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Numerical solutions of differential equations --- Algebras, Linear --- Differential equations --- Algèbre linéaire --- Equations différentielles --- Algèbre linéaire --- Equations différentielles --- lineaire algebra

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Differential equations --- Boundary value problems --- Equations différentielles --- Problèmes aux limites --- Équations différentielles --- Problèmes aux limites --- Équations différentielles linéaires --- Équations différentielles - Problèmes et exercices

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Geometry, Differential. --- Differentiable manifolds. --- Differential equations --- Géométrie différentielle --- Variétés différentiables --- Equations différentielles --- Numerical solutions. --- Solutions numériques --- Differentiable manifolds --- Numerical solutions --- Géométrie différentielle --- Variétés différentiables --- Equations différentielles --- Solutions numériques --- Differential equations - Numerical solutions. --- Differential equations - Numerical solutions

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The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account of homogenization theory and explain how it applies to solving optimal design problems, from both a theoretical and a numerical point of view. The application of greatest practical interest tar­ geted by this book is shape and topology optimization in structural design, where this approach is known as the homogenization method. Shape optimization amounts to finding the optimal shape of a domain that, for example, would be of maximal conductivity or rigidity under some specified loading conditions (possibly with a volume or weight constraint). Such a criterion is embodied by an objective function and is computed through the solution of astate equation that is a partial differential equa­ tion (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is al­ ways assumed to support Neumann boundary conditions (i. e. , isolating or traction-free conditions). In such a setting, shape optimization has a long history and has been studied by many different methods. There is, therefore, a vast literat ure in this field, and we refer the reader to the following short list of books, and references therein [39], [42], [130], [135], [149], [203], [220], [225], [237], [245], [258].

Structural optimization. --- Homogenization (Differential equations) --- Optimisation des structures --- Homogénéisation (Equations différentielles) --- Homogenization (Differential equations). --- Homogénéisation (Equations différentielles) --- Buildings—Design and construction. --- Building. --- Construction. --- Engineering, Architectural. --- Applied mathematics. --- Engineering mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Mechanics. --- Engineering design. --- Civil engineering. --- Building Construction and Design. --- Mathematical and Computational Engineering. --- Analysis. --- Classical Mechanics. --- Engineering Design. --- Civil Engineering. --- Engineering --- Public works --- Design, Engineering --- Industrial design --- Strains and stresses --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- 517.1 Mathematical analysis --- Mathematical analysis --- Engineering analysis --- Architectural engineering --- Buildings --- Construction --- Construction science --- Engineering, Architectural --- Structural design --- Structural engineering --- Architecture --- Construction industry --- Design --- Mathematics --- Design and construction --- Composites --- Structural optimization --- Equations elliptiques/du deuxieme ordre --- Optimalisation morphologique --- Optimisation structurelle