Impact of Load Balancing on Unstructured Adaptive Grid Computations for Distributed-Memory Multiprocessors

The computational requirements for an adaptive solution of unsteady problems change as the simulation progresses. This causes workload imbalance among processors on a parallel machine which, in turn, requires significant data movement at runtime. We present a new dynamic load-balancing framework, called JOVE, that balances the workload across all processors with a global view. Whenever the computational mesh is adapted, JOVE is activated to eliminate the load imbalance. JOVE has been implemented on an IBM SP2 distributed-memory machine in MPI for portability. Experimental results for two model meshes demonstrate that mesh adaption with load balancing gives more than a sixfold improvement over one without load balancing. We also show that JOVE gives a 24-fold speedup on 64 processors compared to sequential execution

RIACS

The Research Institute for Advanced Computer Science (RIACS) was established by the Universities Space Research Association (USRA) at the NASA Ames Research Center (ARC) on June 6, 1983. RIACS is privately operated by USRA, a consortium of universities that serves as a bridge between NASA and the academic community. Under a five-year co-operative agreement with NASA, research at RIACS is focused on areas that are strategically enabling to the Ames Research Center's role as NASA's Center of Excellence for Information Technology. The primary mission of RIACS is charted to carry out research and development in computer science. This work is devoted in the main to tasks that are strategically enabling with respect to NASA's bold mission in space exploration and aeronautics. There are three foci for this work: (1) Automated Reasoning. (2) Human-Centered Computing. and (3) High Performance Computing and Networking. RIACS has the additional goal of broadening the base of researcher in these areas of importance to the nation's space and aeronautics enterprises. Through its visiting scientist program, RIACS facilitates the participation of university-based researchers, including both faculty and students, in the research activities of NASA and RIACS. RIACS researchers work in close collaboration with NASA computer scientists on projects such as the Remote Agent Experiment on Deep Space One mission, and Super-Resolution Surface Modeling

Self-Adaptive Methods for PDE

[no abstract available

Anisotropic Finite Element Mesh Adaptation via Higher Dimensional Embedding

In this paper we provide a novel anisotropic mesh adaptation technique for adaptive finite element analysis. It is based on the concept of higher dimensional embedding, which was exploited in [1], [2], [3], [4] to obtain an anisotropic curvature adapted mesh that fits a complex surface in R3. In the context of adaptive finite element simulation, the solution (which is an unknown function f : Ω ⊂ d → ) is sought by iteratively modifying a finite element mesh according to a mesh sizing field described via a (discrete) metric tensor field that is typically obtained through an error estimator. We proposed to use a higher dimensional embedding, Φf (x):= (x1, …, xd, s f (x1, …, xd), s ▿ f (x1, …, xd))t, instead of the mesh sizing field for the mesh adaption. This embedding contains both informations of the function f itself and its gradient. An isotropic mesh in this embedded space will correspond to an anisotropic mesh in the actual space, where the mesh elements are stretched and aligned according to the features of the function f. To better capture the anisotropy and gradation of the mesh, it is necessary to balance the contribution of the components in this embedding. We have properly adjusted Φf (x) for adaptive finite element analysis. To better understand and validate the proposed mesh adaptation strategy, we first provide a series of experimental tests for piecewise linear interpolation of known functions. We then applied this approach in an adaptive finite element solution of partial differential equations. Both tests are performed on two-dimensional domains in which adaptive triangular meshes are generated. We compared these results with the ones obtained by the software BAMG – a metric-based adaptive mesh generator. The errors measured in the L2 norm are comparable. Moreover, our meshes captured the anisotropy more accurately than the meshes of BAMG

Drift-diffusion models for innovative semiconductor devices and their numerical solution

We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization

HARP: A Dynamic Inertial Spectral Partitioner

Partitioning unstructured graphs is central to the parallel solution of computational science and engineering problems. Spectral partitioners, such recursive spectral bisection (RSB), have proven effecfive in generating high-quality partitions of realistically-sized meshes. The major problem which hindered their wide-spread use was their long execution times. This paper presents a new inertial spectral partitioner, called HARP. The main objective of the proposed approach is to quickly partition the meshes at runtime in a manner that works efficiently for real applications in the context of distributed-memory machines. The underlying principle of HARP is to find the eigenvectors of the unpartitioned vertices and then project them onto the eigerivectors of the original mesh. Results for various meshes ranging in size from 1000 to 100,000 vertices indicate that HARP can indeed partition meshes rapidly at runtime. Experimental results show that our largest mesh can be partitioned sequentially in only a few seconds on an SP2 which is several times faster than other spectral partitioners while maintaining the solution quality of the proven RSB method. A parallel WI version of HARP has also been implemented on IBM SP2 and Cray T3E. Parallel HARP, running on 64 processors SP2 and T3E, can partition a mesh containing more than 100,000 vertices into 64 subgrids in about half a second. These results indicate that graph partitioning can now be truly embedded in dynamically-changing real-world applications