FINITE ELEMENT DUAL SINGULAR FUNCTION METHODS FOR HELMHOLTZ AND HEAT EQUATIONS

초록

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use ShermanMorrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domainincluding n reentrantcorners. However,theDSFMforheatequationneedstopayonly linear solver once per each time iteration to standard numerical method and perform optimal numericalaccuracyforcornersingularityproblems. BecausetheSherman-Morrisonformulais rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

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