We study the stability of Runge-Kutta methods for the time integration of semidiscrete systems associated with time dependent PDEs. These semidiscrete systems amount to large systems of ODEs with the possibility that the matrices involved are far from being normal. The stability question of their Runge-Kutta methods, therefore, cannot be addressed by the familiar scalar arguments of eigenvalues...

Contemporary social and medical changes – such as the rising divorce rates and rates of subsequent remarriage, the introduction of new fertility techniques and rising longevity – trigger public debates about kinship, nature and culture. At the same time, ‘ the master narrative ’ telling how kinship declined in the course of modernization has been largely rejected by historians. Now, however, ‘ ...

Adaptive radiation therapy (ART) is the incorporation of daily images in the radiotherapy treatment process so that the treatment plan can be evaluated and modified to maximize the amount of radiation dose to the tumor while minimizing the amount of radiation delivered to healthy tissue. Registration of planning images with daily images is thus an important component of ART. In this article, th...

We discuss a general framework for recovering edges in piecewise smooth functions with finitely many jump discontinuities, where [f ](x) := f(x+)− f(x−) = 0. Our approach is based on two main aspects—localization using appropriate concentration kernels and separation of scales by nonlinear enhancement. To detect such edges, one employs concentration kernels, K (·), depending on the small scale ...

We present three-dimensional central finite volume methods for solving systems of hyperbolic equations. Based on the Lax–Friedrichs and Nessyahu–Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve an original and a staggered grid in order to avoid the resolution of the Riemann problems at the cell interfaces. The cells of the original grid are Cart...

A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order centra...

We propose a non-oscillatory balanced numerical scheme for a simplified tropical climate model with a crude vertical resolution, reduced to the barotropic and the first baroclinic modes. The two modes exchange energy through highly nonlinear interaction terms. We consider a periodic channel domain, oriented zonally and centered around the equator and adopt a fractional stepping–splitting strate...

Finite volume numerical methods have been widely studied, implemented and parallelized on multiprocessor systems or on clusters. Modern graphics processing units (GPU) provide architectures and new programing models that enable to harness their large processing power and to design computational fluid dynamics simulations at both high performance and low cost. We report on solving the 2D compres...

This paper deals with a sharp smoothing e ect for entropy solutions of one-dimensional scalar conservation laws with a degenerate convex ux. We brie y explain why degenerate uxes are related with the optimal smoothing e ect conjectured by Lions, Perthame, Tadmor for entropy solutions of multidimensional conservation laws. It turns out that generalized spaces of bounded variation BVΦ are particu...

It is well known that the classic Galerkin finite element method is unstable when applied to hyperbolic conservation laws such as the Euler equations for compressible flows. Adding a diffusion term to the equations stabilizes the method but sacrifices too much accuracy to be of any practical use. An elegant solution developed in the context of spectral methods by Eitan Tadmor and coworkers is t...