| We present a new method for adaptive surface meshing and triangulation which controls the local level-of-detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi-orthogonal tensor product wavelet transform (WT) and to ana...

A cut-cell adaptive method is presented for high-order discontinuous Galerkin discretizations in two and three dimensions. The computational mesh is constructed by cutting a curved geometry out of a simplex background mesh that does not conform to the geometry boundary. The geometry is represented with cubic splines in two dimensions and with a tesselation of quadratic patches in three dimensio...

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det⁡∇ψ(x,t)=G∘ψ(x,t). The novelty our approach new so-called perturbation formulation MA, constructs map ψ via composition sequence near-identity deformations reference mesh. Then, we formulate versi...

The Bank-Holst parallel adaptive meshing paradigm [2, 3, 1] is utilised to solve (1) in a combination of domain decomposition and adaptivity. It can be summarised as follows: Step I Mesh Partition: Starting with a coarse mesh TH , the domain is partitioned into non-overlapping subdomains: Ω = ∪pi=1Ωi. Step II Adaptive Meshing: Each processor i is provided with TH and instructed to sequentially ...

We present a new method for adaptive surface meshing and triangulation which controls the local level-of-detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi-orthogonal tensor product wavelet transform (WT) and to analy...

Perhaps the most common approach to solving PDEs in engineering applications is through use of nite-element approximations. In free-boundary problems this usually requires adaptive meshing that tracks the surface motion. These meshing schemes may not be able to handle shock formation or topological changes without arcane logic or user intervention. Inconvenient in simulation, this can cause gra...

This paper describes an adaptive mesh refinement algorithm for improving the accuracy in the solution of electromagnetic problems in transmission lines. A residual error indicator is used for detecting the refinement zones, and two h-refinement techniques for triangular meshes (the longest edge bisection and the regular split) are applied for increasing the degrees of freedom in the mesh. This ...

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoid...

In numerical calculations based on partial differential equations the kind of discretization, in particular the kind of mesh that can bo used is ol almost importance. Unfortunately, meshing is a rather unsolved discipline, especia y in three dimensions. Although some occasional solutions exists there is hardly a tool that has integrated possibilities to handle this problem. This paper presents ...