We consider multiphysics applications from algorithmic and architectural perspectives,
where “algorithmic” includes both mathematical analysis and computational complexity, and …

This book deals with numerical methods for solving partial differential equa tions (PDEs)
coupling advection, diffusion and reaction terms, with a focus on time-dependency. A …

We consider new implicit–explicit (IMEX) Runge–Kutta methods for hyperbolic systems of
conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability …

Additive Runge–Kutta (ARK) methods are investigated for application to the spatially
discretized one-dimensional convection–diffusion–reaction (CDR) equations. Accuracy …

A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for
ordinary differential equations with both stiff and non-stiff terms is presented. Several …

We show that accelerated optimization methods can be seen as particular instances of multi-
step integration schemes from numerical analysis, applied to the gradient flow equation …

The parareal algorithm introduced in 2001 by Lions, Maday, and Turinici is an iterative
method for the parallelization of the numerical solution of ordinary differential equations or …

This thesis deals with a higher order discretization of incompressible flow problems using
the Hybrid Discontinuous Galerkin Method. It aims to introduce an appropriate and …

A stiff, 1 operator-split projection scheme is constructed for the simulation of unsteady two-
dimensional reacting flow with detailed kinetics. The scheme is based on the compressible …

For solving hyperbolic systems with stiff sources or relaxation terms, time stepping methods
should combine favorable monotonicity properties for shocks and steep solution gradients …