Computing Multiple Solutions of Topology Optimization Problems
From MaRDI portal
Publication:4997350
DOI10.1137/20M1326209zbMath1472.35308arXiv2004.11797OpenAlexW3159302551MaRDI QIDQ4997350
I. P. A. Papadopoulos, Thomas M. Surowiec, Patrick E. Farrell
Publication date: 29 June 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2004.11797
Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) PDEs in connection with fluid mechanics (35Q35) Interior-point methods (90C51) Optimization of other properties in solid mechanics (74P10) Compliance or weight optimization in solid mechanics (74P05)
Related Items
A Novel Density Based Approach for Topology Optimization of Stokes Flow ⋮ Numerical analysis of a topology optimization problem for Stokes flow ⋮ A provably efficient monotonic-decreasing algorithm for shape optimization in Stokes flows by phase-field approaches ⋮ Preconditioners for Computing Multiple Solutions in Three-Dimensional Fluid Topology Optimization ⋮ Large-scale parallel topology optimization of three-dimensional incompressible fluid flows in a level set, anisotropic mesh adaptation framework ⋮ The dual approach to optimal control in the coefficients of nonlocal nonlinear diffusion ⋮ A mathematical game for topology optimization of cooling systems ⋮ Numerical Analysis of a Discontinuous Galerkin Method for the Borrvall--Petersson Topology Optimization Problem
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
- A mesh-independence result for semismooth Newton methods.
- Automated solution of differential equations by the finite element method. The FEniCS book
- A control reduced primal interior point method for a class of control constrained optimal control problems
- Superlinear convergence of the control reduced interior point method for PDE constrained optimization
- Primal-dual interior-point methods for PDE-constrained optimization
- Topology optimization of elastic continua using restriction.
- Structural optimization using sensitivity analysis and a level-set method.
- A level-set method for shape optimization.
- State space Newton's method for topology optimization
- The gradient theory of phase transitions and the minimal interface criterion
- Primal-dual Newton-type interior-point method for topology optimization
- A level set method for structural topology optimization.
- Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with deflated continuation
- A nonsmooth version of Newton's method
- Deflation techniques for the calculation of further solutions of a nonlinear system
- Practical bifurcation and stability analysis
- Filters in topology optimization
- Composing Scalable Nonlinear Algebraic Solvers
- Filters in topology optimization based on Helmholtz-type differential equations
- Flexible complementarity solvers for large-scale applications
- Barrier Methods for Optimal Control Problems with State Constraints
- Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
- The method of moving asymptotes—a new method for structural optimization
- A Barrier Method for Large-Scale Constrained Optimization
- On the Topological Derivative in Shape Optimization
- Semismooth Newton Methods for Operator Equations in Function Spaces
- The Primal-Dual Active Set Strategy as a Semismooth Newton Method
- Superlinear Convergence of Affine-Scaling Interior-Point Newton Methods for Infinite-Dimensional Nonlinear Problems with Pointwise Bounds
- Topology Optimization Theory for Laminar Flow
- Optimization of a Multiphysics Problem in Semiconductor Laser Design
- Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
- Interior Methods for Nonlinear Optimization
- Topology optimization of fluids in Stokes flow
- Mesh Dependence in PDE-Constrained Optimisation
- The violation of objectivity in Laplace formulations of the Navier–Stokes equations
- Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations
- ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
- Deflation for semismooth equations
- Topology optimization of nonlinear elastic structures and compliant mechanisms
