SUMMARYA new indirect way of producing all-quad meshes is presented. The method takes advantage of a well known algorithm of the graph theory, namely the Blossom algorithm that computes the minimum cost perfect matching in a graph in polynomial time. The new Blossom-Quad algorithm is compared with standard indirect procedures. Meshes produced by the new approach are better both in terms of element shape and in terms of size field efficiency.

SUMMARY This paper presents multirate explicit time‐stepping schemes for solving partial differential equations with discontinuous Galerkin elements in the framework of Large‐scale marine flows. It addresses the variability of the local stable time steps by gathering the mesh elements in appropriate groups. The real challenge is to develop methods exhibiting mass conservation and consistency. Two multirate approaches, based on standard explicit Runge–Kutta methods, are analyzed. They are well suited and optimized for the discontinuous Galerkin framework. The significant speedups observed for the hydrodynamic application of the Great Barrier Reef confirm the theoretical expectations. Copyright © 2012 John Wiley & Sons, Ltd.

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This paper presents a multirate technique to improve and optimize the time step of a second order 2−stages Explicit Runge-Kutta scheme (ERK). In this technique, the mesh elements are stored in different groups according to their stable time steps. These groups are sorted into two classes. The bulk groups where the 2−stages ERK method is applied once or repeatedly. The buffer groups that used to accommodate transition between two bulks groups. This technique is proposed for accelerating explicit discontinuous Galerkin computations of time domain Maxwell equations. An application example on human skull is proposed to show the efficiency of this technique to simulate wave propagation on complex geometries.