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Showing 1 to 12 of 12 for “"mesh adaptivity"”.
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Multilevel Mesh Adaptivity for Elliptic Boundary Value Problems in two and three Space Dimensions
… construction of a hierarchy of locally optimal meshes starting with a coarse grid for which the location and the connectivity of the nodes is optimised. The grid is then locally refined and the new mesh is optimised in the same manner. Our hybrid algorithm does not need any global solution of …
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Computation of upper and lower bounds in limit analysis using second-order cone programming and mesh adaptivity
Limit analysis is relevant in many practical engineering areas such as the design of mechanical structures or the analysis of soil mechanics. Assuming a rigid, perfectly-plastic solid subject to a static load distribution, the problem of limit analysis consists of finding the minimum multiple of …
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Adaptive unstructured spacetime meshing for four-dimensional spacetime discontinuous Galerkin finite element methods
… methods require the generation of spacetime meshes that satisfy a special causality constraint. This work focuses on the extension of the existing 2d×time spacetime meshing algorithm known as TentPitcher to 3d×time problems. We review existing work based on TentPitcher. Then, we extend …
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Parallel Multigrid Method for Adaptive Finite Elements with Application to 3D Flow Problems
… of error estimation, solution techniques and mesh adaptivity are discussed with regard to the Navier-Stokes equations. Using a well established Navier-Stokes benchmark flow the discussed methods are verified. To cope with the huge systems arising from reactive flow problems a parallel …
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Provably convergent anisotropic output-based adaptation for continuous finite element discretizations
… error estimation combined with metric-based mesh adaptivity provides a powerful means of quantifiably controlling the error in these simulations, for output quantities of interest to engineers and scientists. The Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm, developed …
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Adaptive Finite Element Methods for Optimization in Partial Differential Equations
A new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by (elliptic) partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem …
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Asynchronous parallel solver for hyperbolic problems via the Spacetime Discontinuous Galerkin method
… which makes use of the method's unstructured mesh generation and localized solution technique to achieve a high level of parallel scalability. Our SDG method is different from most traditional adaptive finite element methods in that the solution process generates fully unstructured spacetime …
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Adaptive finite element simulation of fracture: from plastic deformation to crack propagation
… topological and physical aspects of adaptive remeshing for two types of structural systems: quasi-brittle and ductile. For ductile systems, we are interested in modeling the large deformations that occur before rupture of the material. The deformations can be so large that element distortion can …
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An adaptive high order Reynolds-averaged Navier-Stokes solver with transition prediction
… a novel methodology to adapt the boundary layer mesh to the solution "on the fly", based on a measure of the boundary layer thickness that drives the position of the nodes in the mesh, without changing its topology. The proposed algorithm produces accurate solutions with a reduced number of …
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On the role of topology and micro-structure on the adhesion and fracture of soft materials
… fraction of the network nodes is solved. Dynamic mesh adaptivity enables transition between the two representations. The method enables accurate modeling of crack initiation and propagation without apriori constraint on the fracture energy. The accuracy and computational efficiency of the method …
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Simulating and diagnosing three-dimensional multistage hydraulic fracturing with the generalized finite element method
… feature of the method is the fact that the mesh does not need to conform to the fracture geometry. Instead, the fracture is defined based on discontinuous and singular shape functions. This feature makes the method very attractive for the simulation of the complex fractures geometries that …
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Accurate FE-simulation of three-dimensional microstructures
… introduces new nodes into the computational mesh which describes the device geometry. The adaptivity is carried out according to the requirement to reduce the error of the computed solution. The main tool in doing so is error estimation with which we can localize the magnitude of the errors …