Questions tagged [adaptive-mesh-refinement]

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

Filter by
Sorted by
Tagged with
0 votes
0 answers
44 views

Need help with adaptive meshing code

I am trying to understand adaptive meshing and is using this code (https://github.com/esquivas/amr1d) as a reference. However, there is no documentation for it and thus, it is hard for me to ...
newbie125's user avatar
  • 101
1 vote
0 answers
37 views

Best way to find the meshing with lowest number of elements allowing a max error of 1%?

So, I have a reference simulation meshing that's 100% reliable but it's costly in terms of time so I'm looking for optimizing it by finding the minimum mesh allowing at most 1% of error with respect ...
Harold Morgan's user avatar
2 votes
1 answer
117 views

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 ...
Laurent90's user avatar
  • 1,868
1 vote
1 answer
108 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
0 votes
1 answer
133 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....
Dan Doe's user avatar
  • 1,083
5 votes
0 answers
106 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 ...
Maxim Umansky's user avatar
0 votes
0 answers
45 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 ...
Touko Puro's user avatar
5 votes
0 answers
91 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 ...
Warren's user avatar
  • 51
1 vote
1 answer
106 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 ...
Masa's user avatar
  • 194
0 votes
1 answer
184 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 ...
Masa's user avatar
  • 194
3 votes
1 answer
269 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 ...
WhatsupAndThanks's user avatar
2 votes
1 answer
156 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 ...
Al-Farouq's user avatar
3 votes
1 answer
158 views

Proof of R. Verfürth paper on adaptive mesh and bubble functions

I'm studying adaptive meshes, and my professor wrote the following property for a bubble function ( see this scicomp post for the definition I'm using)$b_T$ defined on a triangle $T$. $$||b_T \phi ||_{...
FEGirl's user avatar
  • 333
4 votes
1 answer
154 views

Computing the residual in a Dual Weighted Residual (DWR) method

I am in the process if computing the Dual-Weighted Residual (DWR) for a linear PDE with a linear functional but I am struggling with the residual part of the calculation. For example suppose we want ...
gnikit's user avatar
  • 141
0 votes
1 answer
167 views

Mesh aspect ratio issue with adaptive mesh refinement (AMR)

I am working on implementation of AMR for my finite volume code. Let me use a 2-D mesh to describe my question. Starting with SINGLE initial cell (let the mesh refine level k = 0) as a root of a quad-...
Freewill's user avatar
1 vote
1 answer
779 views

Finite Difference libray C++

What is the best FD library (or collection of libraries) for C++ codes? I am looking for some data structure implementation that offers the possibility to do parallel computations on adaptively ...
omykhron's user avatar
1 vote
1 answer
72 views

Recovery of smoothed continuous stresses using the Z^2 error estimator

I have trouble implementing the $Z^2$ error estimator (The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique by Zienkiewicz and Zhu). For this, I am ...
fruitiest Punch's user avatar
2 votes
0 answers
436 views

Implementation of Z^2 error estimator in Abaqus for adaptive mesh refinement

Currently, I am working on a remeshing routine for my simulations (Abaqus 6.14-1) using python scripts. The simulation deals with the Brinell indentation test and as the remeshing software I use Gmsh ...
fruitiest Punch's user avatar
3 votes
2 answers
571 views

Data structures of AMR(Adaptive Mesh Refinement) with quadtree

I am graduate student and recently tried to implement quad-tree based AMR. Well I have implemented simple Poisson Solver on node-based quadtree, but I am not sure that my data structure is right. To ...
Hoarsehinghing's user avatar
4 votes
2 answers
2k views

simple example of an adaptive mesh refinement code

I have been writing an adaptive mesh refinement (amr) code. As a prototype for the code, I have been looking at an adaptive mesh refinement code written by my adviser (written in c). I find looking at ...
physics_researcher's user avatar
4 votes
2 answers
164 views

Good references for dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)

Can anyone help me with good references (books or papers) where I can learn about dual-weighted residual (DWR) method for goal-oriented adaptive mesh refinement (AMR)?
Adriano's user avatar
  • 63
2 votes
1 answer
67 views

Oscillation term in a posteriori error estimator

Assume that in the a (residual type) posteriori error estimator of some PDE is a term of the form $h_T\|g\|_{L^2(\Omega)}$ involved where $h_T$ is the diameter of an element and $g$ is some known data ...
malwin's user avatar
  • 123
4 votes
3 answers
935 views

How can I make sure the flow is divergence-free when I use moving mesh?

I am using projection method and P2/P1 finite element method to solve the incompressible Navier-Stokes equations while the mesh is constantly adapted as the body moves (edge swapping, splitting and ...
shidi.yan1992's user avatar
3 votes
1 answer
672 views

p-refinement in adaptive methods

Some reference in adaptive techniques say that when the solution $u$ is smooth enough we can use p-refinement instead of h-refinement. And when we have for example singularity, we should use h-...
Rosa's user avatar
  • 533
2 votes
0 answers
157 views

scalable parallel mesh/amr on unstructured grid

I am trying to code a scalable parallel AMR for unstructured grid. There seems to be three approaches for this a) Store some global grid info on each processor and partition with parmetis (The ...
danny's user avatar
  • 233
1 vote
0 answers
66 views

Non-cubic blocks in Adaptive Mesh Refinement

Most Adaptive Mesh Refinement softwares/logic have cubic blocks. I have explored the BoxLib library and it ONLY supports cubic blocks. To be more precise it supports non-cubic blocks at the coarsest ...
Gaurav Saxena's user avatar
1 vote
0 answers
290 views

Algorithm for Adaptive Mesh Refinement

I am trying to implement Adaptive Mesh Refinement. I am not a Mathematics/Computational Science person so I will try to write the algorithm in a simpler way. I will be grateful if experts can comment ...
Gaurav Saxena's user avatar
1 vote
1 answer
273 views

fast adaptive quadrature on equispaced 2-D grid

I need to numerically evaluate 2-D integrals of the form: $$ \mathcal{I}(\theta) = \int_{0}^{1} \int_0^1 \varphi_\theta(x,y) dx dy $$ where $\varphi_\theta$ is a family of smooth functions indexed by ...
lacerbi's user avatar
  • 185
1 vote
0 answers
62 views

Square error estimate for adaptive mesh refinement

In a particular implementation(Finite volume advection using upwind) of adaptive mesh refinement the error square estimate for a cell C is given as $$ \sum_{i = x,y,z} vol * \frac{1}{12} * h^{2} * (\...
datapanda's user avatar
  • 143
0 votes
1 answer
404 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, ...
Rosa's user avatar
  • 533
1 vote
1 answer
539 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 ...
Gaurav Saxena's user avatar
2 votes
2 answers
298 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 ...
Rosa's user avatar
  • 533
3 votes
1 answer
182 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 ...
Gaurav Saxena's user avatar
2 votes
1 answer
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) ...
Gaurav Saxena's user avatar
2 votes
1 answer
108 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 ...
Rosa's user avatar
  • 533
5 votes
1 answer
232 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 ...
James's user avatar
  • 1,889
5 votes
1 answer
647 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 ...
danny's user avatar
  • 233
5 votes
2 answers
2k 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 ...
James's user avatar
  • 1,889
4 votes
1 answer
417 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 ...
yemino's user avatar
  • 515
0 votes
1 answer
144 views

How to define fluxes for two dimensional convection-diffusion equation?

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}= \...
Tanmay Agrawal's user avatar
2 votes
0 answers
423 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 ...
James's user avatar
  • 121
5 votes
1 answer
236 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 ...
Tanmay Agrawal's user avatar
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= \...
Tanmay Agrawal's user avatar
10 votes
0 answers
235 views

Time advance in Adaptive Mesh Refinement method

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 ...
Dantragof's user avatar
  • 131
1 vote
0 answers
134 views

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)....
Tanmay Agrawal's user avatar
0 votes
1 answer
300 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 ...
Tanmay Agrawal's user avatar
4 votes
1 answer
103 views

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 (...
Ben Trettel's user avatar
4 votes
2 answers
289 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 ...
inzombiak's user avatar
  • 115
3 votes
1 answer
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} ...
Tom's user avatar
  • 465
2 votes
0 answers
118 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? ...
Hui Zhang's user avatar
  • 1,319