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The Nested Substructures Method for Solving Large Finite-Element Systems as Applied to Thin-Walled Shells with High Ribs

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Abstract

A direct method is proposed to solve large systems of linear algebraic equations that arise in using the finite-element method. The method suggests to subdivide the initial structure into nonoverlapping, deeply nested substructures. The subdivision is performed automatically by the nested dissection method. Initially, the structure is subdivided into isolated finite elements. The solution process is step-by-step assembly of subsystems with simultaneous elimination of unknowns for completely assembled ones. The efficiency of the method is demonstrated by comparing it with the incomplete Cholesky conjugate-gradient method and the traditional envelope method as applied to a circular cylindrical shell with high ribs

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  1. National Academy of Sciences of Ukraine, S. P. Timoshenko Institute of Mechanics, Kiev

    S. Yu. Fialko

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Fialko, S.Y. The Nested Substructures Method for Solving Large Finite-Element Systems as Applied to Thin-Walled Shells with High Ribs. International Applied Mechanics 39, 324–331 (2003). https://doi.org/10.1023/A:1024474621617

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