Related papers: Object-oriented implementation of algebraic multi-…
We present a platform-agnostic modular architecture that addresses the increasingly fragmented landscape of quantum computing benchmarking by decoupling problem generation, circuit execution, and results analysis into independent,…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
With high computation power and memory bandwidth, graphics processing units (GPUs) lend themselves to accelerate data-intensive analytics, especially when such applications fit the single instruction multiple data (SIMD) model. However,…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
Multiple-precision floating-point branch-free algorithms can significantly accelerate multi-component arithmetic implemented by combining hardware-based binary64 and binary32, particularly for triple- and quadruple-precision computations.…
We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…
We present here the most recent version of FermiQCD, a collection of C++ classes, functions and parallel algorithms for lattice QCD, based on Matrix Distributed Processing. FermiQCD allows fast development of parallel lattice applications…
We propose a convenient matrix-free neural architecture for the multigrid method. The architecture is simple enough to be implemented in less than fifty lines of code, yet it encompasses a large number of distinct multigrid solvers. We…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018),…
In this paper, we propose a deep learning-enhanced multigrid solver for high-frequency and heterogeneous Helmholtz equations. By applying spectral analysis, we categorize the iteration error into characteristic and non-characteristic…
With the ease-of-programming, flexibility and yet efficiency, MapReduce has become one of the most popular frameworks for building big-data applications. MapReduce was originally designed for distributed-computing, and has been extended to…
Lattice QCD solvers encounter critical slowing down for fine lattice spacings and small quark mass. Traditional matrix eigenvalue deflation is one approach to mitigating this problem. However, to improve scaling we study the effects of…
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…
This paper investigates the multi-GPU performance of a 3D buoyancy driven cavity solver using MPI and OpenACC directives on different platforms. The paper shows that decomposing the total problem in different dimensions affects the strong…
Multigrid algorithms are among the fastest iterative methods known today for solving large linear and some non-linear systems of equations. Greatly optimized for serial operation, they still have a great potential for parallelism not fully…
High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel…