Related papers: Vectorization and Minimization of Memory Footprint…

SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software's sustainability. In this publication we solve this sustainability and…

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 this paper we discuss a new and very efficient implementation of high order accurate ADER discontinuous Galerkin (ADER-DG) finite element schemes on modern massively parallel supercomputers. The numerical methods apply to a very broad…

We present an algorithmic framework for matrix-free evaluation of discontinuous Galerkin finite element operators based on sum factorization on quadrilateral and hexahedral meshes. We identify a set of kernels for fast quadrature on cells…

Although prior art has demonstrated negligible accuracy drop in sub-byte quantization -- where weights and/or activations are represented by less than 8 bits -- popular SIMD instructions of CPUs do not natively support these datatypes.…

We present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time to…

Applications with low data reuse and frequent irregular memory accesses, such as graph or sparse linear algebra workloads, fail to scale well due to memory bottlenecks and poor core utilization. While prior work with prefetching,…

This living paper reviews the present High Performance Computing (HPC) capabilities of the Tinker-HP molecular modeling package. We focus here on the reference, double precision, massively parallel molecular dynamics engine present in…

We present a mixed-precision implementation of the high-order discontinuous Galerkin method with ADER time stepping (ADER-DG) for solving hyperbolic systems of partial differential equations (PDEs) in the hyperbolic PDE engine ExaHyPE. The…

Achieving a substantial part of peak performance on todays and future high-performance computing systems is a major challenge for simulation codes. In this paper we address this question in the context of the numerical solution of partial…

This paper advocates for an intertwined design of the dense linear algebra software stack that breaks down the strict barriers between the high-level, blocked algorithms in LAPACK (Linear Algebra PACKage) and the low-level,…

The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit…

High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and…

We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework is based on a Galerkin discretization of the underlying…

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…

Performance optimization is the art of continuous seeking a harmonious mapping between the application domain and hardware. Recent years have witnessed a surge of deep learning (DL) applications in industry. Conventional wisdom for…

We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded…

Processing large-scale graph datasets is computationally intensive and time-consuming. Processor-centric CPU and GPU architectures, commonly used for graph applications, often face bottlenecks caused by extensive data movement between the…

Matrix-free geometric multigrid solvers for elliptic PDEs that have been discretised with Higher-order Discontinuous Galerkin (DG) methods are ideally suited to exploit state-of-the-art computer architectures. Higher polynomial degrees…

Reinforcement learning (RL) workloads take a notoriously long time to train due to the large number of samples collected at run-time from simulators. Unfortunately, cluster scale-up approaches remain expensive, and commonly used CPU…