Adaptive Multilevel Krylov Methods

Adaptive Multilevel Methods with Local Smoothing

A multilevel method on adaptive meshes with hanging nodes is derived. Smoothing is restricted to the interior of the subdomains refined to the current level, thus has optimal computational complexity. Its convergence rates are the same as for the the non-adaptive version. We discuss the implementation in a general finite element code at the example of the deal.II library.

Multilevel Adaptive Methods for Semilinear Equations

Adaptive Multilevel Methods in Three Space Dimensions

We consider the approximate solution of selfadjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non–uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is couple...

Robust Krylov-Subspace Methods for Passive Sonar Adaptive Beamforming

Krylov-subspace methods, such as the multistage Wiener filter and conjugate gradient method, are often used for reduced-dimension adaptive beamforming. These techniques do not, however, allow for steering vector mismatch, which is typically present in many applications of interest, including passive sonar. Here, we discuss recently proposed robust methods that do allow for steering vector misma...

Krylov Subspace Methods for Topology Optimization on Adaptive

Topology optimization is a powerful tool for global and multiscale design of structures, microstructures, and materials. The computational bottleneck of topology optimization is the solution of a large number of extremely ill-conditioned linear systems arising in the finite element analysis. Adaptive mesh refinement (AMR) is one efficient way to reduce the computational cost. We propose a new A...