This paper presents a new approach to a local time-space grid refinement for a staggered-grid finitedifference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that this approach is l...

A straightforward method for generating simplex space-time meshes is presented, allowing arbitrary temporal refinement in selected portions of space-time slabs. The method increases the flexibility of space-time discretizations, even in the absence of dedicated space-time mesh generation tools. The resulting tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes are tested in the ...

An adaptive finite element solver for the numerical calculation of electrostatic coupling between molecules in a solvent environment is developed and tested. At heart goal-oriented posteriori error estimate coupling, derived implemented present work, that gives rise to an orders magnitude improved precision shorter computational time as compared standard difference solvers. The accuracy new ARG...

We will present an approach to numerical simulation on recursively structured adaptive discretisation grids. The respective grid generation process is based on recursive bisection of triangles along marked edges. The resulting refinement tree is sequentialised according to a Sierpinski space-filling curve, which leads to both minimal memory requirements and inherently cache-efficient processing...

We have developed a flexible tool for efficient parallel adaptive mesh refinement on a sphere. Adaptive mesh refinement allows one to concentrate computational resources on regions of interest, and by extending to spheres we have extended their applicability to climatology and other large scale planetary phenomena. The system is effective for our space weather application and as a general purpo...

In this work, simulations with scalene triangle meshes represented by a recently proposed graphbased adaptive mesh refinement technique are described. Previously, simulations exclusively with isosceles right triangles were presented with this graph-based scheme. This data structure represents triangular meshes in finite-volume discretizations in order to solve second-order partial differential ...

This work investigates the Delaunay refinement for curved complexes. A manifold complex is defined as an unambiguous representation for the geometric objects required by a partial differential equation solver. The Chew’s and Ruppert’s Delaunay refinement algorithms, including an extension for curved complexes, are described under a new and arbitrary dimensional perspective. A theorem for strong...

Discretization error occurs during the approximate numerical solution of differential equations. Of the various sources of numerical error, discretization error is generally the largest and usually the most difficult to estimate. The goal of this paper is to review the different approaches for estimating discretization error and to present a general framework for their classification. The first...