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

TL;DR

This paper introduces a multilevel extension of the FETI-DP method that uses approximate solutions for the coarse problem via BDDC, leading to spectral equivalence and improved computational strategies.

Contribution

It develops a multilevel FETI-DP framework incorporating approximate coarse solves with BDDC, establishing spectral equivalence and practical efficiency.

Findings

Spectral equivalence between multilevel FETI-DP and BDDC preconditioned operators.

Numerical experiments demonstrate the effectiveness of the multilevel approach.

Approximate coarse solves with algebraic multigrid are also effective.

Abstract

We study a framework that allows to solve the coarse problem in the FETI-DP method approximately. It is based on the saddle-point formulation of the FETI-DP system with a block-triangular preconditioner. One of the blocks approximates the coarse problem, for which we use the multilevel BDDC method as the main tool. This strategy then naturally leads to a version of multilevel FETI-DP method, and we show that the spectra of the multilevel FETI-DP and BDDC preconditioned operators are essentially the same. The theory is illustrated by a set of numerical experiments, and we also present a few experiments when the coarse solve is approximated by algebraic multigrid.