Outputs (24)

A multiresolution Discrete Element Method for triangulated objects with implicit time stepping (2022)
Journal Article

Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are nonspherical. The most expensive part within such a simulation code is the colli... Read More about A multiresolution Discrete Element Method for triangulated objects with implicit time stepping.

Spherical accretion of collisional gas in modified gravity I: self-similar solutions and a new cosmological hydrodynamical code (2022)
Journal Article

The spherical collapse scenario has great importance in cosmology since it captures several crucial aspects of structure formation. The presence of self-similar solutions in the Einstein-de Sitter (EdS) model greatly simplifies its analysis, making i... Read More about Spherical accretion of collisional gas in modified gravity I: self-similar solutions and a new cosmological hydrodynamical code.

Stabilized Asynchronous Fast Adaptive Composite Multigrid using Additive Damping (2020)
Journal Article

Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an expensive coarse g... Read More about Stabilized Asynchronous Fast Adaptive Composite Multigrid using Additive Damping.

Delayed approximate matrix assembly in multigrid with dynamic precisions (2020)
Journal Article

The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix‐free environment where we have to be able to quickly return... Read More about Delayed approximate matrix assembly in multigrid with dynamic precisions.

Lightweight Task Offloading Exploiting MPI Wait Times for Parallel Adaptive Mesh Refinement (2020)
Journal Article

Balancing the workload of sophisticated simulations is inherently difficult, since we have to balance both computational workload and memory footprint over meshes that can change any time or yield unpredictable cost per mesh entity, while modern supe... Read More about Lightweight Task Offloading Exploiting MPI Wait Times for Parallel Adaptive Mesh Refinement.

Enclave Tasking for DG Methods on Dynamically Adaptive Meshes (2020)
Journal Article

High-order discontinuous Galerkin (DG) methods promise to be an excellent discretization paradigm for hyperbolic differential equation solvers running on supercomputers, since they combine high arithmetic intensity with localized data access, since t... Read More about Enclave Tasking for DG Methods on Dynamically Adaptive Meshes.

ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems (2020)
Journal Article

ExaHyPE (“An Exascale Hyperbolic PDE Engine”) is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are useful in a wi... Read More about ExaHyPE: An engine for parallel dynamically adaptive simulations of wave problems.

The Peano software---parallel, automaton-based, dynamically adaptive grid traversals (2019)
Journal Article

We discuss the design decisions, design alternatives, and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports on... Read More about The Peano software---parallel, automaton-based, dynamically adaptive grid traversals.

Studies on the energy and deep memory behaviour of a cache-oblivious, task-based hyperbolic PDE solver (2019)
Journal Article

We study the performance behaviour of a seismic simulation using the ExaHyPE engine with a specific focus on memory characteristics and energy needs. ExaHyPE combines dynamically adaptive mesh refinement (AMR) with ADER-DG. It is parallelized using t... Read More about Studies on the energy and deep memory behaviour of a cache-oblivious, task-based hyperbolic PDE solver.

A simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topography (2019)
Journal Article

In most classical approaches of computational geophysics for seismic wave propagation problems, complex surface topography is either accounted for by boundary-fitted unstructured meshes, or, where possible, by mapping the complex computational domain... Read More about A simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topography.

Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine (2018)
Journal Article

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 element schemes on modern massively parallel supercomputers. The numerical... Read More about Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine.

A Multi-Core Ready Discrete Element Method With Triangles Using Dynamically Adaptive Multiscale Grids (2018)
Journal Article

The simulation of vast numbers of rigid bodies of non‐analytical shapes and of tremendously different sizes that collide with each other is computationally challenging. A bottleneck is the identification of all particle contact points per time step.... Read More about A Multi-Core Ready Discrete Element Method With Triangles Using Dynamically Adaptive Multiscale Grids.

Quasi-matrix-free hybrid multigrid on dynamically adaptive Cartesian grids (2018)
Journal Article

We present a family of spacetree-based multigrid realizations using the tree’s multiscale nature to derive coarse grids. They align with matrix-free geometric multigrid solvers as they never assemble the system matrices, which is cumbersome for dynam... Read More about Quasi-matrix-free hybrid multigrid on dynamically adaptive Cartesian grids.

Complex additive geometric multilevel solvers for Helmholtz equations on spacetrees (2017)
Journal Article

We introduce a family of implementations of low-order, additive, geometric multilevel solvers for systems of Helmholtz equations arising from Schrödinger equations. Both grid spacing and arithmetics may comprise complex numbers, and we thus can apply... Read More about Complex additive geometric multilevel solvers for Helmholtz equations on spacetrees.

Two Particle-in-Grid Realisations on Spacetrees (2016)
Journal Article

The present paper studies two particle management strategies for dynamically adaptive Cartesian grids at hands of a particle-in-cell code. One holds the particles within the grid cells, the other within the grid vertices. The fundamental challenge fo... Read More about Two Particle-in-Grid Realisations on Spacetrees.

Block Fusion on Dynamically Adaptive Spacetree Grids for Shallow Water Waves (2014)
Journal Article

Spacetrees are a popular formalism to describe dynamically adaptive Cartesian grids. Even though they directly yield a mesh, it is often computationally reasonable to embed regular Cartesian blocks into their leaves. This promotes stencils working on... Read More about Block Fusion on Dynamically Adaptive Spacetree Grids for Shallow Water Waves.

A Geometric Space-time Multigrid Algorithm for the Heat Equation (2012)
Journal Article

A Coupled Approach for Fluid Dynamic Problems Using the PDE Framework Peano (2012)
Journal Article

Peano - A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids (2011)
Journal Article

An Efficient Parallel Implementation of the MSPAI Preconditioner (2010)
Journal Article

The PDE framework Peano applied to fluid dynamics: an efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids (2010)
Journal Article

A Precompiler to Reduce the Memory Footprint of Multiscale PDE Solvers in C++ (2010)
Journal Article

Numerical Simulation of Particle Transport in a Drift Ratchet (2008)
Journal Article

A cache-oblivious self-adaptive full multigrid method (2006)
Journal Article