A note on reference solution based $hp$-adaptive PDE solvers

Dynamic load-balancing for PDE solvers on adaptive unstructured meshes

Modern PDE solvers written for time-dependent problems increasingly employ adaptive unstructured meshes (see Flaherty et al. [4]) in order to both increase e ciency and control the numerical error. If a distributed memory parallel computer is to be used, there arises the signi cant problem of dividing up the domain equally amongst the processors whilst minimising the intersubdomain dependencies...

A Hash Data Structure for Adaptive PDE–Solvers Based on Discontinuous Galerkin Discretizations

Adaptive multiscale methods are among the most effective techniques for the numerical solution of partial differential equations. Efficient grid management is an important task in these solvers. In this paper we focus on this problem for Discontinuous Galerkin discretization methods in 2 and 3 spatial dimensions and present a data structure for handling adaptive grids of different cell types in...

Dynamic Load-Balancing For PDE Solvers Using Adaptive Unstructured Meshes

Modern PDE solvers written for time-dependent problems increasingly employ adaptive unstructured meshes (see Flaherty et al. [4]) in order to both increase e ciency and control the numerical error. If a distributed memory parallel computer is to be used, there arises the signi cant problem of dividing up the domain equally amongst the processors whilst minimising the intersubdomain dependencies...

Parallel dynamic load-balancing for adaptive distributive memory PDE solvers

Many adaptive techniques for the solution of both steady and time-dependent PDEs rely on a hierarchy of meshes: starting with a coarse global mesh and reening this by diierent amounts in diierent regions. Since this reenement (or de-reenement) is part of the solution process it is necessary to dynamically alter the way in which the mesh is partitioned if a parallel implementation of such an alg...

Performance of PDE Sparse Solvers on Hypercubes