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In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…

Modeling transition-continuum hypersonic flows poses significant challenges due to thermodynamic nonequilibrium and the associated breakdown of the continuum assumption. Standard continuum models such as the Navier-Stokes equations are…

Autonomous robots enjoy a wide popularity nowadays and have been applied in many applications, such as home security, entertainment, delivery, navigation and guidance. It is vital to robots to track objects accurately in these applications,…

The overarching goal of this work is to develop an accurate, robust, and stable methodology for finite deformation modeling using strong-form peridynamics (PD) and the correspondence modeling framework. We adopt recently developed methods…

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

A Skeleton-stabilized ImmersoGeometric Analysis technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed formulation fits within the framework of the finite cell method, where essential…

Optimization-based 3D object tracking is known to be precise and fast, but sensitive to large inter-frame displacements. In this paper we propose a fast and effective non-local 3D tracking method. Based on the observation that erroneous…

The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable…

We present a novel structure-preserving numerical scheme for discontinuous finite element approximations of nonlinear hyperbolic systems. The method can be understood as a generalization of the Lax-Friedrichs flux to a high-order staggered…

High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…

The paper deals with the implicit programming approach to a class of Mathematical Programs with Equilibrium Constraints (MPECs) and bilevel programs in the case when the corresponding reduced problems are solved using a bundle method of…

Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…

Legged locomotion is a complex control problem that requires both accuracy and robustness to cope with real-world challenges. Legged systems have traditionally been controlled using trajectory optimization with inverse dynamics. Such…

Compressible flow problems are characterized by highly nonlinear, implicit, and often transcendental governing equations. In undergraduate gas dynamics education, solving these equations traditionally relies on iterative numerical methods…

A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single…

In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…

Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of…

Network alignment task, which aims to identify corresponding nodes in different networks, is of great significance for many subsequent applications. Without the need for labeled anchor links, unsupervised alignment methods have been…