Work

MultiShape: A Spectral Element Method, with Applications to Dynamic Density Functional Theory and PDE-Constrained Optimization

Year: 2022

Type: article

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.

Source: Edinburgh Research Explorer (University of Edinburgh)

DOI: 10.48550/arxiv.2207.05589

Authors: Roden, Jonna C., Mills-Williams, Rory D., Pearson, John W., Goddard, Benjamin D.

Institutions: Maxwell Institute for Mathematical Sciences, University of Edinburgh, Heinrich Heine University Düsseldorf

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Heriot-Watt University, Scottish Funding Council, University of Edinburgh, Engineering and Physical Sciences Research Council