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Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the…

Recently, federated learning has emerged as a promising approach for training a global model using data from multiple organizations without leaking their raw data. Nevertheless, directly applying federated learning to real-world tasks faces…

We describe a new parallel implementation, mplrs, of the vertex enumeration code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the…

We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…

We present a simple and easy to apply methodology for using high-level self-submitting parallel job queues in an MPI environment. Using C++, we implemented a library of functions, MPQueue, both for testing our concepts and for use in real…

In many distributed learning problems, the heterogeneous loading of computing machines may harm the overall performance of synchronous strategies. In this paper, we propose an effective asynchronous distributed framework for the…

We present a locally adapted parametric finite element method for interface problems. For this adapted finite element method we show optimal convergence for elliptic interface problems with a discontinuous diffusion parameter. The method is…

The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…

Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture…

Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser-matter interactions with Particle-In-Cell (PIC)…

This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…

The canonical formulation of federated learning treats it as a distributed optimization problem where the model parameters are optimized against a global loss function that decomposes across client loss functions. A recent alternative…

In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…

Scale-out parallel processing based on MPI is a 25-year-old standard with at least another decade of preceding history of enabling technologies in the High Performance Computing community. Newer frameworks such as MapReduce, Hadoop, and…

Deep Metric Learning (DML) models often require strong local and global representations, however, effective integration of local and global features in DML model training is a challenge. DML models are often trained with specific loss…

Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…

Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…

In practice, objective functions of real-time control systems can have multiple local minimums or can dramatically change over the function space, making them hard to optimize. To efficiently optimize such systems, in this paper, we develop…

Diffusion large language models (dLLMs) represent a significant advancement in text generation, offering parallel token decoding capabilities. However, existing open-source implementations suffer from quality-speed trade-offs that impede…