Arbitrary dimension convection–diffusion schemes for space–time discretizations

Robust Preconditioners for DG–Discretizations with Arbitrary Polynomial Degrees

Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. With a focus on diffusion problems, we consider DG discretizations for elliptic boundary value problems, in particular the efficient solution of the linear systems of equations that arise from the Symmetric Interior Pen...

ENO Multiresolution Schemes with General Discretizations

Harten’s framework is a nonlinear generalization of the wavelet framework. Previously, the choice of discretization (scaling function) in Harten multiresolution schemes has been limited to point-value, cell-average, and hat-based discretization. This paper shows how to construct multiresolution schemes consistent with Harten’s framework for a variety of discretizations. The construction here be...

Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension

Connectivity Compression in Arbitrary Dimension

This paper presents a general lossless connectivity compression scheme for manifolds in any dimension with arbitrary cells, orientable or not, with or without borders. Relying on a generic topological model called generalized maps, our method performs a regiongrowing traversal of its primitive elements while describing connectivity relations with symbols. The set of produced symbols is compress...

Diamond Hierarchies of Arbitrary Dimension

Nested simplicial meshes generated by the simplicial bisection decomposition proposed by Maubach [Mau95] have been widely used in 2D and 3D as multi-resolution models of terrains and three-dimensional scalar fields, They are an alternative to octree representation since they allow generating crack-free representations of the underlying field. On the other hand, this method generates conforming ...