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Vectorized Parallel in Time methods for low-order discretizations with application to Porous Media problems
Christian Engwer, Alexander Schell, Nils-Arne Dreier
High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to l…
A Hardware-aware and Stable Orthogonalization Framework
Nils-Arne Dreier, Christian Engwer
The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram…
Hardware-Oriented Krylov Methods for High-Performance Computing
Nils-Arne Dreier
Krylov subspace methods are an essential building block in numerical simulation software. The efficient utilization of modern hardware is a challenging problem in the development o…
Strategies for the vectorized Block Conjugate Gradients method
Nils-Arne Dreier, Christian Engwer
Block Krylov methods have recently gained a lot of attraction. Due to their increased arithmetic intensity they offer a promising way to improve performance on modern hardware. Rec…