Related papers: Multigrid Solver on Fugaku
Achieving high-performance GPU kernels requires optimizing algorithm implementations to the targeted GPU architecture. It is of utmost importance to fully use the compute and memory hierarchy, as well as available specialised hardware.…
Eigenvalues of the Hermitian Wilson-Dirac operator are of special interest in several lattice QCD simulations, e.g., for noise reduction when evaluating all-to-all propagators. In this paper we present a Davidson-type eigensolver that…
Managing the high computational cost of iterative solvers for sparse linear systems is a known challenge in scientific computing. Moreover, scientific applications often face memory bandwidth constraints, making it critical to optimize data…
Simulating lattice QCD with chiral fermions and indeed using Domain Wall Fermions continues to be challenging project however large are concurrent computers. One obvious bottleneck is the slow pace of prototyping using the low level coding…
Transformer-based Large Language Models (LLMs) have significantly advanced AI capabilities but pose considerable challenges for deployment on edge devices due to high computational demands, memory bandwidth constraints, and energy…
A comparison of PGI OpenACC, FORTRAN CUDA, and Nvidia CUDA pseudospectral methods on a single GPU and GCC FORTRAN on single and multiple CPU cores is reported. The GPU implementations use CuFFT and the CPU implementations use FFTW. Porting…
We present a MATLAB-based framework for two- and three-dimensional fast Fourier transforms on multiple GPUs for large-scale numerical simulations using the pseudo-spectral Fourier method. The software implements two complementary multi-GPU…
In this article, we discuss several classes of Uzawa smoothers for the application in multigrid methods in the context of saddle point problems. Beside commonly used variants, such as the inexact and block factorization version, we also…
The presence of GPU from different vendors demands the Lattice QCD codes to support multiple architectures. To this end, Open Computing Language (OpenCL) is one of the viable frameworks for writing a portable code. It is of interest to find…
The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular…
Unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming…
We report on salient features of a mixed lattice QCD action using valence M\"{o}bius domain-wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
We consider an algebraic multigrid (AMG) scheme for the direct solution of complex- valued square linear systems based on a recursive 2 x 2 block partitioning of the coefficient matrix and study the optimal choices of its components. In…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…
In this paper, we present a structured solver based on the preconditioned conjugate gradient method (PCGM) for solving the linear quadratic (LQ) optimal control problem for $K \times N$ sub-systems connected in a two-dimensional (2D) grid…
This paper reviews the most popular methods which are used in lattice QCD to compute the determinant of the lattice Dirac operator: Gaussian integral representation and noisy methods. Both of them lead naturally to matrix function problems.…
This work presents a GPU-accelerated solver for the unit commitment (UC) problem in large-scale power grids. The solver uses the Primal-Dual Hybrid Gradient (PDHG) algorithm to efficiently solve the relaxed linear subproblem, achieving…
This paper introduces Tiramisu, a polyhedral framework designed to generate high performance code for multiple platforms including multicores, GPUs, and distributed machines. Tiramisu introduces a scheduling language with novel extensions…
We present an OpenCL-based Lattice QCD application using a heatbath algorithm for the pure gauge case and Wilson fermions in the twisted mass formulation. The implementation is platform independent and can be used on AMD or NVIDIA GPUs, as…