Research team

Applied mathematics

Asynchronous Krylov methods with deep pipelines. 01/01/2018 - 31/12/2018

Abstract

In recent years a major trend towards solving scientific problems of ever larger scales that include larger and larger data sets can be observed in practically all academic and industrial applications. These include the simulation of vast ocean circulation models, global climate prediction models, extremely fine-scale combustion models, etc. The representation of these models on a computer requires the solution of a large-scale system of equations that typically consists of millions of unknowns. Due to the huge size of these model calculations, computations are often spread across parallel computer platforms to reduce the time-to-solution. Krylov methods have been established as the benchmark iterative solvers for the sparse linear algebra problems that appear in these applications. However, Krylov methods are not adapted to scale to future parallel hardware due to the long communication latencies. Hence, new numerical methods have to be designed and analyzed mathematically. The aim of this project is to develop and analyze new scalable iterative methods based on asynchronous communication that hide the communication latency by overlapping compute and communication tasks. Furthermore we will develop blocked versions of these algorithms for problems where the same matrix equation needs to be solved for multiple right hand sides. Demonstrators will be built that show the performance improvements for a wide range of applications in data science and scientific computing.

Researcher(s)

Research team(s)

HPC iterative solvers for multi-particle physics simulation. 01/04/2017 - 31/03/2018

Abstract

Current and future physical equipment collects more and more data from multiple scattered fields simultaneously, for example in the imaging of molecules, which adds to the complexity of the reconstruction through numerical simulation. This dramatic increase in data requires new scalable mathematical techniques to reconstruct the high-dimensional object of interest. This project aspires to develop efficient ways to solve the high-dimensional Helmholtz and Schrödinger problem for this purpose. A successful and already awarded initial approach, based on the novel idea of reformulating the PDEs involved on a complex-valued manifold, was recently developed by the applicant. The proposed technique makes the potentially high-dimensional problem more tractable and amenable to large-scale iterative solvers. The main aim of this project is the development and rigorous analysis of scalable HPC iterative solution methods for wave scattering problems.

Researcher(s)

Research team(s)

Project website

Scalable and error resilient iterative solvers for large scale linear algebra problems. 01/10/2016 - 30/09/2019

Abstract

In recent years, a major trend towards solving scientific problems of ever larger scales can be observed in practically all academic and industrial applications. These include the simulation of vast ocean circulation models, global climate prediction models, seismic oil reservoir models spanning hundreds of kilometers, extremely fine-scale combustion models, etc. The representation of these models on a computer requires the solution of a large-scale system of equations that typically consists of millions of unknowns. Due to the huge size of these model calculations, computations are often spread across parallel computer platforms to reduce computational time. Furthermore, only the numerical methods with optimal compute and communication complexity are able to efficiently solve these large scale problems. Krylov methods have been established as the benchmark iterative solvers for sparse linear algebra problems due to their robustness and good performance in function of the number of unknowns. However, present-day Krylov methods are not adapted to scale to future parallel hardware. Hence, new numerical methods have to be designed and analyzed mathematically, taking into account numerical rounding error propagation, which possibly has a detrimental effect on convergence. The aim of this project is to develop and analyze new scalable iterative methods that are numerically stable and resilient to the errors that typically arise in these large-scale computations.

Researcher(s)

Research team(s)