Complexity analysis and scalability of a matrix-free extrapolated geometric multigrid solver for curvilinear coordinates representations from fusion plasma applications
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Tokamak fusion reactors are promising alternatives for future energy production. Gyrokinetic simulations are important tools to understand physical processes inside tokamaks and to improve the design of future plants. In gyrokinetic codes such as Gysela, these simulations involve at each time step the solution of a gyrokinetic Poisson equation defined on disk-like cross sections. The authors of [14] , [15] proposed to discretize a simplified differential equation using symmetric finite differences derived from the resulting energy functional and to use an implicitly extrapolated geometric multigrid scheme tailored to problems in curvilinear coordinates. In this article, we extend the discretization to a more realistic partial differential equation and demonstrate the optimal linear complexity of the proposed solver, in terms of computation and memory. We provide a general framework to analyze floating point operations and memory usage of matrix-free approaches for stencil-based operators. Finally, we give an efficient matrix-free implementation for the considered solver exploiting a task-based multithreaded parallelism which takes advantage of the disk-shaped geometry of the problem. We demonstrate the parallel efficiency for the solution of problems of size up to 50 million unknowns.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 it