views
Complexity of direct solvers? [duplicate]
Possible Duplicate:
How to reorder variables to produce a banded matrix of minimum bandwidth?
What is the time and space complexity of direct sparse solvers (e.g., UMFPACK, SUPERLU, PARDISO, etc.)...
- 800
30
votes
9
answers
2k
views
What is a good way to run parameter studies in C++
The problem
I'm currently working on a Finite Element Navier Stokes simulation and I would like to investigate the effects of a variety of parameters. Some parameters are specified in an input file ...
- 505
8
votes
5
answers
862
views
Recommended Route for Mastering Inverse PDE Problems
I would like to master Inverse PDE Problems particularly with the use of Finite Elements. My problem is I don't know where to start. Should I begin by reading a book on Inverse Problems or on PDE-...
- 81
9
votes
3
answers
2k
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Construction of $C^1$/$H^2$-conforming finite element basis for triangular or tetrahedral mesh
In the paper Hierarchical Conforming Finite Element Methods for the Biharmonic Equation, P. Oswald claimed Clough-Tocher type elements has $C^1$-continuity while being a cubic polynomial on each ...
- 2,552
7
votes
1
answer
309
views
Forced viscous damping in elastodynamics
I have an 2D elastodynamics problem, that is a problem which is driven by the Cauchy equation:
$$\rho\ddot u-\mathrm{div}\sigma=\rho f$$
where $u$ is the displacement, $\sigma$ the Cauchy stress ...
- 265
11
votes
2
answers
7k
views
FEM: singularity of the stiffness matrix
I'm solving the differential equation
$$
\left( \sigma^{2}(x) u ''(x) \right)'' = f(x), \;\;\; 0 \leqslant x \leqslant 1
$$
with initial conditions $u(0) = u(1) = 0$, $u''(...
- 445
5
votes
2
answers
572
views
What does symmetrize mean? (imposing multifreedom constraints to stiffness matrix)
I have a small FEM implementation program. And I want to add imposing multifreedom constraints (MFC) feature to it. The theory of master-slave method is given here (page 10 for general case).
...
- 501
10
votes
2
answers
380
views
What about this simple error estimate for linear PDE?
Let $\Omega$ be a convex polygonally bounded Lipschitz domain in $\mathbb R^2$, let $f \in L^2(\Omega)$.
Then the solution of the Dirichlet problem $\Delta u = f$ in $\Omega$, $\operatorname{trace} u ...
- 3,720
8
votes
2
answers
159
views
Initial guesses for perturbed linear systems
Suppose you solve a linear system $Au = f$ by an iterative method, e.g. conjugate gradients or Richardson iteration. Then you try to solve a linear system that is slightly perturbed in the matrix and ...
- 3,720
9
votes
3
answers
2k
views
Standard format for finite element meshes
Does there exist a standard format for finite element meshes which is widely used in the industry?
Thanks!
- 265
33
votes
9
answers
6k
views
Modern resources for learning FEM
I need to get started using Finite Element Methods. I am about to start reading Numerical solutions of partial differential equations by the finite element method by Claes Johnson, but it's dated 1987....
- 1,739
25
votes
4
answers
4k
views
How to incorporate the boundary conditions with the Galerkin method?
I've been reading some resources on the web about Galerkin methods to solve PDEs, but I'm not clear about something. The following is my own account of what I have understood.
Consider the following ...
- 1,739
4
votes
0
answers
358
views
How does one handle the source term in the Shallow Water Equations when using the discontinuous galerkin method? [closed]
I use the discontinuous galerkin method to solve the steady flow 1D shallow water equations with a bump at the bottom. This flow is frictionless.
I use the runge-kutta method to approximate the time ...
- 57
7
votes
1
answer
187
views
Conjugate Gradient with Hierarchical Basis Functions: How can the hierarchical base be decomposed?
I'm trying to implement a Conjugate Gradient solver using Hierarchical Basis Functions, following this paper.
In section 3 the paper says that the hierarchical basis matrix $S$ can be decomposed into ...
- 435
8
votes
2
answers
2k
views
Shape regularity in higher dimensions
In Finite Element theory, and other methods in scientific computing for PDEs, one uses meshes which fulfill several regularity criteria, many of them being equivalent.
It is of interest to have ...
- 3,720
7
votes
2
answers
2k
views
Reference implementation of Nédélec-Elements
Does anybody know of an implementation of Nédélec elements that does not come along with a huge bulk of additional software?
Is there a small library written in a language like Python, Matlab, or ...
- 3,720
6
votes
2
answers
2k
views
Which libraries have good implementations of Basis splines?
I'm looking to use the finite element method with B-splines as my function basis. Which C/C++ libraries have good B-spline support?
Specifically, I'm looking for an implementation of a stable ...
- 3,355
19
votes
1
answer
6k
views
How to derive the Weak Formulation of a Partial Differential Equation for Finite Element Method?
I have taken a basic introduction to Finite Element Method, which did not emphasize a sophisticated understanding of a 'weak formulation'. I understand that with the galerkin method, we multiply both ...
- 12.2k
11
votes
1
answer
350
views
What are the possible numerical schemes for a diffusion equation with a nonlinear reaction term?
For some simple convex domain $\Omega$ in 2D, we have some $u(x)$ satisfying the following equation:
$$
-\mathrm{div}(A\nabla u)+cu^n = f
$$
with certain Dirichlet and/or Neumann boundary conditions....
- 2,552
10
votes
1
answer
262
views
Quadrature rules, methodologies, and references
There is at least one quite comprehensive encyclopaedia of quadrature rules that doesn't seem to have been updated in quite a while and has restricted access. This source refers to several classical ...
6
votes
0
answers
615
views
How to do FEM in sector elements?
Suppose we have an element in the polar coordinate as $0\leq r\leq 1$, $0\leq\theta\leq \alpha$. What are the correct basis functions in this element? For this kind of mesh, there
are a lot of ...
- 1,319
10
votes
2
answers
2k
views
Are 8 Gauss points required for second order hexahedral finite elements?
Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical ...
- 3,969
5
votes
2
answers
2k
views
Solution oscillations with a small timestep in backward Euler
I am using backward Euler in a FEM scheme for a convection-diffusion problem. On a given mesh, I can take arbitrarily large time steps, as expected. But if I decrease time step, at some point it will ...
- 186
3
votes
2
answers
1k
views
Looking for a library or algorithms to perfom clipping 3D unstructured meshes by a set of surfaces
We have a 3D (volume) unstructured, possibly hybrid, degenerative irregular mesh data structure that we are capable of generating (mostly composed of hexahedra and general polyhedra, using a mix of ...
9
votes
1
answer
725
views
What numerical quadrature to choose to integrate a function with singularities?
For example, I would like to numerically compute the $L^2$-norm of $\displaystyle u = \frac{1}{(x^2+y^2+z^2)^{1/3}}$ in some domain that includes zero, I tried Gauss quadrature and it fails, it is ...
- 2,552
8
votes
2
answers
246
views
Is there one general approach to build a projection methods for different problems?
My question is probably going to be too general to answer it with a couple words. Could you please suggest a good reading in that case. Projection methods are used to reduce size of the solution space ...
- 501
55
votes
5
answers
11k
views
What are criteria to choose between finite-differences and finite-elements
I am used to thinking of finite-differences as a special case of finite-elements, on a very constrained grid. So what are the conditions on how to choose between Finite Difference Method (FDM) and ...
- 3,720
5
votes
5
answers
1k
views
Introductions to hp-FEM
do you know good introductions into or surveys $hp$-adaptive finite elements?
In particular I do not know how the heuristics for choosing spatial refinement or increased polynomial degree are ...
- 3,720
13
votes
1
answer
2k
views
What are possible methods to solve compressible Euler equations
I would like to write my own solver for compressible Euler equations, and most importantly I want it to work robustly in all situations. I would like it to be FE based (DG is ok). What are the ...
- 2,930
9
votes
2
answers
803
views
Coupling FEM DG methods to Riemann solvers
Are there any good papers and or codes that couple discontinuous galerkin finite element solvers with Riemann solvers?
I need to explore coupling elliptic and hyperbolic problems but most splitting ...
- 3,624
14
votes
1
answer
463
views
What spatial discretizations work for incompressible flow with anisotropic boundary meshes?
High Reynolds number flows produce very thin boundary layers. If wall resolution is used in Large Eddy Simulation, the aspect ratio may be on the order of $10^6$. Many methods become unstable in this ...
- 25.8k