# Adaptive BDDC in Three Dimensions

## TL;DR

This paper extends the adaptive BDDC method to three-dimensional problems, introducing a new implementation that enhances parallelism and efficiency for solving large-scale engineering simulations.

## Contribution

It presents a novel 3D adaptive BDDC approach with a global formulation and a parallel multifrontal solver, avoiding explicit coarse problems.

## Key findings

- Effective on several engineering problems
- Preserves sparsity through generalized change of variables
- Achieves massive parallelism with a multifrontal solver

## Abstract

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems.