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 present a data-driven approach to iteratively solve the discrete
heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine …

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

We propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of
unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a …

We present a deep learning-based iterative approach to solve the discrete heterogeneous
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …

This work presents the efficient, matrix-free finite-element library hyper. deal for solving
partial differential equations in two up to six dimensions with high-order discontinuous …

We present a communication-and data-sensitive formulation of ADER-DG for hyperbolic
differential equation systems. Sensitive here has multiple flavours: First, the formulation …

Full waveform inversion (FWI) is a process in which seismic numerical simulations are fit to
observed data by changing the wave velocity model of the medium under investigation. The …

We present a deep learning–based iterative approach to solve the discrete heterogeneous
Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers …

The Helmholtz equation arises when modeling wave propagation in the frequency domain.
The equation is discretized as an indefinite linear system, which is difficult to solve at high …