An Adaptive Material Interpolation for the Reconstruction of P-Wave Velocity Models with Sharp Interfaces using the Topology Optimization Method

A topology optimization (TO) approach is used to reconstruct P-wave velocity models with sharp interfaces. The concept of material model (interpolation), usually applied in TO to design structures and multi-physics devices, is explored in this work to solve this inverse problem. An adaptive interpolation rule is proposed to deal with the reconstruction problem as a transition from a single- to a multi-material approach combining the Solid Isotropic Material with Penalization (SIMP) and peak function material models. Data collected during the optimization process is used to find material candidates by means of a curve fitting strategy based on generalized simulated annealing (GSA), if this information is not available. The numerical analysis is carried out using a finite element (FE) approach in the frequency domain. Both forward and adjoint problems are solved aided by an open source Domain-Specific Language (DSL) framework and automated derivation tool, while the optimization problem is solved by using a BFGS algorithm. Numerical results for 2D examples demonstrated that proposed material interpolation can lead to solutions with sharper interfaces and improved resolution without including any type of regularization or extra constraint in the optimization problem.