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Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE solver that can be operated with the convenience of MATLAB yet achieves efficiency near that of hand-coded Fortran and scales to the largest supercomputers. This is achieved by using Python for most of the code while employing automatically-wrapped Fortran kernels for computationally intensive routines, and using Python bindings to interface with a parallel computing library and other numerical packages. The software described here is PyClaw, a Python-based structured grid solver for general systems of hyperbolic PDEs cite{pyclaw}. PyClaw provides a powerful and intuitive interface to the algorithms of the existing Fortran codes Clawpack and SharpClaw, simplifying code development and use while providing massive parallelism and scalable solvers via the PETSc library. The package is further augmented by use of PyWENO for generation of efficient high-order weighted essentially non-oscillatory reconstruction code. The simplicity, capability, and performance of this approach are demonstrated through application to example problems in shallow water flow, compressible flow and elasticity.
In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF 2D (http://www. univ-orleans.fr/mapmo/soft/FullSWOF/ that solves shallow water equations for applications in hydrology) based on
We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, di
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution of one pro
The paper derives and analyses the (semi-)discrete dispersion relation of the Parareal parallel-in-time integration method. It investigates Parareals wave propagation characteristics with the aim to better understand what causes the well documented s
We present an analysis of the additive average Schwarz preconditioner with two newly proposed adaptively enriched coarse spaces which was presented at the 23rd International conference on domain decomposition methods in Korea, for solving second orde