7,111 research outputs found
A short note on a Bernstein-Bezier basis for the pyramid
We introduce a Bernstein-Bezier basis for the pyramid, whose restriction to
the face reduces to the Bernstein-Bezier basis on the triangle or
quadrilateral. The basis satisfies the standard positivity and partition of
unity properties common to Bernstein polynomials, and spans the same space as
non-polynomial pyramid bases in the literature.Comment: Submitte
Residual based adaptivity and PWDG methods for the Helmholtz equation
We present a study of two residual a posteriori error indicators for the
Plane Wave Discontinuous Galerkin (PWDG) method for the Helmholtz equation. In
particular we study the h-version of PWDG in which the number of plane wave
directions per element is kept fixed. First we use a slight modification of the
appropriate a priori analysis to determine a residual indicator. Numerical
tests show that this is reliable but pessimistic in that the ratio between the
true error and the indicator increases as the mesh is refined. We therefore
introduce a new analysis based on the observation that sufficiently many plane
waves can approximate piecewise linear functions as the mesh is refined.
Numerical results demonstrate an improvement in the efficiency of the
indicators
GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations
We discuss the development, verification, and performance of a GPU
accelerated discontinuous Galerkin method for the solutions of two dimensional
nonlinear shallow water equations. The shallow water equations are hyperbolic
partial differential equations and are widely used in the simulation of tsunami
wave propagations. Our algorithms are tailored to take advantage of the single
instruction multiple data (SIMD) architecture of graphic processing units. The
time integration is accelerated by local time stepping based on a multi-rate
Adams-Bashforth scheme. A total variational bounded limiter is adopted for
nonlinear stability of the numerical scheme. This limiter is coupled with a
mass and momentum conserving positivity preserving limiter for the special
treatment of a dry or partially wet element in the triangulation. Accuracy,
robustness and performance are demonstrated with the aid of test cases. We
compare the performance of the kernels expressed in a portable threading
language OCCA, when cross compiled with OpenCL, CUDA, and OpenMP at runtime.Comment: 26 pages, 51 figure
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