Nonlinear Optimization and Inverse Problems

ALEA is a free python library for research in Uncertainty Quantification (UQ). Its focus is on functional spectral approximations on the basis of polynomial chaos and on the treatment of high-dimensional discretisations. For this, methods for adaptive sparse grid quadrature and low-rank approximations based on hierarchical tensors are incorporated.

Based on coupled generalized finite/boundary elements and gradient type optimization methods this program package provides simulation and optimization of periodic diffractive structures with multilayer stacks.

Simulation of multi-frequency induction hardening for arbitrary workpiece geometries in 3D. The software uses the finite element method for Maxwell's equations based on edge elements, adaptive grid generation and efficient solvers for the linearized systems of partial differential equations.