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

In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …

In this paper we generalise to non-uniform grids of quad-tree type the Compact WENO
reconstruction of Levy et al.(SIAM J Sci Comput 22 (2): 656–672, 2000), thus obtaining a …

An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any
other parabolic or hyperbolic system of partial differential equations, should allow local …

Differential equations arising in many practical applications are characterized by multiple
time scales. Multirate time integration seeks to solve them efficiently by discretizing each …

We develop an efficient local time-step** algorithm for the method of lines approach to
numerical solution of transient partial differential equations. The need for local time-step** …

Locally refined meshes impose severe stability constraints on explicit time-step** methods
for the numerical simulation of time dependent wave phenomena. Local time-step** …

Traditional time discretization methods use a single timestep for the entire system of interest
and can perform poorly when the dynamics of the system exhibits a wide range of time …

We present a higher‐order cut cell immersed boundary method (IBM) for the simulation of
high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time …

In this paper we construct extrapolated multirate discretization methods that allows one to
efficiently solve problems that have components with different dynamics. This approach is …