Ordnungsreduktion linearer zeitinvarianter Finite-Elemente-Modelle mit multivariater polynomieller Parametrierung (Model Order Reduction of Linear Finite Element Models Parameterized by Polynomials in Several Variables)

Abstract Der vorliegende Beitrag stellt ein Verfahren zur Ordnungsreduktion linearer Gleichungssysteme vor, die durch Polynome in mehreren Variablen parametriert sind und aus der Finite-Elemente-Methode hervorgehen. Der vorgeschlagene Ansatz beruht auf multivariaten Krylov-Unterräumen und erweitert bestehende Verfahren in zweierlei Hinsicht: Erstens beinhaltet er einen neuen Algorithmus zur Berechnung einer stabilen Basis für das reduzierte System, und zweitens verallgemeinert er das Konzept der Krylov-Unterräume höherer Ordnung auf Mehrparametersysteme.

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