Two-level screening designs derived from binary nonlinear codes

Nonregular fractional factorial designs can provide economical designs in screening experiments. In this paper, two criteria are proposed for evaluating the projectivity and uniformity properties of projections onto active factors in two-level nonregular fractional factorial designs. Moreover, two-level nonregular fractional factorial designs derived from binary nonlinear codes with 12, 24, 32 and 40 codewords and various lengths are evaluated using the new criteria. Such designs are also evaluated under the known E(s2) criterion for optimal designs in screening experiments, and are compared to Plackett-Burman designs or to projections of Plackett-Burman designs. Results show that some binary nonlinear codes can provide useful two-level nonregular fractional factorial designs in screening experiments. A search method is proposed for finding good designs with a large number of factors, starting from a good design with the same number of runs but with a smaller number of factors

Boussinesq-Peregrine water wave models and their numerical approximation

© 2020 Elsevier Inc. In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and dispersive terms are compared. A detailed study of the convergence properties of the standard Galerkin method, using various finite element spaces on unstructured triangular grids, is presented. Along with the study of the Peregrine system, a new Boussinesq system of BBM-BBM type is derived. The new system has the same structure in its momentum equation but differs slightly in the mass conservation equation compared to the Peregrine system. Further, the finite element method applied to the new system has better convergence properties, when used for its numerical approximation. Due to the lack of analytical formulas for solitary wave solutions for the systems under consideration, a Galerkin finite element method combined with the Petviashvili iteration is proposed for the numerical generation of accurate approximations of line solitary waves. Various numerical experiments related to the propagation of solitary and periodic waves over variable bottom topography and their interaction with the boundaries of the domains are presented. We conclude that both systems have similar accuracy when approximate long waves of small amplitude while the Galerkin finite element method is more efficient when applied to BBM-BBM type systems