Related papers: A parallel and matrix free framework for global st…
Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of…
Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully…
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…
In the present work, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure…
Predictor-based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal…
We present a Bayesian hierarchical framework for a principled data analysis pipeline of peculiar velocity surveys, which makes explicit the inference problem of constraining cosmological parameters from redshift-independent distance…
A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered…
The classical theorems of inviscid stability have been extended for compressible flows past compliant surfaces. We consider normal modes imposed on a plane parallel compressible flow past compliant walls modelled as spring-backed plates and…
Modal stability analysis provides information about the long-time growth or decay of small-amplitude perturbations around a steady-state solution of a dynamical system. In fluid flows, exponentially growing perturbations can initiate…
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes…
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…
This paper presents a framework that supports the implementation of parallel solutions for the widespread parametric maximum flow computational routines used in image segmentation algorithms. The framework is based on supergraphs, a special…
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…
In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…
In this relation I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of…
We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization…
Conditions for input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs).…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…
The main objective of this work is to develop a unified framework that can be used as a lens to quantitatively assess and augment a wide range of coarse-grained models of turbulence, viz. large eddy simulations (LES), hybrid…