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A structured preconditioned conjugate gradient (PCG) solver is developed for the Newton steps in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics…
We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…
The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…
Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given…
We introduce a fusion of GPU accelerated primal heuristics for Mixed Integer Programming. Leveraging GPU acceleration enables exploration of larger search regions and faster iterations. A GPU-accelerated PDLP serves as an approximate LP…
The observed and expected continued growth in the number of nodes in large-scale parallel computers gives rise to two major challenges: global communication operations are becoming major bottlenecks due to their limited scalability, and the…
Performance tools for emerging heterogeneous exascale platforms must address two principal challenges when analyzing execution measurements. First, measurement of large-scale executions may record mountains of performance data. Second,…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…
We present a distributed framework of the Primal-Dual Hybrid Gradient (PDHG) algorithm for solving massive-scale linear programming (LP) problems. Although PDHG-based solvers demonstrate strong performance on single-node GPU architectures,…
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…
We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be…
GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…
For computational fluid dynamics (CFD) applications with a large number of grid points/cells, parallel computing is a common efficient strategy to reduce the computational time. How to achieve the best performance in the modern…
We present a new algorithm to quickly generate high-performance GPU implementations of complex imaging and vision pipelines, directly from high-level Halide algorithm code. It is fully automatic, requiring no schedule templates or…
CPU-GPU heterogeneous systems are now commonly used in HPC (High-Performance Computing). However, improving the utilization and energy-efficiency of such systems is still one of the most critical issues. As one single program typically…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
The Legendre spectral Galerkin method of self-adjoint second order elliptic equations usually results in a linear system with a dense and ill-conditioned coefficient matrix. In this paper, the linear system is solved by a preconditioned…
In this paper, we develop a new parallel auxiliary grid algebraic multigrid (AMG) method to leverage the power of graphic processing units (GPUs). In the construction of the hierarchical coarse grid, we use a simple and fixed coarsening…