New tools to solve PDEs in Julia with Gridap.jl

07/30/2021, 1:20 PM1:30 PM UTC
Purple

Abstract:

In this talk, we explore the novel capabilities of Gridap to solve Partial Differential Equations (PDEs) in Julia. This includes new features like a high-level API to write the PDE weak form with a syntax almost identical to the math notation, support for automatic differentiation, and simulation of PDEs on manifolds and domains of mixed geometrical dimensions. We will showcase these techniques with representative applications and performance comparisons against codes implemented in C/C++.

Description:

Gridap is a new, open-source, finite element (FE) library implemented in the Julia programming language. The main goal of Gridap is to adopt a more modern programming style than existing FE applications written in C/C++ or Fortran in order to simplify the simulation of challenging problems in science and engineering and improve productivity in the research of new discretization methods. The library is a feature-rich general-purpose FE code able to solve a wide range of partial differential equations (PDEs), including linear, nonlinear, and multi-physics problems. Gridap is extensible and modular. One can implement new FE spaces, new reference elements, and use external mesh generators, linear solvers, and visualization tools. In addition, it blends perfectly well with other packages of the Julia package ecosystem, since Gridap is implemented 100% in Julia.

One of the distinctive features of the library is a high-level API allowing one to simulate complex PDEs with very few lines of code. This API makes possible to write the PDE weak form in a syntax almost identical to the mathematical notation. In some sense, the high-level API of Gridap resembles to the one of FE codes based on symbolic domain-specific languages like UFL in FEniCS, but, in contrast, Gridap does not consider any compiler of variational forms nor C/C++ code generation facilities. Instead, the library takes advantage of the Julia JIT compiler to generate efficient machine code for the particular problem the user wants to solve, which makes the Gridap much easier to maintain and extend.

The Gridap project was initially presented in last year's JuliaCon. Since then, a number of new important features have been added, including an enhanced syntax for writing the PDE weak form, the support of more PDE types, and the support of more numerical techniques. In JuliaCon2021, we would like to showcase these updates via a set of representative use cases and challenging applications such as fluid-structure interaction problems.

Platinum sponsors

Julia Computing

Gold sponsors

Relational AI

Silver sponsors

Invenia LabsConningPumas AIQuEra Computing Inc.King Abdullah University of Science and TechnologyDataChef.coJeffrey Sarnoff

Media partners

Packt Publication

Fiscal Sponsor

NumFOCUS