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Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…
Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B connected via a linker C. The existing ISAPT algorithm displays…
We consider L-scheme and Newton based solvers for Biot model under small or large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Further, the fluid compressibility is assumed to be nonlinear. A…
This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the…
In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…
Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…
In this paper, we consider the numerical solution of a binary fluid-surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg-Landau double well potential, and a logarithmic Flory-Huggins…
The Parareal algorithm, which is related to multiple shooting, was introduced for solving evolution problems in a time-parallel manner. The algorithm was then extended to solve time-periodic problems. We are interested here in time-periodic…
In this paper, we consider a coupled system of mixed hyperbolic-parabolic type which describes the Biot consolidation model in poro-elasticity. We establish a local Carleman estimate for Biot consilidation system. Using this estimate, we…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
We investigate the effectiveness of different dynamical decoupling protocols for storage of a single qubit in the presence of a purely dephasing bosonic bath, with emphasis on comparing quantum coherence preservation under uniform vs.…
We investigate how dynamical decoupling methods may be used to manipulate the time evolution of quantum many-body systems. These methods consist of sequences of external control operations designed to induce a desired dynamics. The systems…
The present paper aims at providing a numerical strategy to deal with PDE-constrained optimization problems solved with the adjoint method. It is done through out a unified formulation of the constraint PDE and the adjoint model. The…
We investigate a multirate time step approach applied to decoupled methods in fluid and structure interaction(FSI) computation, where two different time steps are used for fluid and structure respectively. For illustration, the multirate…
A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
This paper investigates two distinct approaches to the dynamic modeling of aerial continuum manipulators (ACMs): the decoupled and the coupled formulations. Both open-loop and closed-loop behaviors of a representative ACM are analyzed. The…
We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…