Accuracy Enhancing Interface Treatment Algorithm: the Back and Forth Error Compensation and Correction method

TL;DR

This paper introduces a BFECC-based interface treatment algorithm that enhances accuracy in domain decomposed problems, achieving up to third and super convergence orders through iterative correction and interpolation techniques.

Contribution

The paper presents a systematic study of a novel BFECC-based interface treatment algorithm that improves accuracy and demonstrates super convergence in domain decomposition problems.

Findings

Achieves local 3rd order accuracy through iterative interpolation.

Discovers super convergence (4th order) at specific grid configurations.

Numerical experiments confirm theoretical accuracy improvements.

Abstract

The accuracy of information transmission while solving domain decomposed problems is crucial to smooth transition of a solution around the interface/overlapping region. This paper describes a systematical study on an accuracy enhancing interface treatment algorithm based on the back and forth error compensation and correction method (BFECC). By repetitively employing a low order interpolation technique (normally local 2\ts{nd} order) 3 times, this algorithm achieves local 3\ts{rd} order accuracy. Analytical derivations for 1D \& 2D cases are made, and the "super convergence" phenomenon (4\ts{th} order accuracy) is found for specific positioning of the donor and target grids. A set of numerical experiments based on various relative displacements, relative rotations, mesh ratios, and meshes with perturbation have been tested, and the results match the derivations. Different interface treatments are compared with 3D examples: corner flow and cavity flow. The component convergence rate analysis shows that the BFECC method positively affects the accuracy of solutions.