Meshless methods: An overview and recent developments

This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book, which can also form the basis of one or more graduate-level courses.

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Atmospheric Modeling, Data Assimilation and Predictability

A survey of microstrip antenna elements is presented, with emphasis on theoretical and practical design techniques. Available substrate materials are reviewed along with the relation between dielectric constant tolerance and resonant frequency of microstrip patches. Several theoretical analysis techniques are summarized, including transmission-line and modal-expansion (cavity) techniques as well as numerical methods such as the method of moments and finite-element techniques. Practical procedures are given for both standard rectangular and circular patches, as well as variations on those designs including circularly polarized microstrip patches. The quality, bandwidth, and efficiency factors of typical patch designs are discussed. Microstrip dipole and conformal antennas are summarized. Finally, critical needs for further research and development for this antenna are identified.

Microstrip antenna technology

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge–Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier–Stokes equations, and Hamilton–Jacobilike equations.

Review Article Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

— The paper is devoted to a gênerai finite element approximation ofthe solution of the Stokes équations for an incompressible viscous fluid, Both conforming and nonconforming finite element methods are studied and various examples of simplicial éléments well suitedfor the numerical treatment of the incompressibility condition are given. Optimal error estimâtes are derived in the energy norm and in the L-norm.

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D. S. Griffin

Papers

An Analysis of the Finite Element Method