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Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes. (English) Zbl 1360.65240
Summary: In this work we consider inverse modeling of the shape of cells in the outermost layer of human skin. We propose a novel algorithm that combines mathematical shape optimization with high-performance computing. Our aim is to fit a parabolic model for drug diffusion through the skin to data measurements. The degree of freedom is not the permeability itself, but the shape that distinguishes regions of high and low diffusivity. These are the cells and the space in between. The key part of the method is the computation of shape gradients, which are then applied as deformations to the finite element mesh, in order to minimize a tracking type objective function. Fine structures in the skin require a very high resolution in the computational model. We therefor investigate the scalability of our algorithm up to millions of discretization elements.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
49Q10 Optimization of shapes other than minimal surfaces
49N45 Inverse problems in optimal control
65K10 Numerical optimization and variational techniques
65Y05 Parallel numerical computation
92-08 Computational methods for problems pertaining to biology
92C37 Cell biology
92C05 Biophysics
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