论文标题
Multishape：一种光谱元素方法，应用于动态密度功能理论和PDE受限优化
MultiShape: A Spectral Element Method, with Applications to Dynamic Density Functional Theory and PDE-Constrained Optimization
论文作者
论文摘要
开发了一个数值框架来解决复杂域上的各种PDE，包括稳定和时间依赖性，非线性和非本地PDE，具有不同的边界条件，其中也可能包括非线性和非局部项。这个称为Multishape的数值框架是MATLAB中的类，该软件是开源的。我们证明了多座类型与其他数值方法兼容，例如差分方程求解器和优化算法。该数值实现旨在用户友好，大多数设置和计算由多式制品自动完成，并且具有直观的操作员定义，符号和用户界面。在我们介绍了由动态密度功能理论和PDE受限优化中应用的三个示例之前提出验证测试，以说明该方法的多功能性。
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.
