Who is the author of adaptive mesh refinement?
In this lecture we will discuss an adaptive mesh refinement algorithm that was developed by Berger and Oliger ( J. Computational Physics, 53:484-512, 1984) and later refined by Berger and Colella ( J. Computational Physics, 82 (1):64-84, May 1989.) It is based in part on Bolstad’s earlier work in one dimension.
How does non uniform mesh reduce memory consumption?
Thus, a non-uniform mesh not only reduces the cost of the computation, but often more importantly it reduces memory consumption significantly.
How are grids used in structured adaptive mesh refinement?
Grids also communicate within a level, which is known as intra-level communication. This entails ghost cell information as in rb2D. We note, however, that owing to the presence of coarse-fine interfaces grids must also employ inter-level communication to fill in ghost cells. We haven’t yet said how we generated the refinements.
How are refinement structures represented in adaptive quadrature?
Refinement structures may not generally be represented as a tree, e.g. a quad-tree or oct-tree, which are employed in adaptive quadrature . A 3 level refinement structure. The base mesh is pink, and is refined by two blue level-2 grids.
How is adaptive mesh refinement used in problem solving?
In adaptive methods, one adjusts the computational effort locally to maintain a uniform level of accuracy throughout the problem domain. Adaptive Mesh Refinement (AMR) Modified equation analysis: finite difference solutions to partial differential equations behave like solutions to the original equations with a modified right-hand side.
How is the mesh organized in structured Amr?
In structured AMR we don’t represent each point on the mesh with its own value of h. Rather, we form a composite mesh organized into levels, each succeeding level with a finer spacing than the previous one. This is shown in the following figure