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In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms. [ABSTRACT FROM AUTHOR]

Starting from constitutive equations of a piezoelectric material, we built a Koiter shell model coupled with a piezoelectric actuator. After a mechanical interpretation of the effect of the actuator we prove a result of existence and uniqueness of the coupled model. We then discuss controllability results of Galerkin approximations of the model. The numerical tests carried out show the effectiveness of different control algorithms such as the projected Riccati algorithm. This efficiency depends strongly on the position and the shape of the actuator. We then study an algorithm for shape optimization based on the minimization of a criterion. The latter depends on the geometry of the actuator. The gradient of this criterion is calculated using domain derivation techniques. [ABSTRACT FROM AUTHOR]

Transformational High Dimensional Model Representation has been used for continous structures with different transformations before. This work is inventive because not only for the transformation type but also its usage. Mo¨bius Transformational High Dimensional Model Representation has been used at multi-way arrays, by using truncation approximant and inverse transformation an approximation has been obtained for original multi-way array. [ABSTRACT FROM AUTHOR]

Vector Fitting (VF) has been introduced as a partial-fraction basis response fitting methodology for over a decade. Because of its reliability and versatility, VF has been applied and extended to a number of areas. In this book chapter, we will discuss the applications of VF in the context of macromodeling of linear structures in signal/power integrity analyses. We will also discuss main features of VF along three directions: data, algorithms and models. Two practical examples are given to demonstrate the merits of VF. An alternative P-norm approximation criterion is proposed to enhance the accuracy of the macromodeling process. [ABSTRACT FROM AUTHOR]