6 papers
Neural Network Preconditioning: A Case Study for the Solution of the Parametric Helmholtz Equation
Luc Giraud, Carola Kruse, Paul Mycek +2
This work presents a hybrid numerical approach for solving linear systems arising from the discretization of the two-dimensional parametric Helmholtz equation. A convolutional neur…
On some orthogonalization schemes in Tensor Train format
Olivier Coulaud, Luc Giraud, Martina Iannacito
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particu…
A robust GMRES algorithm in Tensor Train format
Olivier Coulaud, Luc Giraud, Martina Iannacito
We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in term…
Resiliency in Numerical Algorithm Design for Extreme Scale Simulations
Emmanuel Agullo, Mirco Altenbernd, Hartwig Anzt +33
This work is based on the seminar titled ``Resiliency in Numerical Algorithm Design for Extreme Scale Simulations'' held March 1-6, 2020 at Schloss Dagstuhl, that was attended by a…
Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined Conjugate Gradient method
Siegfried Cools, Emrullah Fatih Yetkin, Emmanuel Agullo +2
Pipelined Krylov subspace methods typically offer improved strong scaling on parallel HPC hardware compared to standard Krylov subspace methods for large and sparse linear systems.…
Deflation and augmentation techniques in Krylov subspace methods for the solution of linear systems
Olivier Coulaud, Luc Giraud, Pierre Ramet +1
In this paper we present deflation and augmentation techniques that have been designed to accelerate the convergence of Krylov subspace methods for the solution of linear systems o…