Analysis of efficient preconditioner for solving Poisson equation with Dirichlet boundary condition in irregular three-dimensional domains

Geonho Hwang, Yesom Park, Yueun Lee, Myungjoo Kang

Abstract: Highlights•This study extends the analysis of the Gibou method to irregular three-dimensional domains, demonstrating second-order convergence in irregular domains.•This section presents proof of the optimality of the MILU preconditioner, which reduces the condition number of the discretized system from O(h−2)<math><mi mathvariant="script" is="true">O</mi><mrow is="true"><mo stretchy="true" is="true">(</mo><msup is="true"><mrow is="true"><mi is="true">h</mi></mrow><mrow is="true"><mo linebreak="badbreak" linebreakstyle="after" is="true">−</mo><mn is="true">2</mn></mrow></msup><mo stretchy="true" is="true">)</mo></mrow></math> to O(h−1)<math><mi mathvariant="script" is="true">O</mi><mrow is="true"><mo stretchy="true" is="true">(</mo><msup is="true"><mrow is="true"><mi is="true">h</mi></mrow><mrow is="true"><mo linebreak="badbreak" linebreakstyle="after" is="true">−</mo><mn is="true">1</mn></mrow></msup><mo stretchy="true" is="true">)</mo></mrow></math>.•It introduces and theoretically demonstrates the SMILU preconditioner with sectorized ordering, which improves parallel computing efficiency while maintaining optimal conditioning.•Comprehensive theoretical analyses and numerical experiments are conducted to confirm the theoretical analyses in both 2D and 3D scenarios.•This study contributes to the advancement of computational efficiency in solving large-scale Poisson problems in scientific and engineering domains.

External IDs:dblp:journals/jcphy/HwangPLK24