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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 ...
Adaptive methods are used to improve the accuracy of the solutions. The adaptive method is referred to as ‘h’ method if mesh refinement is used, ‘r’ method if the number of grid point is fixed and not redistributed and ‘p’ if the order of solution scheme is increased in finite-element theory.
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 ...
gpops2.com. GPOPS-II (pronounced "GPOPS 2") is a general-purpose MATLAB software for solving continuous optimal control problems using hp-adaptive Gaussian quadrature collocation and sparse nonlinear programming. The acronym GPOPS stands for " G eneral P urpose OP timal Control S oftware", and the Roman numeral "II" refers to the fact that ...
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 ...
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]
mesh adaptive-refinement: Yes, full adaptive mesh refinement (h-refinement); no p-refinement but several higher-order elements are included. Mesh adaptation on the whole or parts of the geometry, for stationary, eigenvalue, and time-dependent simulations and by rebuilding the entire mesh or refining chosen mesh elements.