Optimal shape design of defense structures for minimizing short wave impact

The paper presents coastal structures design in the presence of waves by the minimization of a cost function. It aims to show that shape optimization can be efficiently applied to ocean engineering. This is an underlying guiding principle for the design of harbors or offshore breakwaters. We compute the solution of a specific simplified boundary value problem describing the short wave propagation toward a vertical sea cliff or vertical wall and modify accordingly the shape of defense structures in order to minimize a pre-defined cost function taking into account the strength (energy) of the water waves. The optimization procedure relies on a global semi-deterministic search algorithm able to escape from local minima.

[1]  Bijan Mohammadi,et al.  Optimization of aerodynamic and acoustic performances of supersonic civil transports , 2004 .

[2]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[3]  J. Lions,et al.  Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles , 1968 .

[4]  R. Dalrymple,et al.  Coastal Processes with Engineering Applications , 2001 .

[5]  J. Berkhoff,et al.  Computation of Combined Refraction — Diffraction , 1972 .

[6]  Timothy A. Davis,et al.  A column pre-ordering strategy for the unsymmetric-pattern multifrontal method , 2004, TOMS.

[7]  A. T. Hoop Handbook of radiation and scattering of waves , 1995 .

[8]  Olivier Pironneau,et al.  Applied Shape Optimization for Fluids, Second Edition , 2009, Numerical mathematics and scientific computation.

[9]  R. Dautray,et al.  Analyse mathématique et calcul numérique pour les sciences et les techniques , 1984 .

[10]  C. Mei The applied dynamics of ocean surface waves , 1983 .

[11]  Timothy A. Davis,et al.  An Unsymmetric-pattern Multifrontal Method for Sparse Lu Factorization , 1993 .

[12]  C. Vincent,et al.  REFRACTION-DIFFRACTION OF IRREGULAR WAVES OVER A MOUND , 1989 .

[13]  S. Ta'asan,et al.  ANALYSIS OF THE HESSIAN FOR AERODYNAMIC OPTIMIZATION: INVISCID FLOW , 1996 .

[14]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[15]  A. Sommerfeld Partial Differential Equations in Physics , 1949 .

[16]  Olivier Durand,et al.  Semi-deterministic versus genetic algorithms for global optimisation of multichannel optical filters , 2006, Int. J. Comput. Sci. Eng..

[17]  B. Mohammadi,et al.  Shape optimization of geotextile tubes for sandy beach protection , 2008 .

[18]  Moïse Sibony Contrôle des systèmes gouvernés par des équations aux dérivées partielles , 1970 .

[19]  Juan G. Santiago,et al.  Semi‐deterministic and genetic algorithms for global optimization of microfluidic protein‐folding devices , 2006 .