AMReX-Codes/amrex: AMReX 19.05.1
Ann AlmgrenVince BecknerJohannes BlaschkeCy ChanMarc DayBrian FriesenKevin GottDaniel GravesMaximilian KatzAndrew MyersTan NguyenAndrew NonakaMichele RossoSamuel WilliamsWeiqun ZhangM. Zingale
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Adaptive mesh refinement has the potential of making the finite element computation of magnetic field problems completely automatic. In adaptive procedures, the field problem is solved iteratively, beginning with a coarse mesh and refining it in locations of greatest error. Methods of mesh refinement for triangular finite element grids are surveyed and the use of local error estimates in the adaptive process is described. It is concluded that the Delaunay triangulation provides the best method of mesh refinement, while complementary variational principles provide accurate error bounds on the solution.
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Abstract A simple strategy to adaptively refine three dimensional tetrahedral meshes has been implemented. A method of refinement for both plane faced and curve faced elements is presented in this paper. Examples are presented in which the rcmeshing is based on a refinement ratio determined from an a-posteriori error indicator obtained from the finite element solution of the problem. The resulting finite element meshes have a smooth gradient in element size. Example meshes are included to show the adaptive nature of the remesher when applied over several solution cycles.
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An effective method of nonlinear finite element analysis is proposed. In the method, a coarse mesh is employed at the beginning of the analysis and elements are refined progressively in an incremental procedure if the amount of absorbed strain energy reaches a given value. Stresses of refined elements are determined under the assumption that they can be interpolated by the same function as displacements. The mixed shape functions are used for "odd" elements having 5, 6, 7 or 8 nodes which are generated by the mesh refinement. To demonstrate the validity of the present algorithm, a series of numerical results are shown, where the calculated load-displacement curves approach the accurate curves as initial meshes are refined progressively in highly distorted areas.
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In the applications of FEM. a compromise between the accuracy and the computation cost is often required, especially when 3D cases are concerned Adaptive mesh refinement is a good answer to this demand.
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An upgrade of an a posteriori error-estimation algorithm, based on the residual evaluation, is presented. This extension overcomes a drawback of the original algorithm, which estimates the error just on the solution of the problem, by also estimating the error on the gradient of the solution. For some test cases, the performance of the method is assessed by comparison with analytical results.< >
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In this paper h-adaptive finite element scheme is presented. It involves the a-posteriori error estimating, the prediction of local mesh refinement with element size calculating and adaptive mesh regeneration.
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