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.
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