Related papers: Sequential Refinement Solver using Space-Time Doma…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
We propose a new method for linear second-order cone programs. It is based on the sequential quadratic programming framework for nonlinear programming. In contrast to interior point methods, it can capitalize on the warm-start capabilities…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share "nonlocal" interfaces of the size of…
We study the effect of adaptive mesh refinement on a parallel domain decomposition solver of a linear system of algebraic equations. These concepts need to be combined within a parallel adaptive finite element software. A prototype…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…
In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall often needs to be locally refined in the region approached…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of…
A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…
Deep neural networks are a promising solution for applications that solve problems based on learning data sets. DNN accelerators solve the processing bottleneck as a domain-specific processor. Like other hardware solutions, there must be…
As one of the fundamental tasks in computer vision, semantic segmentation plays an important role in real world applications. Although numerous deep learning models have made notable progress on several mainstream datasets with the rapid…
Sequential Residual Methods try to solve nonlinear systems of equations $F(x)=0$ by iteratively updating the current approximate solution along a residual-related direction. Therefore, memory requirements are minimal and, consequently,…
Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
This is an overview paper written in style of research proposal. In recent years we introduced a general framework for large-scale unconstrained optimization -- Sequential Subspace Optimization (SESOP) and demonstrated its usefulness for…