Efficient adaptive strategy for solving inverse problems

The paper describes the strategy for efficient solving of difficult inverse problems, utilizing Finite Element Method (FEM) as a direct problem solver. The strategy consists of finding an optimal balance between the accuracy of global optimization method and the accuracy of an hp-adaptive FEM used for the multiple solving of the direct problem. The crucial relation among errors was found for the objective function being the energy of the system defining the direct problem. The strategy was applied for searching the thermal expansion coefficient (CTE) parameter in the Step-and-flash Imprint Lithography (SFIL) process.