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This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity…
Many important applications across science, data analytics, and AI workloads depend on distributed matrix multiplication. Prior work has developed a large array of algorithms suitable for different problem sizes and partitionings including…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…
One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve…
To address distribution shifts between training and test data, domain generalization (DG) leverages multiple source domains to learn a model that generalizes well to unseen domains. However, existing DG methods often overfit to the source…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
We present an MPI-parallel algorithm for the in-situ visualization of computational data that is built around a distributed linear forest-of-octrees data structure. Such octrees are frequently used in element-based numerical simulations;…
We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
This article describes a geometric partitioning software that can be used for quick computation of data partitions on many-core HPC machines. It is most suited for dynamic applications with load distributions that vary with time.…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
We develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the…
From tabulated nuclear and degenerate equations of state to photon and neutrino opacities, to nuclear reaction rates: tabulated data is ubiquitous in computational astrophysics. The dynamic range that must be covered by these tables…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…