Multi-Scale PDE-Based Design of Hierarchically Structured Porous Catalysts

Optimization problems involving the solution of partial differential equations (PDEs) often arise in the context of optimal design, optimal control and parameter estimation. Based on the reduced gradient method, a general strategy is proposed to solve these problems by using existing optimization packages and PDE solvers. For illustration purposes, this strategy was employed to solve a PDE-based optimization problem that arises from the optimal design of hierarchically structured porous catalysts. A Fortran program was developed that combines a gradientbased optimization package, NLPQL, a multigrid PDE solver, MGD9V, and a limited amount of in-house coding.

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