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0
votes
1answer
19 views

Adaptive mesh refinement algorithms and the difference between AMR and moving mesh

I'm working on my thesis and a part of it has to do with adaptive mesh refinement. As a computer science major, I'm not too familiar with this field. The best way I can put my knowledge of AMR is: I ...
3
votes
1answer
67 views

Fast methods to solve an elliptic PDE if high accuracy is needed only in part of the domain

Does someone know a method to get cheap approximation of harmonic problems (and possibly local approximations)? Let me explain: I need to compute the solution of an harmonic problem \begin{equation} ...
0
votes
0answers
27 views

what is the best way to insert node for local adaptive refinement?

Let the domain $\Omega$ (for example a square) is covered by triangles. I want to refine mesh locally. The used procedure is in the following: New nodes are inserted by looping the surrounding ...
2
votes
0answers
55 views

Adaptive Mesh vs Uniform Mesh for multiple source/boundary/initial Data

I'm going to ask some beginners' questions. Adaptive mesh can save many DOFs than a uniform mesh. But it also needs to solve linear systems changing with mesh adaptive process. Is this not problem? ...
3
votes
1answer
184 views

Meshes in codes that do AMR

In light of this question and some stuff I read online I am wondering if large FE libs (e.g., deal.ii, libmesh etc.) that do AMR keep the entire mesh or possibly a coarse version of the entire mesh on ...
9
votes
3answers
782 views

Finite Element Method vs Extended Finite Element Method (FEM vs XFEM)

What are main differences between FEM and XFEM? When should we (not) use XFEM intead of FEM and vice versa? In other words, when I meet a new problem, how I can know to use which one of them?
0
votes
0answers
32 views

library for Refine a tetrahedral volume domain over the intersection points of the edges and a level surface

I tried with fenics and tetgen but these libraries has not this functionality. an example is fenics fenics qa the idea is simple given a tetrahedrical domain $\Omega$ and a surface $\psi(x,y,z)=0$ ...
6
votes
2answers
187 views

Proving convergence of adaptive finite elements - min res FEM?

There's a body of work out there dealing with the discrete convergence of adaptive finite element methods using error estimators. Most deal with proving the property $\|u-u_{k+1}\|_U \leq (1-\alpha) ...
5
votes
3answers
249 views

Conforming mesh refinement for quads/hex elements

The context - I'm working with a spectral FE (higher order interpolation at GLL nodes) code on conforming hexahedral meshes, and our PI is interested in improving mesh quality, possibly with adaptive ...
7
votes
2answers
93 views

Convergence of adaptive finite elements with inexact solves

I'm working on some adaptive discontinuous Galerkin codes for time harmonic wave propagation, currently just Helmholtz, but will be branching out once I have a working prototype in this case. There ...
2
votes
1answer
65 views

Scalable, effective and mesh quality assuring local dynamic tetrahedral mesh refinement algorithm

I have been reading about Tetrahedral Mesh Refinement algorithms, but the literature covering this is very wide. My work involves implementation of different 3D computational geometry algorithms, and ...
10
votes
3answers
347 views

What are the basic principles behind generating a moving mesh?

I am interested in implementing an moving mesh for an advection-diffusion problem. Adaptive Moving Mesh Methods gives a good example of how to do this for Burger's equation in 1D using ...
2
votes
0answers
113 views

Adaptive mesh data structure for Fast Marching Method to overcome RAM limit

On an uniform mesh of positions in space $\ (xi,yj,zk)$: $\ xi = x0 + i*dx, 0 <=i<nx$ $\ yj = y0 + j*dy, 0 <=j<ny$ $\ zk = z0 + k*dz, 0 <=k<nz$ I have a velocity function: ...
5
votes
2answers
275 views

Interpolation schemes to move data between cells and nodes

I work on non-graded quadtree grids where the entire grid is a hierarchy of cells specified using a quadtree data structure, where, in general, there is no constraint regarding the relative size of ...
5
votes
2answers
255 views

Efficiency of a Dynamic Mesh vs. a Static Mesh for a Propagating Shockwave

I have a low speed flow with a high voltage discharge occurring within it between two spherical electrodes. We have quite a bit of data from the experiment and have performed 0-D modeling of the ...
5
votes
1answer
534 views

What are the strategies for local Adaptive Mesh Refinement (local AMR) on unstructured meshes?

I am interested in local AMR on unstructured meshes. Currently, I'm working with the OpenFOAM library - it supports completely unstructured local AMR: cell refinement criteria determine a list of ...
8
votes
1answer
188 views

Adaptive mesh refinement with perfectly matched layers?

We have an adaptive mesh refinement (AMR) code for solving the elastic wave equation with frictional fault interfaces (based on Chombo for those that are interested). One of the things that we have ...
7
votes
1answer
170 views

Red(-Green)-Refinement vs. Newest-Vertex-Bisection

What are the "Pros and Cons" for these two methods of mesh-refinement? Both seem to be the prevalent methods. I can naturally imagine that global red refinement is comparatively easy to implement and ...
18
votes
2answers
536 views

What simple methods are there for adaptively sampling a 2D function?

I have a two-dimensional function $f(x,y)$ whose values I would like to sample. The function is very expensive to compute and it has a complex shape, so I need to find a way to get the most ...
9
votes
4answers
1k views

Is there a general-purpose library for structured grid adaptive mesh refinement?

Adaptive mesh refinement (AMR) is a common technique for dealing with the problem of widely varying spatial scales in the numerical solution of PDEs. What general-purpose libraries exist for AMR on ...