Large-scale topology optimization using preconditioned Krylov subspace methods with recycling

Large-scale topology optimization using preconditioned Krylov subspace methods with recycling

The computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis. We propose fast iterative solvers for large threedimensional topology optimization problems to address this problem. Since the linear systems in the sequence of optimization steps change slowly from one step to the next, we can significantly reduce th...

Large Scale Topology Optimization Using Preconditioned Krylov Subspace Recycling and Continuous Approximation of Material Distribution

Large-scale topology optimization problems demand the solution of a large number of linear systems arising in the finite element analysis. These systems can be solved efficiently by special iterative solvers. Because the linear systems in the sequence of optimization steps change slowly from one step to the next, we can significantly reduce the number of iterations and the runtime of the linear...

Preconditioned Krylov Subspace Methods in Nonlinear Optimization

One of the possible ways of solving general problems of constrained nonlinear optimization is to convert them into a sequence of unconstrained problems. Then the need arises to solve an unconstrained optimization problem reliably and efficiently. For this aim, Newton methods are usually applied, often in combination with sparse Cholesky decomposition. In practice, however, this approach may not...

Preserving Symmetry in Preconditioned Krylov Subspace Methods

We consider the problem of solving a linear system Ax = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M . In the symmetric case, we can recover symmetry by using M -inner products in the conjugate gradient (CG) algorithm. This idea can also be used in the nonsymmetric case, and near symmetry can be preserved similarly. Like CG, the ne...

Preconditioned Krylov Subspace Methods for Eigenvalue Problems