Related papers: ExaHyPE: An Engine for Parallel Dynamically Adapti…
We present the first results on the construction of an exascale hyperbolic PDE engine (ExaHyPE), a code for the next generation of supercomputers with the objective to evolve dynamical spacetimes of black holes, neutron stars and binaries.…
ExaGRyPE describes a suite of solvers for numerical relativity, based upon ExaHyPE 2, the second generation of our Exascale Hyperbolic PDE Engine. The presented generation of ExaGRyPE solves the Einstein equations in the CCZ4 formulation…
In an era where we can not afford to checkpoint frequently, replication is a generic way forward to construct numerical simulations that can continue to run even if hardware parts fail. Yet, replication often is not employed on larger…
First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock waves, electromagnetic interactions, and even general…
Wave equations help us to understand phenomena ranging from earthquakes to tsunamis. These phenomena materialise over very large scales. It would be computationally infeasible to track them over a regular mesh. Yet, since the phenomena are…
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…
In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively…
The ISO C++17 standard introduces \emph{parallel algorithms}, a parallel programming model promising portability across a wide variety of parallel hardware including multi-core CPUs, GPUs, and FPGAs. Since 2019, the NVIDIA HPC SDK compiler…
The development of a high performance PDE solver requires the combined expertise of interdisciplinary teams with respect to application domain, numerical scheme and low-level optimization. In this paper, we present how the ExaHyPE engine…
The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…
The Smoothed Particles Hydrodynamics (SPH) is a particle-based, meshfree, Lagrangian method used to simulate multidimensional fluids with arbitrary geometries, most commonly employed in astrophysics, cosmology, and computational…
Exascale computers offer transformative capabilities to combine data-driven and learning-based approaches with traditional simulation applications to accelerate scientific discovery and insight. However, these software combinations and…
Exascale computers will offer transformative capabilities to combine data-driven and learning-based approaches with traditional simulation applications to accelerate scientific discovery and insight. These software combinations and…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…
The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding.…
Optimizing high-performance power electronic equipment, such as power converters, requires multiscale simulations that incorporate the physics of power semiconductor devices and the dynamics of other circuit components, especially in…
Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…