2born (2born) wrote,
2born
2born

О спектральных методах в численном интегрировании уравнений в частных производных

Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods: https://arxiv.org/abs/1905.10388

Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using spectral methods. Dedalus translates plain-text strings describing partial differential equations into efficient solvers. This paper details the numerical method that enables this translation, describes the design and implementation of the codebase, and illustrates its capabilities with a variety of example problems. The numerical method is a first-order generalized tau formulation that discretizes equations into banded matrices. This method is implemented with an object-oriented design. Classes for spectral bases and domains manage the discretization and automatic parallel distribution of variables. Discretized fields and mathematical operators are symbolically manipulated with a basic computer algebra system. Initial value, boundary value, and eigenvalue problems are efficiently solved using high-performance linear algebra, transform, and parallel communication libraries. Custom analysis outputs can also be specified in plain text and stored in self-describing portable formats. The performance of the code is evaluated with a parallel scaling benchmark and a comparison to a finite-volume code. The features and flexibility of the codebase are illustrated by solving several examples: the nonlinear Schrodinger equation on a graph, a supersonic magnetohydrodynamic vortex, quasigeostrophic flow, Stokes flow in a cylindrical annulus, normal modes of a radiative atmosphere, and diamagnetic levitation. The Dedalus code and the example problems are available online at this http URL.

Comments: 40 pages, 18 figures
Tags: matlab, наука, разгребая arXiv'ы
Subscribe

  • Водолюб

    Его страхолюдную личинку я видел в жизни дважды, а его самого - сегодня впервые в жизни! Заметил случайно и снял кое-как: он весьма ловко и шустро…

  • В этот день 9 лет назад

    Этот пост был опубликован 9 лет назад! См. также: 2019-07-20-пастель_smart_blur_25 © qedqed.iMGSRC.RU

  • Умер Вайнберг

    Только что узнал от уважаемого istanaro:((( Уходят великие...

  • Post a new comment

    Error

    default userpic

    Your reply will be screened

    Your IP address will be recorded 

    When you submit the form an invisible reCAPTCHA check will be performed.
    You must follow the Privacy Policy and Google Terms of use.
  • 0 comments