Related papers: FlashMP: Fast Discrete Transform-Based Solver for …
Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…
Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…
Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…
Elliptic equations play a crucial role in turbulence models for magnetic confinement fusion. Regardless of the chosen modeling approach - whether gyrokinetic, gyrofluid, or drift-fluid - the Poisson equation and Amp\`{e}re's law lead to…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…
Sparse Matrix-matrix Multiplication (SpMM) and Sampled Dense-dense Matrix Multiplication (SDDMM) are important sparse operators in scientific computing and deep learning. Tensor Core Units (TCUs) enhance modern accelerators with superior…
A tridiagonal matrix algorithm (TDMA), Pipelined-TDMA, is developed for multi-GPU systems to resolve the scalability bottlenecks caused by the sequential structure of conventional divide-and-conquer TDMA. The proposed method pipelines…
Recent research has focused on developing GPU-accelerated first-order solvers for linear programming (LP). This line of work, however, has largely overlooked the role of presolving, and thus prior results do not fully reflect the speedups…
The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in…
Graphics Processing Units (GPUs) are high performance co-processors originally intended to improve the use and quality of computer graphics applications. Once, researchers and practitioners noticed the potential of using GPU for general…
This paper presents a GPU-accelerated framework for solving block tridiagonal linear systems that arise naturally in numerous real-time applications across engineering and scientific computing. Through a multi-stage permutation strategy…
The Multilevel Fast Multipole Algorithm (MLFMA) has known applications in scientific modeling in the fields of telecommunications, physics, mechanics, and chemistry. Accelerating calculation of far-field using GPUs and GPU clusters for…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
In this paper, we use multithreaded fast Fourier transforms provided in three highly optimized packages, FFTW-2.1.5, FFTW-3.3.7, and Intel MKL FFT, to present a novel model-based parallel computing technique as a very effective and portable…
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…
An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…
Development of highly scalable and robust algorithms for large-scale CFD simulations has been identified as one of the key ingredients to achieve NASA's CFD Vision 2030 goals. In order to improve simulation capability and to effectively…
Normalization layers are ubiquitous in large language models (LLMs) yet represent a compute bottleneck: on hardware with distinct vector and matrix execution units, the RMS calculation blocks the subsequent matrix multiplication, preventing…
Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are…
This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An…