Hyperbolic PDEs

On Strong Stability of Runge-Kutta Methods

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B1 L4 R4214

Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems of ODEs that are solved subsequently, resulting in fully discrete schemes. However, certain stability investigations of high-order methods for hyperbolic conservation laws are often conducted only for the semidiscrete versions.

Unveiling the potential of energy/entropy stable numerical methods for hyperbolic/mixed hyperbolic-parabolic PDEs

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B9 L2 H1

Abstract The demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future PDEs solvers. At the algorithmic level, hardware compatibility and efficiency are of paramount importance in determining viability on future hardware. However, equally important (if not more so) is provable algorithmic robustness which becomes progressively more challenging to achieve as problem size and physics complexity increase. We show that rigorously designed adaptive semi- and fully-discrete

Xiaokai Huo

Short Bio Xiaokai Huo received a bachelor degree in Mathematics from Tsinghua University, China in 2012 and a Ph.D degree in Mathematics from Tsinghua University China, 2017. He was a Postdoctoral fellow in the Applied PDE group at KAUST in the period October 2017 - October 2020. In October 2020 he joined the Institute of Analysis and Scientific Computing, Vienna University of Technology as a Postdoctoral Fellow. Xiaokai Huo's research interests lie in the area of Hyperbolic PDEs, Fluid Mechanics and Non-equilibrium Thermodynamics. Education Profile Ph. D. Mathematics, Tsinghua University