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By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal…
Recently developed machine learning techniques, in association with the Internet of Things (IoT) allow for the implementation of a method of increasing oil production from heavy-oil wells. Steam flood injection, a widely used enhanced oil…
For manufacturing of aerospace composites, several parts may be processed simultaneously using convective heating in an autoclave. Due to uncertainties including tool placement, convective Boundary Conditions (BCs) vary in each run. As a…
Leveraging the latent heat of phase change materials (PCMs) can reduce the peak temperatures and transient variations in temperature in electronic devices. But as the power levels increase, the thermal conduction pathway from the heat…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate Neumann-Neumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In…
Latent heat thermal energy storage (LHTES) systems are compelling candidates for energy storage, primarily owing to their high storage density. Improving their performance is crucial for developing the next-generation efficient and cost…
Unconditionally stable time stepping schemes are useful and often practically necessary for advancing parabolic operators in multi-scale systems. However, serious accuracy problems may emerge when taking time steps that far exceed the…
Model predictive control (MPC) has become a hot cake technology for various applications due to its ability to handle multi-input multi-output systems with physical constraints. The optimization solvers require considerable time, limiting…
We present a novel hybrid incompressible flow/material point method solver for simulating the combustion of flammable solids. Our approach utilizes a sparse grid representation of solid materials in the material point method portion of the…
Performance-, power-, and energy-aware scheduling techniques play an essential role in optimally utilizing processing elements (PEs) of heterogeneous systems. List schedulers, a class of low-complexity static schedulers, have commonly been…
The hot-rolling process is a critical stage in sheet metal production within the heavy steel industry. Traditionally, parameter adjustments such as sheet metal velocity and roll gap are performed manually, leading to inefficiencies and…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Memory tiering systems seek cost-effective memory scaling by adding multiple tiers of memory. For maximum performance, frequently accessed (hot) data must be placed close to the host in faster tiers and infrequently accessed (cold) data can…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to…
Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…