Open AccessDOI
The FEniCS Project Version 1.5
Martin Sandve Alnæs,Jan Blechta,Johan Hake,August Johansson,Benjamin Kehlet,Anders Logg,Chris N. Richardson,Johannes Ring,Marie E. Rognes,Garth N. Wells +9 more
- Vol. 3, Iss: 100, pp 9-23
TLDR
The FEniCS Project is a collaborative project for the development of innovative concepts and tools for automated scientific computing, with a particular focus on the solution of differential equations by finite element methods.Abstract:
The FEniCS Project is a collaborative project for the development of innovative concepts and tools for automated scientific computing, with a particular focus on the solution of differential equations by finite element methods. The FEniCS Projects software consists of a collection of interoperable software components, including DOLFIN, FFC, FIAT, Instant, UFC, UFL, and mshr. This note describes the new features and changes introduced in the release of FEniCS version 1.5.read more
Citations
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Journal ArticleDOI
Physics-informed machine learning
TL;DR: Some of the prevailing trends in embedding physics into machine learning are reviewed, some of the current capabilities and limitations are presented and diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems are discussed.
Journal ArticleDOI
Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
TL;DR: This paper provides a methodology that incorporates the governing equations of the physical model in the loss/likelihood functions of the model predictive density and the reference conditional density as a minimization problem of the reverse Kullback-Leibler (KL) divergence.
Journal ArticleDOI
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
Yinhao Zhu,Nicholas Zabaras +1 more
TL;DR: This approach achieves state of the art performance in terms of predictive accuracy and uncertainty quantification in comparison to other approaches in Bayesian neural networks as well as techniques that include Gaussian processes and ensemble methods even when the training data size is relatively small.
Journal ArticleDOI
MOOSE: Enabling Massively Parallel Multiphysics Simulation.
Cody J. Permann,Derek Gaston,David Andrs,Robert W. Carlsen,Fande Kong,Alexander Lindsay,Jason M. Miller,John W. Peterson,Andrew E. Slaughter,Roy H. Stogner,Richard C. Martineau +10 more
TL;DR: The Multiphysics Object Oriented Simulation Environment (MOOSE) aims to enable development by providing simplified interfaces for specification of partial differential equations, boundary conditions, material properties, and all aspects of a simulation without the need to consider the parallel, adaptive, nonlinear, finite-element solve that is handled internally.
Book ChapterDOI
Phase-field modeling of fracture
TL;DR: This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician.
References
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Journal ArticleDOI
The NumPy Array: A Structure for Efficient Numerical Computation
TL;DR: In this article, the authors show how to improve the performance of NumPy arrays through vectorizing calculations, avoiding copying data in memory, and minimizing operation counts, which is a technique similar to the one described in this paper.
Journal ArticleDOI
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
George Karypis,Vipin Kumar +1 more
TL;DR: This work presents a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of theSize of the final partition obtained after multilevel refinement, and presents a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening.
Journal ArticleDOI
The NumPy array: a structure for efficient numerical computation
TL;DR: This effort shows, NumPy performance can be improved through three techniques: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts.
PETSc Users Manual
Satish Balay,Shrirang Abhyankar,Mark F. Adams,Jed Brown,Peter R. Brune,Kristopher R. Buschelman,Lisandro Dalcin,Alp Dener,Eijkhout,William Gropp,Dmitry Karpeyev,Dinesh K. Kaushik,Matthew G. Knepley,Dave A. May,L. Curfman McInnes,Richard T. Mills,Todd Munson,Karl Rupp,Patrick Sanan,Barry Smith,Stefano Zampini,Hong Zhang +21 more
TL;DR: The Portable, Extensible Toolkit for Scientific Computation (PETSc), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations that supports MPI, and GPUs through CUDA or OpenCL, as well as hybrid MPI-GPU parallelism.
Book ChapterDOI
Efficient management of parallelism in object-oriented numerical software libraries
TL;DR: The PETSc 2.0 package as discussed by the authors uses object-oriented programming to conceal the details of the message passing, without concealing the parallelism, in a high-quality set of numerical software libraries.
Related Papers (5)
PETSc Users Manual
Satish Balay,Shrirang Abhyankar,Mark F. Adams,Jed Brown,Peter R. Brune,Kristopher R. Buschelman,Lisandro Dalcin,Alp Dener,Eijkhout,William Gropp,Dmitry Karpeyev,Dinesh K. Kaushik,Matthew G. Knepley,Dave A. May,L. Curfman McInnes,Richard T. Mills,Todd Munson,Karl Rupp,Patrick Sanan,Barry Smith,Stefano Zampini,Hong Zhang +21 more