Adaptive refinement of finite element approximations on tetrahedral meshes is generally considered to be a non-trivial task. (We wish to stress that this paper deals with mesh refinement as opposed to remeshing.) The splitting individual finite elements needs to be done with much care to prevent significant deterioration of the shape quality of the elements of the refined meshes. Considerable c...

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The adaptivity is driven by the residual error estimator. We prove convergence even with optimal algebraic convergence rates. In particular, our analysis covers gene...

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and ma...

We present a method for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The method uses an octree as the background grid from which to build the final graded conforming meshes. The algorithm is fast and robust. It produces a small number of mesh elements and provides guaranteed bounds on the smallest dihedral angle and the two-sided Hausdorff distance betw...

In this paper we present dynamic adaptive meshes, a scheme for maintaining a conforming triangulation of time-varying surfaces. The user supplies an initial mesh, a surface sampling procedure and a set of adaptation criteria. The mesh is automatically modified in order to conform to user defined characteristics, while the surface changes over time. Our scheme is very simple to implement. It emp...

This paper presents an efficient method for the dynamic simulation of inextensible cloth. The triangle mesh for our cloth model is simulated using an impulse-based approach which is able to solve hard constraints. Using hard distance constraints on the edges of the triangle mesh removes too many degrees of freedom, resulting in a rigid motion. This is known as the locking problem which is typic...

In this work, we introduce a novel boundary-conforming mesh-update method that is particularly designed for problems with large boundary displacements and topology changes. This method, which call the surface-reconstruction virtual-region mesh update integrates virtual region approach surface reconstruction process to handle complex movements. The allows having an activated deactivated part of ...

While an indispensable tool in analysis and design applications, Computational Fluid Dynamics (CFD) is still plagued by insufficient automation and robustness in the geometryto-solution process. This thesis presents two ideas for improving automation and robustness in CFD: output-based mesh adaptation for high-order discretizations and simplex, cut-cell mesh generation. First, output-based mesh...

A great challenge for flow simulators of new generation is to gain more accuracy at well proximity within complex geological structures. For this purpose, a new approach based on hybrid mesh modeling was proposed in 2D in [1]. In this hybrid mesh, the reservoir is described by a structured quadrilateral mesh and drainage areas around wells are represented by radial circular meshes. In order to ...