Engineering topics

Keyes, David

Publications and source records attributed to Keyes, David.

4 records

DOE OSTI2026

Linear complexity

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathscr{H}^{2}$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathscr{H}^{2}$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ‘blackbox’ in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

Boukaram, Wajih↗

NASA NTRS1999

Parallel Implementation of the Discontinuous Galerkin Method

This paper describes a parallel implementation of the discontinuous Galerkin method. 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 all 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.

Baggag, Abdalkader↗

NASA NTRS1999

Parallelization of an Object-Oriented Unstructured Aeroacoustics Solver

A computational aeroacoustics code based on the discontinuous Galerkin method is ported to several parallel platforms using MPI. The discontinuous Galerkin method is a compact high-order method that retains its accuracy and robustness on non-smooth unstructured meshes. In its semi-discrete form, the discontinuous Galerkin method can be combined with explicit time marching methods making it well suited to time accurate computations. The compact nature of the discontinuous Galerkin method also makes it well suited for distributed memory parallel platforms. The original serial code was written using an object-oriented approach and was previously optimized for cache-based machines. The port to parallel platforms was achieved simply by treating partition boundaries as a type of boundary condition. Code modifications were minimal because boundary conditions were abstractions in the original program. Scalability results are presented for the SCI Origin, IBM SP2, and clusters of SGI and Sun workstations. Slightly superlinear speedup is achieved on a fixed-size problem on the Origin, due to cache effects.

Baggag, Abdelkader↗

NASA NTRS1994

A simple hyperbolic model for communication in parallel processing environments

We introduce a model for communication costs in parallel processing environments called the 'hyperbolic model,' which generalizes two-parameter dedicated-link models in an analytically simple way. Dedicated interprocessor links parameterized by a latency and a transfer rate that are independent of load are assumed by many existing communication models; such models are unrealistic for workstation networks. The communication system is modeled as a directed communication graph in which terminal nodes represent the application processes that initiate the sending and receiving of the information and in which internal nodes, called communication blocks (CBs), reflect the layered structure of the underlying communication architecture. The direction of graph edges specifies the flow of the information carried through messages. Each CB is characterized by a two-parameter hyperbolic function of the message size that represents the service time needed for processing the message. The parameters are evaluated in the limits of very large and very small messages. Rules are given for reducing a communication graph consisting of many to an equivalent two-parameter form, while maintaining an approximation for the service time that is exact in both large and small limits. The model is validated on a dedicated Ethernet network of workstations by experiments with communication subprograms arising in scientific applications, for which a tight fit of the model predictions with actual measurements of the communication and synchronization time between end processes is demonstrated. The model is then used to evaluate the performance of two simple parallel scientific applications from partial differential equations: domain decomposition and time-parallel multigrid. In an appropriate limit, we also show the compatibility of the hyperbolic model with the recently proposed LogP model.

Stoica, Ion↗