Exploring the frontiers of computational mathematics
We design numerical algorithms and high-performance software that let scientific applications make full use of modern supercomputers, from the mathematics of sparse linear algebra to production code that runs portably on CPUs and GPUs from every major vendor.
Sparse operations such as the sparse matrix-vector product (SpMV) are the building blocks of most simulations, and their speed is limited by memory bandwidth and load imbalance. We design balanced, compressed storage formats and kernels, and evaluate how emerging CPU and GPU architectures change the picture for sparse linear algebra.
Selected papers
Krylov methods solve large sparse systems iteratively, and a good preconditioner can cut the number of iterations by orders of magnitude. We develop preconditioners that run well in parallel: threshold ILU, sparse approximate inverses, multigrid and domain decomposition.
Selected papers
Moving data costs more than computing with it. We store data in lower-precision or compressed formats while keeping the arithmetic, and the final accuracy, in high precision: from memory accessors and compressed Krylov bases to three-precision multigrid and randomized sketching in low precision.
Selected papers
Many applications must solve thousands of small, independent linear systems at once, for example one per grid cell or mesh node. Our batched solvers and preconditioners handle all of them in a single GPU kernel, portably across GPU vendors.
Selected papers
Global synchronization becomes a bottleneck at scale. Asynchronous iterative methods let every processor continue with the newest data available instead of waiting for the others. We implement them on GPUs and multi-GPU clusters and model how they converge.
Selected papers
Our methods and software are used in, and shaped by, simulations across science and engineering.
Scalable solvers and preconditioners for whole-heart simulations with sub-cellular resolution.
Faster, higher-resolution runs of the ICON climate model on GPU supercomputers.
GPU-resident sparse direct solvers for AC optimal power flow analysis.
Batched sparse iterative solvers for the many small linear systems in chemistry simulations.
We are committed to building high-performance open-source software.
Some research software that we actively develop are:
Ginkgo is a high-performance sparse linear algebra library for many-core systems. A single interface targets CUDA, HIP, SYCL and OpenMP, with composable Krylov solvers and preconditioners, plus distributed and batched functionality.
ICON is a flexible, scalable, high-performance modelling framework for weather, climate and environmental prediction, available under the open-source BSD-3 licence. We contribute to ICON within the WarmWorld project.
A performance-portable finite-volume CFD framework built on NeoN, with OpenFOAM-equivalent solvers that run on CPUs and on NVIDIA, AMD and Intel GPUs.
NeoN is an open-source C++ library that provides the data structures, parallel algorithms and numerical infrastructure for finite-volume CFD on modern heterogeneous systems. Built on Kokkos and Ginkgo, it lets developers write fluid-flow solvers once and run them on CPUs, MPI clusters and NVIDIA, AMD and Intel GPUs.
The OpenFOAM Ginkgo Layer: brings Ginkgo's GPU-accelerated solvers and preconditioners to OpenFOAM.
pyGinkgo is a lightweight, Pythonic interface to the Ginkgo library, bringing high-performance sparse linear algebra to Python on CUDA, HIP, and OpenMP backends with a NumPy- and PyTorch-compatible interface.
Our research is supported by various national and international funding agencies.
MICROCARD builds software that can simulate cardiac electrophysiology using whole-heart models with sub-cellular resolution, on exascale supercomputers. We are part of work-package 2, which aims to deliver efficient large-scale distributed preconditioners and solvers.
WarmWorld advances ICON, a globally coupled, convection-resolving climate model, towards faster runs on finer grids, so that processes such as cloud formation and eddies can be resolved directly.
Completed projects that shaped our research and software.
The US Exascale Computing Project delivered applications, an integrated software stack and hardware advances for the first exascale supercomputers. Ginkgo was developed as one of ECP's math libraries, providing portable sparse linear algebra to ECP science applications.
Funded by: US DOE Office of Science, NNSA
Duration: 2016 – 2024
MICROCARD developed an exascale application platform for cardiac electrophysiology simulations at the cellular scale, moving from continuum models to cell-by-cell representations of the heart. We contributed scalable solvers and preconditioners for the resulting large linear systems.
Funded by: EuroHPC JU (Horizon 2020), BMBF
Duration: April 2021 – September 2024