Publication

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations

Publications associées (30)

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2022

High Performance Computing for gravitational lens modeling: Single vs double precision on GPUs and CPUs

Christoph Ernst René Schäfer, Jean-Paul Richard Kneib, Markus Rexroth

Strong gravitational lensing is a powerful probe of cosmology and the dark matter distribution. Efficient lensing software is already a necessity to fully use its potential and the performance demands will only increase with the upcoming generation of tele ...

ELSEVIER2020

Mixed-Precision Deep Learning Based on Computational Memory

Irem Boybat Kara, Abu Sebastian, Evangelos Eleftheriou

Deep neural networks (DNNs) have revolutionized the field of artificial intelligence and have achieved unprecedented success in cognitive tasks such as image and speech recognition. Training of large DNNs, however, is computationally intensive and this has ...

FRONTIERS MEDIA SA2020

High-order essentially nonoscillatory methods based on radial basis functions

Fabian Mönkeberg

Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely employed to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well s ...

EPFL2020

On the choice of metric in gradient-based theories of brain function

Wulfram Gerstner, Jean-Pascal Théodor Pfister, Johanni Michael Brea

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to ...

2020

Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

PERGAMON-ELSEVIER SCIENCE LTD2019

Design of approximate and precision-scalable circuits for embedded multimedia and neural-network processing

Vincent Frédéric Camus

Density, speed and energy efficiency of integrated circuits have been increasing exponentially for the last four decades following Moore's law. However, power and reliability pose several challenges to the future of technology scaling. Approximate computin ...

EPFL2019

Review and Benchmarking of Precision-Scalable Multiply-Accumulate Unit Architectures for Embedded Neural-Network Processing

Christian Enz, Vincent Frédéric Camus

The current trend for deep learning has come with an enormous computational need for billions of Multiply-Accumulate (MAC) operations per inference. Fortunately, reduced precision has demonstrated large benefits with low impact on accuracy, paving the way ...

2019

Survey of Precision-Scalable Multiply-Accumulate Units for Neural-Network Processing

Christian Enz, Vincent Frédéric Camus

IEEE2019