SUMMARY Metamaterials are generally defined as a class of artificial effective media which macroscopically exhibit extraordinary electromagnetic properties that may not be found in nature, and are composed of periodically structured dielectric, or magnetic, or metallic materials. This paper reviews recently developed electromagnetic modeling methods of metama-tericals and their inherent basic i...

In the last decades, more or less complex physically-based hydrological models, have been developed that solve the shallow water equations or their approximations using various numerical methods. Model users may not necessarily know the different hypothesis lying behind these development and simplifications, and it might therefore be difficult to judge if a code is well adapted to their objecti...

For many elliptic PDE problems, finite-difference and finite-element methods are the techniques of choice. In a finite-difference approach, a solution uk on a set of discrete gridpoints 1, . . . , k is searched for. The discretized partial differential equation and boundary conditions create linear relationships between the different values of uk. In the finite-element method, the solution is e...

Article history: Received 30 March 2013 Received in revised form 21 July 2013 Accepted 5 February 2014 Available online 14 February 2014

A third-order Energy Stable Weighted Essentially Non–Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter (AIAA 2008–2876, 2008) was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables “energy stable” modifications for existing WENO s...

Article history: Received 18 September 2013 Received in revised form 26 March 2014 Accepted 29 March 2014 Available online 4 April 2014

We compare several On Surface Radiation Boundary Conditions in two dimensions, for solving the Helmholtz equation exterior to an ellipse. We also introduce a new boundary condition for an ellipse based on amodal expansion inMathieu functions. We compare the OSRC to a finite difference method. © 2009 Elsevier B.V. All rights reserved.

Article history: Received 5 June 2014 Received in revised form 11 September 2014 Accepted 12 September 2014 Available online 22 September 2014