For questions about AMR, a technique for dynamically updating the precision of a grid to ensure a certain accuracy for a given region.

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### AMR framework for efficient simulation of PDEs, potentially with boundary layers

I am aiming at developing a simulation software mostly aimed at reactive fluid flows applications. Here are a simplified list of points to drive the initial choices (code structure, libraries...): I ...
1 vote
88 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 ...
116 views

### AMR-Capable meshing software that is not based on quad/octrees

I am looking for AMR/re-meshing software (structured grids would suffice) that is NOT based on quad-octrees, i.e., a fixed refinement rate of 2 but (ideally) something user defined, i.e., ratios of 1....
97 views

### Grid rearrangement for anisotropic transport simulations

In computational plasma physics, one often faces problems with extremely high transport anisotropy, 1e6 and more, since transport along the magnetic field is much faster than across. To deal with this ...
36 views

### Refluxing step on Finite difference AMR

Hi I am a computer scientist working on MHD code for astrophysics simulation. We use a finite difference scheme where we first solve the spatial derivatives and with them solve the right hand side and ...
89 views

### How to get an "optimal point" for refinement in FEM adaptive mesh refinement?

Consider the following 1D problem \begin{align*} \begin{cases} \displaystyle -\frac{d^2u}{dx^2} = f(x), \hspace{0.5cm} x\in (a,b) \\[4mm] u(a) = u_{a}, \ \ u(b) = u_{b} \end{cases} \end{align*} I ...
1 vote
99 views

### numerical integration of integrals in the p-adaptive version of the finite element method

In the p-adaptive version of the finite element method, elements are allowed to have shape functions with arbitrary different polynomial orders. Therefore regarding a 2D problem with quadrilateral ...
159 views

### Mesh refinement in the Finite Element Method

I need some good references on how to implement programmatically the hp-refinement of meshes in the Finite Element Method in two/three-dimension. I've searched the web a lot and read many articles and ...
206 views

### Comparison on adaptive mesh refinement on finite elements and finite differences

My current work requires using (Adaptive Mesh Refinement) AMR to resolve multi scale physics. I have a general question whether finite element is better than finite difference in this aspect or not. I ...
138 views

### Connectivity of octree as grid

What is the algorithm which transforms the octree/quadtree into a grid? i.e, getting the adjacency or connectivity between the cells in order to be able to perform interpolation, gradient,...etc. I am ...
147 views

401 views

### How to deal with transition elements in adaptive fem

It is necessary for me to solve a Poisson equation by adaptive finite element method with transition elements technique to get conforming mesh. For the first local refinement everything is OK, ...
1 vote
490 views

### Non-uniform finite difference Adaptive Mesh Refinement

Assuming that the crosses in the figure below are unknowns in a vertex-centered finite difference scheme in an Adaptive Mesh, how can I calculate the double derivate (Laplacian) at the Red x ? The Red ...
264 views

### Finite element results by different meshes

There are some technique to generate mesh in a domain. My qustion is that: Is there any difference between the results using different techniques for mesh generation? If yes which one is better. For ...
177 views

### Refinement in AMR

Assume I start with an 8x8 coarse mesh (see Fig 1) where the vertices (except boundary vertices) represent the unknown variable. After iterative approximation - I ...
1k views

### Implementing Finite Difference Adaptive Mesh Refinement code

For a start I need to implement a 2-D, vertex centered, finite difference scheme, Adaptive mesh refinement serial code. I have the following doubts before starting: Is the input to AMR (say 2-D) ...
105 views

### Strategies for controlling number of new elements in adaptive mesh refinement

I am working on adaptive techniques for solving some elliptic equations. The technique is based on residual on elements. My problem is that when I use a predefined tolerance for refining elements, the ...
217 views

### Using finite element error estimators for adaptive mesh refinement

I am in the process of implementing adaptive mesh refinement for a finite element code that solves the Poisson equation. I have had some trouble finding good references on deciding which elements to ...
633 views

### unstructured grid AMR

Are there libraries for conducting parallel AMR on an unstructured grid ? For a finite volume code, polyhedral cells with arbitrarily shaped faces are as easy to handle as hexahedra, and infact ...
1k views

### How to implement adaptive mesh refinement using conformal triangles

I am trying to implement adaptive mesh refinement for a finite element code. The code uses (at least for now) linear triangles and so when I do the mesh refinement I want the triangular mesh to remain ...
411 views

### Finite element mesh software

I'm looking for a program to obtain meshes to finite element codes 2D and 3D as complete as possible, preferably in fortran 90 or C/C++. For example, softwares "Triangle" or "TetGen" generate meshes ...
136 views

I want to solve the following differential equation using control volume approach on a Cartesian mesh: $$\frac{\partial T}{\partial t} + \frac{\partial T}{\partial x} + \frac{\partial T}{\partial y}= \... 2 votes 0 answers 411 views ### Adaptive Finite Element Method - Laplace I'm currently attempting to turn my code for solving the laplace equation using finite element approximations into an adaptive one using the dual weighted residual as my error estimator: i.e. my ... 5 votes 1 answer 231 views ### Flux at coarse-fine mesh grid interface? I am trying to solve one dimensional inviscid Burger's equation using adaptive mesh refinement. This is the PDE:$$\frac{\delta U}{\delta t} + \frac{\delta F}{\delta x} = 0$$where the flux F of the ... 4 votes 2 answers 2k views ### How to discretize Burger's equation? I am trying to solve the very simple one dimensional burgers equation which is:$$\frac{\delta U}{\delta t} + \frac{\delta F}{\delta x} = 0$$where the flux F of some variable U is defined as$$ F= \...
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I am working on solving complex system of 2D PDEs governing the behaviour of plasma in a gas lamp during discharge. Recent tests have shown that because of steep gradients in temperature field and ...
1 vote
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### Conservation at grid interface in adaptive mesh refinement

I am using adaptive mesh refinement to solve one dimensional inviscid Burgers equation. However I am facing some difficulty to handle grid interfaces which are not uniform (coarse-fine grid interface)....
288 views

### Adaptive mesh refinement basic conceptual problem

I am a beginner in adaptive mesh refinement (AMR). After I am done with the first two papers by Dr. Marsha Berger, I was trying to write my own code for a problem which has a parabolic partial ...
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### How can I compare errors in PDE solvers with non-uniform grids?

Is there a standard approach to testing codes with refined regions? Specifically, I am interested in testing whether the refinement is working correctly. For the sake of simplicity, let's consider a (...
276 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 ...
107 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} ...
108 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? ...