Parallelization of FDM/FEM computation for PDEs on PARAM YUVA-II cluster of Xeon Phi coprocessors
Bibliographic record
Abstract
This paper discusses an efficient implementation of finite difference method (FDM) and finite element method (FEM) computations for Partial Differential Equation (Poisson Equation) on a message passing cluster with Intel Xeon Phi coprocessors[6,15]. We have performed computations on PARAM YUVA-II [9] which is a message passing cluster with compute nodes as Xeon multi-core processors and Xeon Phi coprocessors [6,15,17-19]. A combination of OpenMP [4] and MPI [5,19,20] is used for structured grid FDM computations. The unstructured triangular and hexahedral meshes and graph partitioning software METIS [10] are used in FEM computations. The Jacobi iterative method is used to solve resulting matrix system of linear equations. A detailed performance analysis of optimizations on Xeon Phi coprocessor using OpenMP and MPI framework are presented. Our experiments indicate that MPI-OpenMP codes on FDM computations achieve 2X to 3X speed-ups for large mesh sizes. The FEM implementation has shown marginal improvement in speed-up on Xeon Phi Cluster.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".