Climate modeling encompasses an enormous range of spatial and temporal scales. One of its great remaining challenges is bridging the scale gaps between global climate processes, basinscale and regional impacts, and smaller-scale ecosystem dynamics. Improving and accessing enhanced computational resources will help bridge this gap. Nonetheless, enhanced computer power alone is insufficient witho...

The spectral element method (SEM) is a high order numerical method for solving partial differential equations that inherits the accuracy of spectral methods and the geometrical flexibility of the finite element method. These lectures provide an introduction to the SEM for graduate students in Earth science. The construction of the method is described for a model problem in 1D and 2D. The elemen...

This article presents an analysis of free vibration of elastically supported Timoshenko beams by using the spectral element method. The governing partial differential equation is elaborated to formulate the spectral stiffness matrix. Effectively, the non classical end boundary conditions of the beam are the primordial task to calibrate the phenomenon of the Timoshenko beam-soil foundation inter...

Higher order and spectral methods have been used with success for elliptic and parabolic initial and boundary value problems with smooth solutions. On the other hand, higher order methods have been applied to hyperbolic problems with less success, as higher order approximations of discontinuous solutions suffer from the Gibbs phenomenon. We extend past work and show that spectral methods yield ...

A spectral-element method for solving the scattering problem of timeharmonic sound waves in a homogeneous compressible fluid by an obstacle is developed in this paper. The method is based on a boundary perturbation technique coupled with an efficient spectral-element solver. Ample numerical results are presented to show the accuracy and stability of the method.

We examine the dual graph representation of simplicial manifolds in causal dynamical triangulations (CDT) as a means to build observables and propose new based on finite element methods (FEM). In particular, with application FEM techniques, we extract (low-lying) spectrum Laplace-Beltrami (LB) operator Sobolev space ${H}^{1}$ scalar functions piecewise flat compare them corresponding results ob...