Solveurs temporel

 |^−→E_i | A_i+ R |^−→U_i |   avec,

– ^−→U_i, le vecteur approximation de la solution, – ^−→E_i, l’erreur estimée dans ce vecteur,

– N, le nombre de degrés de liberté,

– Ai, la tolérance absolue spécifiée pour le degré de liberté i, – R, la tolérance relative fixée par l’utilisateur.

E.3.1.1. Solveurs temporel

Deux solveurs temporels sont disponibles : le solveur BDF (Backward Differentiation Formula) et le solveur generalized alpha.

1. Le solveur BDF utilise une formulation différentielle implicite d’ordre m va-riable m = [1, 5]. Il est utilisé pour sa stabilité et sa robustesse. Néanmoins, quand l’ordre m du solveur est petit, il peut produire de grands effets d’amor-tissement sur les hautes fréquences.

2. Le solveur generalized alpha utilise également une formulation différentielle im-plicite de second ordre mais contient un paramètre α (α = [0, 1]) qui contrôle le degré d’amortissement des hautes fréquences. Pour α = 1, il n’y a pas d’amor-tissement numérique alors que pour α = 0, le maximum d’amord’amor-tissement est obtenu.

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