By: K.P. Singh and Burton Paul
Publisher: Computer Methods in Applied Mechanics and Engineering
Abstract: Improperly-posed (or Hadamard-incorrect) problems may arise when numerical solutions arc extremely sensitive to a discretization process. The nonconformal contact problem in three-dimensional clastostatics fulls into this cate-gory. It is shown how such contact stress problems may be formulated and successfully solved using the “Functional Regularization Method” of Tychonov. The Functional Regularization Method requires the use of a parameter, called the Regularization Parameter. Although no general rules for the choice of such a parameter appear lo exist, we have determined appropriate bounds on the parameter for a wide class of contact problems /including that of Hertz). The method developed should be capable of extension to more general ill-posed problems. It is also shown that refinements in the discretization process such as reduced mesh lengths or higher order quadrature formulas may postpone, but do not necessarily remove the numerical difficulties associated with the physics of the problem.
Citation: Singh, K. & Paul, B. “A Method for Solving Ill-Posed Integral Equations of the First Kind,” Computer Methods in Applied Mechanics and Engineering 2 (1973) 339-348.