No abstract

Abstract. The spectral element method is well known as an efficient way to obtain high-order numerical solutions on unstructured finite element grids. However, the oscillatory nature of the method's advection operator makes it unsuitable for many applications. One popular way to address this problem is with high-order discontinuous-Galerkin methods. In this work, an alternative solution which fits within the continuous Galerkin formulation of the spectral element method is proposed. Making use of a compatible formulation of spectral elements, a natural way to implement conservative non-oscillatory reconstructions for spectral element advection is shown. The reconstructions are local to the element and thus preserve the parallel efficiency of the method. Numerical results from a low-order quasi-monotone reconstruction and a higher-order signpreserving reconstruction are presented.

No abstract

High-order finite element methods for the atmospheric shallow water equations are reviewed. The accuracy and efficiency of nodal continuous and discontinuous Galerkin spectral elements are evaluated using the standard test problems proposed by Williamson et al (1992). The relative merits of strong-stability preserving (SSP) explicit Runge-Kutta and multistep time discretizations are discussed. Distributed memory MPI implementations are compared on the basis of the total computation time required, sustained performance and parallel scalability. Because a discontinuous Galerkin method permits the overlap of computation and communication, higher sustained execution rates are possible at large processor counts.

SUMMARYIn order to image complex geological structures, seismic surveys acquire an increasingly large amount of data. While the resulting data sets enable higher-resolution images of the subsurface, they also contain redundant information and require large computational resources for processing. One approach for mitigating this trend is blended imaging, which combines the original shot records into a smaller number of blended shots at the expense of crosstalk in the final image. Since the cost of imaging is roughly proportional to the number of shots, blended imaging directly leads to a faster imaging process. In contrast to the existing shot encoding schemes, we establish a novel connection between blended imaging and dimensionality reduction using the Johnson-Lindenstrauss lemma. We introduce three new shot encoding schemes based on random projections and evaluate their performance. Our experiments on three data sets show that our random shot encoding schemes are competitive with existing shot encoding schemes and outperform decimated shot encoding for small numbers of shots.