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 …

Abstract ExaHyPE (“An Exascale Hyperbolic PDE Engine”) is a software engine for solving
systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are …

In this paper we first review the development of high order ADER finite volume and ADER
discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in …

We present a new class of high-order accurate numerical algorithms for solving the
equations of general-relativistic ideal magnetohydrodynamics in curved space–times. In this …

In this paper we discuss a new and very efficient implementation of high order accurate
arbitrary high order schemes using derivatives discontinuous Galerkin (ADER-DG) finite …

Earthquake fault zones are more complex, both geometrically and rheologically, than an
idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear …

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 paper, we propose a novel family of semi-implicit hybrid finite volume/finite element
schemes for computational fluid dynamics (CFD), in particular for the approximate solution of …

The finite cell method (FCM) is an immersed domain finite element method that combines
higher‐order non‐boundary‐fitted meshes, weak enforcement of Dirichlet boundary …

We present the design and implementation details of a geometric multigrid method on
adaptively refined meshes for massively parallel computations. The method uses local …