Related papers: Vectorization and Minimization of Memory Footprint…
In this paper, we apply a specifically designed dissipative spatial filter as sub-grid scale model within the increasingly popular discontinuous Galerkin methods and the closely related flux reconstruction high order methods for large eddy…
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…
Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank…
This work presents GALAEXI as a novel, energy-efficient flow solver for the simulation of compressible flows on unstructured meshes leveraging the parallel computing power of modern Graphics Processing Units (GPUs). GALAEXI implements the…
Volume reconstruction by backprojection is the computational bottleneck in many interventional clinical computed tomography (CT) applications. Today vendors in this field replace special purpose hardware accelerators by standard hardware…
In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet…
We present a discontinuous Galerkin-finite-difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple.…
This paper presents an overview of the functionalities and applications of Exasim, an open-source code for generating high-order discontinuous Galerkin codes to numerically solve parametrized partial differential equations (PDEs). The…
The way developers implement their algorithms and how these implementations behave on modern CPUs are governed by the design and organization of these. The vectorization units (SIMD) are among the few CPUs' parts that can and must be…
We present a technique for automatically transforming kernel-based computations in disparate, nested loops into a fused, vectorized form that can reduce intermediate storage needs and lead to improved performance on contemporary hardware.…
We improve on GenASM, a recent algorithm for genomic sequence alignment, by significantly reducing its memory footprint and bandwidth requirement. Our algorithmic improvements reduce the memory footprint by 24$\times$ and the number of…
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
Molecular dynamics simulations, an indispensable research tool in computational chemistry and materials science, consume a significant portion of the supercomputing cycles around the world. We focus on multi-body potentials and aim at…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
We present an analysis on optimizing performance of a single C++11 source code using the Alpaka hardware abstraction library. For this we use the general matrix multiplication (GEMM) algorithm in order to show that compilers can optimize…
As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
Sparse Matrix-Vector Multiplication (SpMV) is a critical operation for the iterative solver of Finite Element Methods on computer simulation. Since the SpMV operation is a memory-bound algorithm, the efficiency of data movements heavily…
In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (10pJ/word on-die to 10,000pJ/word on the network). To increase memory locality at the hardware level and reduce…