2018/06/04 by Oana Marin, Marin, Oana, Emil M. Constantinescu +3
Mathematics · Computer Science · Engineering · #Numerical methods for differential equations #Matrix Theory and Algorithms #Electromagnetic Simulation and Numerical Methods
paper · pdf · doi:10.48550/arxiv.1806.01422
We provide a new approach for the efficient matrix-free application of the\ntranspose of the Jacobian for the spectral element method for the adjoint based\nsolution of partial differential equation (PDE) constrained optimization. This\nresults in optimizations of nonlinear PDEs using explicit integrators where the\nintegration of the adjoint problem is not more expensive than the forward\nsimulation. Solving PDE constrained optimization problems entails combining\nexpertise from multiple areas, including simulation, computation of\nderivatives, and optimization. The Portable, Extensible Toolkit for Scientific\ncomputation (PETSc) together with its companion package, the Toolkit for\nAdvanced Optimization (TAO), is an integrated numerical software library that\ncontains an algorithmic/software stack for solving linear systems, nonlinear\nsystems, ordinary differential equations, differential algebraic equations, and\nlarge-scale optimization problems and, as such, is an ideal tool for performing\nPDE-constrained optimization. This paper describes an efficient approach in\nwhich the software stack provided by PETSc/TAO can be used for large-scale\nnonlinear time-dependent problems. While time integration can involve a range\nof high-order methods, both implicit and explicit. The PDE-constrained\noptimization algorithm used is gradient-based and seamlessly integrated with\nthe simulation of the physical problem.\n