70 citations · 323 across the 27 of their papers we have counts for
29 papers
Nonlocal Boundary Conditions for Truncated-Fractional Differential Equations Posed on Bounded Domains
Mikil Foss, Adam Larios, Michael Pieper
Nonlocal models have found great success in recent years. In particular, models that replace spatial derivatives with strongly singular integral operators involving finite interact…
Application of Continuous Data Assimilation in High-Resolution Ocean Modeling
Adam Larios, Mark R. Petersen, Collin Victor
We demonstrate a formulation of the Azouani-Olson-Titi (AOT) algorithm in the MPAS-Ocean implementation of the primitive equations of the ocean, presenting global ocean simulations…
Continuous Data Assimilation for the 3D and Higher-Dimensional Navier--Stokes equations with Higher-Order Fractional Diffusion
Adam Larios, Collin Victor
We study the use of the Azouani-Olson-Titi (AOT) continuous data assimilation algorithm to recover solutions of the Navier--Stokes equations modified to have higher-order fractiona…
Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: The 2D Navier-Stokes equations paradigm
Elizabeth Carlson, Adam Larios, Edriss S. Titi
We study a nonlinear-nudging modification of the Azouani-Olson-Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier-Stokes equations. We give…
The second-best way to do sparse-in-time continuous data assimilation: Improving convergence rates for the 2D and 3D Navier-Stokes equations
Adam Larios, Yuan Pei, Collin Victor
We study different approaches to implementing sparse-in-time observations into the the Azouani-Olson-Titi data assimilation algorithm. We propose a new method which introduces a "d…
Identifying the body force from partial observations of a 2D incompressible velocity field
Aseel Farhat, Adam Larios, Vincent R. Martinez +1
Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number…
Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three
Adam Larios, Mohammad Mahabubur Rahman, Kazuo Yamazaki
We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability crite…
The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations
Trenton Franz, Adam Larios, Collin Victor
We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations.…
Dynamically learning the parameters of a chaotic system using partial observations
Elizabeth Carlson, Joshua Hudson, Adam Larios +3
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assum…
A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture
Siavash Jafarzadeh, Farzaneh Mousavi, Adam Larios +1
We introduce a general and fast convolution-based method (FCBM) for peridynamics (PD). Expressing the PD integrals in terms of convolutions and computing them by fast Fourier trans…
Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation
Adam Larios, Elizabeth Carlson
We rigorously prove the well-posedness of the formal sensitivity equations with respect to the Reynolds number corresponding to the 2D incompressible Navier-Stokes equations. Moreo…
Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations
Matthew Gardner, Adam Larios, Leo G. Rebholz +2
We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vor…
On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation
Adam Larios, Kazuo Yamazaki
The Kuramoto-Sivashinsky equations (KSE) arise in many diverse scientific areas, and are of much mathematical interest due in part to their chaotic behavior, and their similarity t…
Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methods
Siavash Jafarzadeh, Adam Larios, Florin Bobaru
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution i…
Parameter Recovery and Sensitivity Analysis for the 2D Navier-Stokes Equations Via Continuous Data Assimilation
Elizabeth Carlson, Joshua Hudson, Adam Larios
We study a continuous data assimilation algorithm proposed by Azouani, Olson, and Titi (AOT) in the context of an unknown Reynolds number. We determine the large-time error between…
Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study
Adam Larios, Collin Victor
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as tim…
Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data
Adam Larios, Yuan Pei
We propose a data assimilation algorithm for the 2D Navier-Stokes equations, based on the Azouani, Olson, and Titi (AOT) algorithm, but applied to the 2D Navier-Stokes-Voigt equati…
Global in time stability and accuracy of IMEX-FEM data assimilation schemes for the Navier-Stokes equations
Adam Larios, Leo G. Rebholz, Camille Zerfas
We study numerical schemes for incompressible Navier-Stokes equations using IMEX temporal discretizations, finite element spacial discretizations, and equipped with continuous data…
Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations
Adam Larios, Yuan Pei, Leo Rebholz
The velocity-vorticity formulation of the 3D Navier-Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose…
Continuous data assimilation for the magnetohydrodynamic equations in 2D using one component of the velocity and magnetic fields
Animikh Biswas, Joshua Hudson, Adam Larios +1
We propose several continuous data assimilation (downscaling) algorithms based on feedback control for the 2D magnetohydrodynamic (MHD) equations. We show that for sufficiently lar…
Nonlinear Continuous Data Assimilation
Adam Larios, Yuan Pei
We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Ol…
On the local well-posedness and a Prodi-Serrin type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion
Adam Larios, Yuan Pei
We prove a Prodi-Serrin-type global regularity condition for the three-dimensional Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal diffusion, in terms of…
A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization
Adam Larios, Mark Petersen, Edriss S. Titi +1
We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related…
A Blow-Up Criterion for the 3D Euler Equations Via the Euler-Voigt Inviscid Regularization
Adam Larios, Edriss S. Titi
We propose a new blow-up criterion for the 3D Euler equations of incompressible fluid flows, based on the 3D Euler-Voigt inviscid regularization. This criterion is similar in chara…