The present book provides an introduction to using space-filling curves (SFC) as tools in
scientific computing. Special focus is laid on the representation of SFC and on resulting …

We present a parallel multigrid method for solving variable-coefficient elliptic partial
differential equations on arbitrary geometries using highly adapted meshes. Our method is …

We discuss the design decisions, design alternatives, and rationale behind the third
generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from …

In this article, we present a parallel geometric multigrid algorithm for solving variable-
coefficient elliptic partial differential equations on the unit box (with Dirichlet or Neumann …

This paper presents the first classical Convolutional Neural Network (CNN) that can be
applied directly to data from unstructured finite element meshes or control volume grids …

We introduce an approach for solving the incompressible Navier-Stokes equations on a
forest of Octree grids in a parallel environment. The methodology uses the p4est library of …

High-order discontinuous Galerkin (DG) methods promise to be an excellent discretization
paradigm for hyperbolic differential equation solvers running on supercomputers, since they …

In this article, we present Dendro, a suite of parallel algorithms for the discretization and
solution of partial differential equations (PDEs) involving second-order elliptic operators …

This paper presents the first classical Convolutional Neural Network (CNN) that can be
applied directly to data from unstructured finite element meshes or control volume grids …

Hilbert's two-dimensional space-filling curve is appreciated for its good locality-preserving
properties and easy implementation for many applications. However, Hilbert did not …