We present a new approach to the use of parallel computers with adaptive finite element methods. This approach addresses the load balancing problem in a new way, requiring far less communication than current approaches. It also allows existing sequential adaptive PDE codes such as PLTMG and MC to run in a parallel environment without a large investment in recoding. In this new approach, the loa...

In this work, we study mesh regularization in Bank-Holst parallel adaptive paradigm when adaptive enrichment in both h (geometry) and p (degree) is used. The paradigm was first introduced by Bank and Holst in [2, 3, 1] and later extended to hp-adaptivity in [5]. In detail, the paradigm can be summarized in the following steps. Step 1 Load Balancing: The problem is solved on a coarse mesh, and a...

Complex geometries can be embedded in a mesh by using an implicit boundary representation as in the level set method or any equivalent scalar field. Such approaches enable a much more flexible way for building complex multi-domain simulations than classical body-fitted techniques that required to constraint boundaries and interfaces into the volume mesh. However, the geometrical accuracy of imp...

This paper describes a novel numerical algorithm for simulating interfacial dynamics of non-Newtonian fluids. The interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. The property and evolution of the interfacial layer is governed by a phase-field variable / that obeys a Cahn–Hilliard type of convection-diffusi...

Efficient and accurate space-charge calculations are essential for the design of high-brightness charged particle sources. Space-charge calculations in the General Particle Tracer (GPT) code make use of an efficient multigrid Poisson solver developed for non-equidistant meshes at Rostock University. GPT uses aggressive mesh-adaptation with highly non-equidistant spacing to speed up calculation ...

This report presents a mesh adaptation method for higher-order (p > 1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier-Stokes equations. The method uses a mesh of triangular elements that are not required to conform to the boundary. This triangular, cut-cell approach permits anisotropic adaptation without the difficulty of constructing meshes that conform...

This paper presents an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data primarily Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). The extracted tetrahedral and hexahedral meshes are extensively used in the Finite Element Method (FEM). Our comprehensive approach combines bilateral and anisotropic (feature specific) diffusion filtering, with...

The bounda y element method (BEM) is well suited for the electrostatic analysis of large, geometrically complex structures. When highly accurate solutions are required, the discretization (meshing) of the geometry becomes increasingly important. A scheme is required to construct optimal meshes, in the sense that maximum accuracy of the solution can be achieved with minimal computational eflort....

This paper describes an algorithm to extract adaptive and quality quadrilateral/hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without in...

This paper describes a parallel procedure for anisotropic mesh adaptation with boundary layers for use in scalable CFD simulations. The parallel mesh adaptation algorithm operates with local mesh modification operations developed for both unstructured and boundary layer parts of the mesh. The adaptive approach maintains layered elements near the viscous walls and accounts for the mesh modificat...