Well‐ and ill‐considered numerical solution constructions

One requirement for a prediction problem to be well posed is that its solution must not be unduly sensitive to small changes in the problem specification. A similar requirement can be demanded for the numerical construction of the solution of a well‐posed problem to be well considered; the achieved solution must not be unduly sensitive to small numerical errors that are unavoidable in the construction’s implementation. Ill‐considered constructions typically result on reformulating a well‐posed problem, now as a series of sub problems, one of which is ill posed. Three classes of potentially ill‐considered constructions of the steady state vibration field in a bounded continuous structure and of the narrow band acoustic field in an extended propagation environment appear prominently in the literature. One class is solution constructions based on ‘‘marching.’’ A second class is solution constructions based on ‘‘substructuring’’ the computational domain. A third class is solution constructions that are based ...