Inexact and primal multilevel FETI‐DP methods: a multilevel extension and interplay with BDDC

New Coupled-Inductor Based Multilevel Inverter with Extension Capability

Multilevel inverters have been developed due to limitations of the conventional two-level voltage source inverters (VSIs). Most of the topologies of multilevel inverters that have been presented in the literature are based on the sharing of the rated voltage between the switches so that the switches with lower voltage ratings can be used. In these topologies, the current rating of all of the sw...

Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization

We present a class of inexact adaptive multilevel trust-region SQP-methods for the efficient solution of optimization problems governed by nonlinear partial differential equations. The algorithm starts with a coarse discretization of the underlying optimization problem and provides during the optimization process 1) implementable criteria for an adaptive refinement strategy of the current discr...

Multilevel Extension 99

Inexact BDDC methods for the cardiac Bidomain model

The cardiac Bidomain model consists in a reaction-diffusion system of PDEs for the intraand extra-cellular cardiac potentials coupled with a nonlinear system of ODEs accounting for the cellular model of ionic currents. Fully implicit methods in time have been considered in a few studies, see e.g. [16] and references therein. As in most of previous work (see [18] for a review), in this study we ...

Parallel Multilevel and Multigrid Methods

1. Preliminaries. Multigrid methods originated earlier this century, in the personnel computing era. Someone who needed to compute an approximation to the solution of a partial di erential equation during that era would ll a room with people. After using very simple mechanical calculators to compute parts of the approximation, these people would pass their parts to the other people in the room ...