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 …

Fault tolerant massively parallel multigrid methods for elliptic partial differential equations
are a step towards resilient solvers. Here, we combine domain partitioning with geometric …

Substantial modifications of both the choice of the grids, the combination coefficients, the
parallel data structures and the algorithms used for the combination technique lead to …

Ultra-large–scale simulations via solving partial differential equations (PDEs) require very
large computational systems for their timely solution. Studies shown the rate of failure grows …

With future exascale computers expected to have millions of compute units distributed
among thousands of nodes, system faults are predicted to become more frequent. Fault …

The solution of high-dimensional problems, especially high-dimensional partial differential
equations (PDEs) that require the joint discretization of more than the usual three spatial …

As the generation of exascale high-performance clusters begins, it has become evident that
numerical algorithms will greatly benefit from built-in resilience features that can handle …

Plasma fusion is one of the promising candidates for an emission-free energy source and is
heavily investigated with high-resolution numerical simulations. Unfortunately, these …

We describe two algorithms to detect and filter silent data corruption (SDC) when solving
time-dependent PDEs with the Sparse Grid Combination Technique (SGCT). The SGCT …

In this work, we discuss measures to increase the scalability, robustness, and efficiency of
the Combination Technique. In particular, we introduce an asynchronous variant and …