MultiShape: A Spectral Element Method, with Applications to Dynamic Density Functional Theory and PDE-Constrained Optimization
Abstract
A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local terms. This numerical framework, called MultiShape, is a class in Matlab, and the software is open source. We demonstrate that MultiShape is compatible with other numerical methods, such as differential--algebraic equation solvers and optimization algorithms. The numerical implementation is designed to be user-friendly, with most of the set-up and computations done automatically by MultiShape and with intuitive operator definition, notation, and user-interface. Validation tests are presented, before we introduce three examples motivated by applications in Dynamic Density Functional Theory and PDE-constrained optimization, illustrating the versatility of the method.
Cite
@article{arxiv.2207.05589,
title = {MultiShape: A Spectral Element Method, with Applications to Dynamic Density Functional Theory and PDE-Constrained Optimization},
author = {Jonna C. Roden and Rory D. Mills-Williams and John W. Pearson and Benjamin D. Goddard},
journal= {arXiv preprint arXiv:2207.05589},
year = {2022}
}