Related papers: A user-guide to Gridap -- grid-based approximation…
This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory…
MultiPrecisionArrays.jl is a Julia package. This package provides data structures and solvers for several variants of iterative refinement. It will become much more useful when half precision (aka Float16) is fully supported in LAPACK/BLAS.…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
scida is a Python package for reading and analyzing large scientific data sets with support for various cosmological and galaxy formation simulations out-of-the-box. Data access is provided through a hierarchical dictionary-like data…
In scientific computing, more computational power generally implies faster and possibly more detailed results. The goal of this study was to develop a framework to submit computational jobs to powerful workstations underused by nonintensive…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded…
Partial differential equations describing the dynamics of physical systems rarely have closed-form solutions. Fourier spectral methods, which use Fast Fourier Transforms (FFTs) to approximate solutions, are a common approach to solving…
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…
Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…
We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic…
Scientific legacy code in MATLAB/Octave not compatible with modernization of research workflows is vastly abundant throughout academic community. Performance of non-vectorized code written in MATLAB/Octave represents a major burden. A new…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
The Simplex algorithm for solving linear programs-one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century-is an important topic in many algorithms courses. While the Simplex algorithm relies on…
We present FreeBird, an extensible Julia-based platform for computational studies of phase equilibria at generic interfaces. The package supports a range of system configurations, from atomistic solid surfaces to coarse-grained…
We present the preliminary high-level design and features of DynamicPPL.jl, a modular library providing a lightning-fast infrastructure for probabilistic programming. Besides a computational performance that is often close to or better than…
Operator-splitting methods are widespread in the numerical solution of differential equations, especially the initial-value problems in ordinary differential equations that arise from a method-of-lines discretization of partial differential…
This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…
Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…
In this paper we introduce DiffSharp, an automatic differentiation (AD) library designed with machine learning in mind. AD is a family of techniques that evaluate derivatives at machine precision with only a small constant factor of…