相关论文: Preconditioners for computing multiple solutions i…

Numerical investigation of compressible flows faces two main challenges. In order to accurately describe the flow characteristics, high-resolution nonlinear numerical schemes are needed to capture discontinuities and resolve wide…

Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…

This paper is concerned with topology optimization based on a level set method using (doubly) nonlinear diffusion equations. Topology optimization using the level set method is called level set-based topology optimization, which is possible…

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…

We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…

Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…

We introduce a novel monolithic formulation that employs Lagrange multipliers (LMs) to couple a fluid flow governed by the time-dependent Stokes equations with a poroelastic structure described by the Biot equations. The formulation is…

We investigate a novel monolithic algebraic multigrid (AMG) preconditioner for the Taylor-Hood ($\pmb{\mathbb{P}}_2/\mathbb{P}_1$) and Scott-Vogelius ($\pmb{\mathbb{P}}_2/\mathbb{P}_1^{disc}$) discretizations of the Stokes equations. The…

This paper studies the characteristics and applicability of the CutFEM approach as the core of a robust topology optimization framework for 3D laminar incompressible flow and species transport problems at low Reynolds number (Re < 200).…

Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the…

The phase separation processes are typically modeled by Cahn-Hilliard equations. This equation was originally introduced to model phase separation in binary alloys, where phase stands for concentration of different components in alloy. When…

We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…

A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…

In this paper we consider multiple saddle point problems with block tridiagonal Hessian in a Hilbert space setting. Well-posedness and the related issue of preconditioning are discussed. We give a characterization of all block structured…

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…

The Stokes-Brinkman equations model fluid flow in highly heterogeneous porous media. In this paper, we consider the numerical solution of the Stokes-Brinkman equations with stochastic permeabilities, where the permeabilities in subdomains…

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…

In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…

An articulated body is defined as a finite number of rigid bodies connected by a set of arbitrary constraints that limit the relative motion between pairs of bodies. Such a general definition encompasses a wide variety of situations in the…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…