A BDDC method with an adaptive coarse space for three-dimensional advection-diffusion problems

TL;DR

This paper introduces an adaptive BDDC method with edge eigenvalue problems for 3D advection-diffusion systems, reducing primal unknowns and computational time despite a slight increase in iterations.

Contribution

It presents a novel adaptive BDDC approach incorporating edge eigenvalue problems to efficiently solve NSPD systems from advection-diffusion problems.

Findings

Reduces the number of primal unknowns compared to conventional methods.

Significantly decreases overall computational time.

Maintains acceptable iteration counts despite problem complexity.

Abstract

The solution of nonsymmetric but positive definite (NSPD) systems arising from advection-diffusion problems is an important research topic in science and engineering. Balancing domain decomposition by constraints with an adaptive coarse space(adaptive BDDC) constitute a significant class of nonoverlapping domain decomposition methods, commonly used for symmetric positive definite problems. In this paper, we propose an adaptive BDDC method that incorporates a class of edge generalized eigenvalue problems based on prior selected primal constraints to solve NSPD systems from advection-diffusion problems. Compared with the conventional adaptive BDDC method for such systems, the proposed approach further reduces the number of primal unknowns. Numerical experiments show that although the iteration count increases slightly, the overall computational time is significantly reduced.