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Many computer systems for calculating the proper organization of memory are among the most critical issues. Using a tier cache memory (along with branching prediction) is an effective means of increasing modern multi-core processors'…
To analyze large sets of grid states, e.g. when evaluating the impact from the uncertainties of the renewable generation with probabilistic Monte Carlo simulation or in stationary time series simulation, large number of power flow…
Graphics Processing Units (GPUs) have become the standard in accelerating scientific applications on heterogeneous systems. However, as GPUs are getting faster, one potential performance bottleneck with GPU-accelerated applications is the…
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…
This article presents a new high-level parallel computational model named BSF - Bulk Synchronous Farm. The BSF model extends the BSP model to deal with the compute-intensive iterative numerical methods executed on distributed-memory…
Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models…
The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse…
The fast marching method is well-known for its worst-case optimal computational complexity in solving the Eikonal equation, and has been employed in numerous scientific and engineering fields. However, it has barely benefited from…
Vertex-patch smoothers are essential for the robust convergence of geometric multigrid methods in high-order finite element applications, yet their adoption is traditionally hindered by the prohibitive cost of solving local patch problems.…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
In addition to hardware wall-time restrictions commonly seen in high-performance computing systems, it is likely that future systems will also be constrained by energy budgets. In the present work, finite difference algorithms of varying…
Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…
Sparse triangular solve (SpTRSV) is widely used in various domains. Numerous studies have been conducted using CPUs, GPUs, and specific hardware accelerators, where dataflows can be categorized into coarse and fine granularity. Coarse…
The study deals with the parallelization of 2D and 3D finite element based Navier-Stokes codes using direct solvers. Development of sparse direct solvers using multifrontal solvers has significantly reduced the computational time of direct…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018),…
Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…