相关论文: Vectorization and Minimization of Memory Footprint…
In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field…
This paper is concerned with the PDE and numerical analysis of a modified one-dimensional intravascular stent model originally proposed in [4]. It is proved that the modified model has a unique weak solution using the Galerkin method…
In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
Pipeline Parallelism (PP) serves as a crucial technique for training Large Language Models (LLMs), owing to its capability to alleviate memory pressure from model states with relatively low communication overhead. However, in long-context…
Power density constraints are limiting the performance improvements of modern CPUs. To address this we have seen the introduction of lower-power, multi-core processors such as GPGPU, ARM and Intel MIC. To stay within the power density…
Leveraging the SIMD capability of modern CPU architectures is mandatory to take full benefit of their increasing performance. To exploit this feature, binary executables must be explicitly vectorized by the developers or an automatic…
To fully exploit the performance potential of modern multi-core processors, machine learning and data mining algorithms for big data must be parallelized in multiple ways. Today's CPUs consist of multiple cores, each following an…
The performance of lattice-Boltzmann solver implementations usually depends mainly on memory access patterns. Achieving high performance requires then complex code which handles careful data placement and ordering of memory transactions. In…
Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the…
We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
Power density constraints are limiting the performance improvements of modern CPUs. To address this we have seen the introduction of lower-power, multi-core processors such as GPGPU, ARM and Intel MIC. To stay within the power density…
As the size of artificial intelligence and machine learning (AI/ML) models and datasets grows, the memory bandwidth becomes a critical bottleneck. The paper presents a novel extended memory hierarchy that addresses some major memory…
Iterative memory-bound solvers commonly occur in HPC codes. Typical GPU implementations have a loop on the host side that invokes the GPU kernel as much as time/algorithm steps there are. The termination of each kernel implicitly acts the…
We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special…
The dedicated memory of hardware accelerators can be insufficient to store all weights and/or intermediate states of large deep learning models. Although model parallelism is a viable approach to reduce the memory pressure issue,…
As transformer sequence lengths grow, existing pipeline parallelisms incur suboptimal performance due to the quadratic attention computation and the substantial memory overhead. To relieve these challenges, we propose HelixPipe, a novel…
Matrix-free finite element implementations of massively parallel geometric multigrid save memory and are often significantly faster than implementations using classical sparse matrix techniques. They are especially well suited for…
Single Instruction, Multiple Data (SIMD) vectorization is a major driver of performance in current architectures, and is mandatory for achieving good performance with codes that are limited by instruction throughput. We investigate the…