Numerical Analysis of a Discontinuous Galerkin Method for the Borrvall--Petersson Topology Optimization Problem
DOI10.1137/21M1438943zbMath1503.35180arXiv2108.03930OpenAlexW3187787899MaRDI QIDQ5866599
Publication date: 22 September 2022
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2108.03930
finite element methoddiscontinuous Galerkin methodmultiple solutionstopology optimizationnonconvex variational problem
Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10) PDEs in connection with fluid mechanics (35Q35) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Flow control and optimization for incompressible viscous fluids (76D55) PDE constrained optimization (numerical aspects) (49M41)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
- Topology optimization of channel flow problems
- Topology optimization of steady Navier-Stokes flow with body force
- Topology optimization of unsteady incompressible Navier-Stokes flows
- Numerical computations with \(H(\mathop{div})\)-finite elements for the Brinkman problem
- A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations
- Two families of mixed finite elements for second order elliptic problems
- Mixed finite elements for second order elliptic problems in three variables
- Mixed finite elements in \(\mathbb{R}^3\)
- State space Newton's method for topology optimization
- Multigrid methods for a parameter-dependent problem in primal variables
- A Reynolds-robust preconditioner for the Scott-Vogelius discretization of the stationary incompressible Navier-Stokes equations
- Numerical analysis of a topology optimization problem for Stokes flow
- Pressure-induced locking in mixed methods for time-dependent (Navier-)Stokes equations
- Topology optimization of Stokes flow with traction boundary conditions using low-order finite elements
- A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations
- H(div)-CONFORMING FINITE ELEMENTS FOR THE BRINKMAN PROBLEM
- Topology optimization for unsteady flow
- Divergence-free finite elements on tetrahedral grids for $k\ge6$
- Firedrake
- Flexible complementarity solvers for large-scale applications
- A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow
- Compact embeddings of broken Sobolev spaces and applications
- Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
- A Finite Element Analysis of Optimal Variable Thickness Sheets
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Local Discontinuous Galerkin Methods for the Stokes System
- Topology optimization of fluids in Stokes flow
- Computing Multiple Solutions of Topology Optimization Problems
- On high-order pressure-robust space discretisations, their advantages for incompressible high Reynolds number generalised Beltrami flows and beyond
- An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier--Stokes Equations at High Reynolds Number
- A Flexible Inner-Outer Preconditioned GMRES Algorithm
- On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows
- Topology optimization of slightly compressible fluids
- Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations
- Deflation for semismooth equations
- Shape optimization by the homogenization method
