Related papers: A Fully Discrete Adjoint Method for Optimization o…
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…
Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
This paper develops a framework connecting discrete adjoint gradient-error analysis with an optimization method that uses directional error tolerances, and applies it to airfoil shape optimization governed by a conservative full-potential…
Robust and efficient solvers for coupled-adjoint linear systems are crucial to successful aerostructural optimization. Monolithic and partitioned strategies can be applied. The monolithic approach is expected to offer better robustness and…
The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard…
We introduce a novel primal-dual flow for affine constrained convex optimization problems. As a modification of the standard saddle-point system, our primal-dual flow is proved to possess the exponential decay property, in terms of a…
In this study, we find the optimal control boundary (i.e., actuator velocity) that cancels the acoustic reverberations inside drop-on-demand inkjet printheads at a specific time. We formulate an optimization problem to minimize the total…
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability…
The authors propose a recycling Krylov subspace method for the solution of a sequence of self-adjoint linear systems. Such problems appear, for example, in the Newton process for solving nonlinear equations. Ritz vectors are automatically…
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
The optimal control of thermally convective flows is usually modeled by an optimization problem with constraints of Boussinesq equations that consist of the Navier-Stokes equation and an advection-diffusion equation. This optimal control…
This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation…
The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…
High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…
Adjoint based shape optimization is a powerful technique in fluid-dynamics optimization, capable of identifying an optimal shape within only dozens of design iterations. However, when extended to rarefied gas flows, the computational cost…
In the finite element analysis with fast decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow, we investigate strong nonlinear behavior in 2D creeping contraction flow. The algorithm is applicable in the whole…
Various distributed gradient descent algorithms for multi-agent optimization have incorporated the Nesterov accelerated gradient method, where the use of momentum enhances convergence rates. These algorithms have found broad applications in…
In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control variables. We develop an…