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Explore cutting-edge time integration methods for climate and weather simulations in this 51-minute NHR PerfLab seminar. Delve into the challenges posed by evolving computer architectures and learn about innovative approaches to improve simulation efficiency. Discover techniques like Exponential Integration, Rational Approximation of Exponential Integration (REXI), Parallel Full Approximation Scheme in Space and Time (PFASST), and Semi-Lagrangian methods combined with Parareal and MultiGrid Reduction In Time (MGRIT). Gain insights from Univ.-Prof. Dr. Martin Schreiber, an expert in high-performance computing and applied mathematics, as he presents promising solutions to enhance the ratio of wall clock time vs. error in dynamical cores. Understand the potential impact of these methods on operational weather and climate systems, and explore the intersection of HPC and applied mathematics in solving partial differential equations.