Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems

Authors:
Tianbing Chen;John Strain
Affiliations:
Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, CA 94720-3840, United States;Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, CA 94720-3840, United States
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

A new piecewise-polynomial interface method (PIM) for discretizing elliptic problems with complex interfaces between high-contrast materials is derived, analyzed and tested. A Krylov-accelerated interface multigrid approach (IMG) solves the discretization efficiently. Stability and convergence are proved in one dimension, while an extensive array of numerical experiments with complex interfaces and large coefficient transitions demonstrate the accuracy, efficiency and robustness of the method in two dimensions.