This video lecture focuses on implementing distributed parallelism using HPX to solve large linear algebra systems (LLAS) equations. The instructor revisits the SPMD model and CSP model from a previous lecture, then demonstrates how to implement a Jacobi method for distributed computation, addressing challenges like data dependencies across partitions and optimizing for performance.
SPMD Model and Data Decomposition: The lecture emphasizes using the SPMD (Single Program, Multiple Data) model for distributed applications. The problem is decomposed into partitions, each handled by a node, requiring careful consideration of data distribution to ensure a collectively exhaustive dataset.
Jacobi Method and Ghost Cells: The Jacobi method is presented as a way to solve LLAS equations without using matrices. To overcome data dependencies across partitions (a problem inherent in this approach), "ghost cells" are introduced – extra rows added to partitions to allow computations using only local data, mimicking a globally accessible dataset. These ghost cells are updated after each time step via communication with neighboring partitions.
Bulk Synchronous Programming (BSP) and its limitations: The communication-computation lock step inherent in the BSP model is highlighted. Uneven work distribution across nodes can cause significant performance bottlenecks because the system waits for the slowest node, leading to wasted computational resources.
Asynchronous Communication for Performance Improvement: To mitigate the BSP limitations, asynchronous communication is introduced. This allows computation on inner grid cells to proceed concurrently with communication for ghost cells, maximizing resource utilization and reducing idle time. The use of futures and co-await helps manage asynchronous operations without significantly increasing code complexity.
