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Adaptive mesh refinement. In numerical analysis, adaptive mesh refinement (AMR) is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated. When solutions are calculated numerically, they are often limited to predetermined ...
In adaptive mesh refinement, elements are split (h-refinement) in areas where the function being calculated has a high gradient. Meshes are also coarsened, removing elements for efficiency. The multigrid method does something similar to refinement and coarsening to speed up the numerical solve, but without actually changing the mesh.
The Bolshoi simulation employs a version of an adaptive mesh refinement (AMR) algorithm called an adaptive refinement tree (ART), in which a cube in space with more than a predefined density of matter is recursively divided into a mesh of smaller cubes. The subdivision continues to a limiting level, chosen to avoid using too much supercomputer ...
hp-FEM is a generalization of the finite element method (FEM) for solving partial differential equations numerically based on piecewise-polynomial approximations. hp-FEM originates from the discovery by Barna A. Szabó and Ivo Babuška that the finite element method converges exponentially fast when the mesh is refined using a suitable combination of h-refinements (dividing elements into ...
These wavelet methods can be combined with multigrid methods. [15] [16] For example, one use of wavelets is to reformulate the finite element approach in terms of a multilevel method. [17] Adaptive multigrid exhibits adaptive mesh refinement, that is, it adjusts the grid as the computation proceeds, in a manner dependent upon the computation ...
Adaptive mesh refinement (AMR) as a numerical method has roots that go well beyond its first application in the field of numerical relativity. Mesh refinement first appears in the numerical relativity literature in the 1980s, through the work of Choptuik in his studies of critical collapse of scalar fields.
Website. mfem.org. MFEM is an open-source C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore National Laboratory and the MFEM open-source community on GitHub. MFEM is free software released under a BSD license. [1]
Delaunay refinement. In mesh generation, Delaunay refinements are algorithms for mesh generation based on the principle of adding Steiner points to the geometry of an input to be meshed, in a way that causes the Delaunay triangulation or constrained Delaunay triangulation of the augmented input to meet the quality requirements of the meshing ...