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In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
This work is concerned with the rigorous analysis on the Generalized Multiscale Finite Element Methods (GMsFEMs) for elliptic problems with high-contrast heterogeneous coefficients. GMsFEMs are popular numerical methods for solving flow…
Message Passing Interface (MPI) plays a crucial role in distributed memory parallelization across multiple nodes. However, parallelizing MPI code manually, and specifically, performing domain decomposition, is a challenging, error-prone…
In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-GFEM) developed in [I. Babu\v{s}ka and R. Lipton, Multiscale Modeling and Simulation 9 (2011), pp. 373--406]. We outline the numerical implementation of…
This paper considers flow problems in multiscale heterogeneous porous media. The multiscale nature of the modeled process significantly complicates numerical simulations due to the need to compute huge and ill-conditioned sparse matrices,…
In this paper, we propose an efficient and accurate message-passing interface (MPI)-based parallel simulator for streamer discharges in three dimensions using the fluid model. First, we propose a new second-order semi-implicit scheme for…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
We introduce Model-Distributed Inference for Large-Language Models (MDI-LLM), a novel framework designed to facilitate the deployment of state-of-the-art large-language models (LLMs) across low-power devices at the edge. This is…
The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
What is a systematic way to efficiently apply a wide spectrum of advanced ML programs to industrial scale problems, using Big Models (up to 100s of billions of parameters) on Big Data (up to terabytes or petabytes)? Modern parallelization…
To leverage the last two decades' transition in High-Performance Computing (HPC) towards clusters of compute nodes bound together with fast interconnects, a modern scalable CFD code must be able to efficiently distribute work amongst…
The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e. coefficients with…
In this work, we describe a simple finite element approach that is able to resolve weak discontinuities in interface problems accurately. The approach is based on a fixed patch mesh consisting of quadrilaterals, that will stay unchanged…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
Generalized linear models (GLMs) arguably represent the standard approach for statistical regression beyond the Gaussian likelihood scenario. When Bayesian formulations are employed, the general absence of a tractable posterior distribution…
A high-performance gas kinetic solver using multi-level parallelization is developed to enable pore-scale simulations of rarefied flows in porous media. The Boltzmann model equation is solved by the discrete velocity method with an…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…