G. Formica1, F. Milicchio2
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 199-220, 2010, DOI:10.3970/cmes.2010.060.199
Abstract This manuscript introduces a novel sufficient condition for the unconditionally stable convergence of the general class of trapezoidal integrators. Contrary to standard energy-based approaches, this convergence criterion is derived from the power principles, in terms of both balance and dissipation. This result improves the well-known condition of stable convergence based on the energy method, extending its applicative spectrum to a variety of physical problems, whose constitutive prescriptions may be more appropriately characterized by means of evolving field equations.
Our treatment, tailored for generalized trapezoidal integrators, addresses both linear and nonlinear problems, extending its applicability to contexts where standard energy-based schemes… More >
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