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Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…

We present an efficient open-source implementation of the multiparticle collision dynamics (MPCD) algorithm that scales to run on hundreds of graphics processing units (GPUs). We especially focus on optimizations for modern GPU…

Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO2 containment as a climate change mitigation strategy. These simulations involve solving numerous…

Subgraph isomorphism is a well-known NP-hard problem that is widely used in many applications, such as social network analysis and query over the knowledge graph. Due to the inherent hardness, its performance is often a bottleneck in…

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…

This work presents and evaluates a novel input parameterization method which improves the tractability of model predictive control (MPC) for high degree of freedom (DoF) robots. Experimental results demonstrate that by parameterizing the…

Evolution can be broadly described in terms of mutations of the genotype and the subsequent selection of the phenotype. The full enumeration of a given genotype-phenotype (GP) map is therefore a powerful technique in examining evolutionary…

Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…

The conjugate gradient solver (CG) is a prevalent method for solving symmetric and positive definite linear systems Ax=b, where effective preconditioners are crucial for fast convergence. Traditional preconditioners rely on prescribed…

Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…

Edge computing's growing prominence, due to its ability to reduce communication latency and enable real-time processing, is promoting the rise of high-performance, heterogeneous System-on-Chip solutions. While current approaches often…

We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening…

Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…

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…

The performance of graph programs depends highly on the algorithm, the size and structure of the input graphs, as well as the features of the underlying hardware. No single set of optimizations or one hardware platform works well across all…

We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…

This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…

Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…

In this paper a simple, robust, and general purpose approach to implement the Incompressible Smoothed Particle Hydrodynamics (ISPH) method is proposed. This approach is well suited for implementation on CPUs and GPUs. The method is…

Solving elliptic PDEs in more than one dimension can be a computationally expensive task. For some applications characterised by a high degree of anisotropy in the coefficients of the elliptic operator, such that the term with the highest…