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We present Gridap, a new scientific software library for the numerical approximation of partial differential equations (PDEs) using grid-based approximations. Gridap is an open-source software project exclusively written in the Julia programming language. The main motivation behind the development of this library is to provide an easy-to-use framework for the development of complex PDE solvers in a dynamically typed style without sacrificing the performance of statically typed languages. This work is a tutorial-driven user guide to the library. It covers some popular linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element discretizations, on structured and unstructured meshes of simplices and hexahedra.
Phase retrieval refers to the recovery of signals from the magnitudes (and not the phases) of linear measurements. While there has been a recent explosion in development of phase retrieval methods, the lack of a common interface has made it difficult
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations (SPDEs). Using an
Applications that exploit the architectural details of high-performance computing (HPC) systems have become increasingly invaluable in academia and industry over the past two decades. The most important hardware development of the last decade in HPC
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential
We propose a physical analogy between finding the solution of an ordinary differential equation (ODE) and a $N$ particle problem in statistical mechanics. It uses the fact that the solution of an ODE is equivalent to obtain the minimum of a functiona