Questions tagged [adaptive-mesh-refinement]

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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 ...
4
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219 views

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

On an uniform mesh of positions in space $\ (x_i,y_j,z_k)$: $$\ x_i = x_0 + i\Delta x,\quad i=0,\ldots,n_x$$ $$\ y_j = y_0 + j\Delta y,\quad j=0,\ldots,n_y$$ $$\ z_k = z_0 + k\Delta z,\quad k=0,\...
2
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0answers
114 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 ...
2
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332 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 ...
2
votes
0answers
97 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? ...
1
vote
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52 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 ...
1
vote
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128 views

Preventing numerical oscillations with Cash-Karp method

I am implementing an ODE solver using the Cash-Karp method on equations with the following form: $$ \frac {d E}{d z} = - \frac {1}{\mu_0c} \frac {d ^2 E}{d z^2} + \frac {i}{\mu_0c}E \tag{1} $$ And ...
1
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176 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 ...
1
vote
0answers
51 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} * (\...
1
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104 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)....