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In this thesis we develop techniques to efficiently solve numerical Partial Differential Equations (PDEs) using Graphical Processing Units (GPUs). Focus is put on both performance and re--usability of the methods developed, to this end a…

We introduce the CUDA Tensor Transpose (cuTT) library that implements high-performance tensor transposes for NVIDIA GPUs with Kepler and above architectures. cuTT achieves high performance by (a) utilizing two GPU-optimized transpose…

The significant resource demands in LLM serving prompts production clusters to fully utilize heterogeneous hardware by partitioning LLM models across a mix of high-end and low-end GPUs. However, existing parallelization approaches often…

This paper presents novel approaches to parallelizing particle interactions on a GPU when there are few particles per cell and the interactions are limited by a cutoff distance. The paper surveys classical algorithms and then introduces two…

The objective of this work is to present a novel approach for the solution of Pentadiagonal Toeplitz systems of equations that is both faster and more effective than existing classical direct methods. The distinctive structure of…

Recent enhancements to the Primal-Dual Hybrid Gradient (PDHG) algorithm have enabled GPUs to efficiently solve large linear programming problems, often faster than the long-dominant simplex and interior-point methods. The solutions found by…

This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging…

Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor…

Graphical Processing Units (GPUs) are more and more frequently used for lattice QCD calculations. Lattice studies often require computing the quark propagators for several masses. These systems can be solved using multi-shift inverters but…

Matrix-accelerated stencil computation is a hot research topic, yet its application to three-dimensional (3D) high-order stencils and HPC remains underexplored. With the emergence of matrix units on multicore CPUs, we analyze matrix-based…

Edge computing's growing prominence, due to its ability to reduce communication latency and enable real-time processing, is promoting the rise of high-performance, heterogeneous System-on-Chip solutions. While current approaches often…

Modeling data sharing in GPU programs is a challenging task because of the massive parallelism and complex data sharing patterns provided by GPU architectures. Better GPU caching efficiency can be achieved through careful task scheduling…

We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of…

Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…

As modern LLMs support thousands to millions of tokens, KV caches grow to hundreds of gigabytes, stressing memory capacity and bandwidth. Existing solutions, such as KV cache pruning and offloading, alleviate these but underutilize hardware…

Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU. This algorithm is based on first bi-vectorizing a triangular matrices of…

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be…

We present a design space exploration for synthesizing optimized, high-throughput implementations of multiple multi-dimensional tridiagonal system solvers on FPGAs. Re-evaluating the characteristics of algorithms for the direct solution of…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…