Parallel Implementation of the Discontinuous Galerkin Method

Abstract

This paper describes a parallel implementation of the discontinuous Galerkin method. The discontinuous Galerkin is a spatially compact method that retains its accuracy and robustness on non-smooth unstructured grids and is well suited for time dependent simulations. Several parallelization approaches are studied and evaluated. The most natural and symmetric of the approaches has been implemented in an object-oriented code used to simulate aeroacoustic scattering. The parallel implementation is MPI-based and has been tested on various parallel platforms such as the SGI Origin, IBM SP2, and clusters of SGI and Sun workstations. The scalability results presented for the SGI Origin show slightly superlinear speedup on a fixed-size problem due to cache effects. MotivationThe discontinuous Galerkin (DG) method is a robust and compact finite element projection method that provides a practical framework for the development of high-order accurate methods using unstructured grids. The method is well suited for large-scale time-dependent computations in which high accuracy is required. An important distinction between the DG method and the usual finite-element method is that in the DG method the resulting equations are local to the generating element. The solution within each element is not reconstructed by looking to neighboring elements. Thus, each element may be thought of as a separate entity that merely needs to obtain some boundary data from its neighbors. The compact form of the DG method makes it well suited for parallel computer platforms. This compactness also allows a heterogeneous treatment of problems. That is, the element topology, the degree of approximation and even the choice *

The MPI parallelization of the diffusion-drift algorithm for quantitative analysis of breast tumor electric signals

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Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics – a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

“…We have allowed the computation of auxiliary diagnostic variables between the call of send and receive. Further code revision could include the computation of the right-hand side and internal flux computations as described in Baggag et al (1999). In Algorithm 3 we describe how we overlap the computation of auxiliary variables and the computation of the gradient of the solution for the diffusion operator with the communication of the fluxes.…”

“…This allows the computation of internal edge and element integra communication. We have allowed the computation of auxiliary diagnostic variables between th Further code revision could include the computation of the right hand side and internal flux co (Baggag et al (1999)). In Algorithm 3 we describe how we overlap the computation of auxiliary va 8 Most notable about the implementation explained above is that, even in the absence of additional computation to be completed during communication, the packing and unpacking of the buffers provides some data movement to be accomplished while waiting for messages to be received.…”

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