page_title: Topology optimization
section_title: Thermoelectric energy conversion
hierarchical_section_title: Topology optimization / Examples / Multiphysics problems / Thermoelectric energy conversion
caption_attribution_description: English: design-sketch
context_page_description: Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions and constraints with the goal of maximizing the performance of the system. TO is different from shape optimization and sizing optimization in the sense that the design can attain any shape within the design space, instead of dealing with predefined configurations.
  The conventional TO formulation uses a finite element method to evaluate the design performance. The design is optimized using either gradient-based mathematical programming techniques such as the optimality criteria algorithm and the method of moving asymptotes or non gradient-based algorithms such as genetic algorithms.
  Topology Optimization has a wide range of applications in aerospace, mechanical, bio-chemical and civil engineering. Currently, engineers mostly use TO at the concept level of a design process. Due to the free forms that naturally occur, the result is often difficult to manufacture. For that reason the result emerging from TO is often fine-tuned for manufacturability.
context_section_description: Thermoelectricity is a multi-physic problem which concerns the interaction and coupling between electric and thermal energy in semi conducting materials. Thermoelectric energy conversion can be described by two separately identified effects: The Seebeck effect and the Peltier effect. The Seebeck effect concerns the conversion of thermal energy into electric energy and the Peltier effect concerns the conversion of electric energy into thermal energy. By spatially distributing two thermoelectric materials in a two dimensional design space with a topology optimisation methodology, it is possible to exceed performance of the constitutive thermoelectric materials for thermoelectric coolers and thermoelectric generators.
caption: A sketch of the design problem. The aim of the design problem is to spatially distribute two materials, Material A and Material B, to maximise a performance measure such as cooling power or electric power output
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