Big Data applications are typically associated with systems involving large numbers of users, massive complex software systems, and large-scale heterogeneous computing and storage architectures. The construction of such systems involves many distributed design choices. The end products (e.g., recommendation systems, medical analysis tools, real-time game engines, speech recognizers) thus involve many tunable configuration parameters. These parameters are often specified and hard-coded into the software by various developers or teams. If optimized jointly, these parameters can result in significant improvements. Bayesian optimization is a powerful tool for the joint optimization of design choices that is gaining great popularity in recent years. It promises greater automation so as to increase both product quality and human productivity. This review paper introduces Bayesian optimization, highlights some of its methodological aspects, and showcases a wide range of applications.

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Taking the Human Out of the Loop: A Review of Bayesian Optimization

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

https://hal.archives-ouvertes.fr/hal-01461938/document

Extended finite element method for cohesive crack growth

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.

https://publications.lib.chalmers.se/records/fulltext/228672/local_228672.pdf

The FEniCS Project Version 1.5

A model which allows the introduction of displacements jumps to conventional finite elements is developed. The path of the discontinuity is completely independent of the mesh structure. Unlike so-called ‘embedded discontinuity’ models, which are based on incompatible strain modes, there is no restriction on the type of underlying solid finite element that can be used and displacement jumps are continuous across element boundaries. Using finite element shape functions as partitions of unity, the displacement jump across a crack is represented by extra degrees of freedom at existing nodes. To model fracture in quasi-brittle heterogeneous materials, a cohesive crack model is used. Numerical simulations illustrate the ability of the method to objectively simulate fracture with unstructured meshes. Copyright © 2001 John Wiley & Sons, Ltd.

A new method for modelling cohesive cracks using finite elements

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled, and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This article discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.

/pdf/dolfin-automated-finite-element-computing-snstayxhsm.pdf

DOLFIN: Automated finite element computing

We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.

Garth N. Wells

Papers

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

The FEniCS Project Version 1.5

A new method for modelling cohesive cracks using finite elements

DOLFIN: Automated finite element computing

DOLFIN: Automated Finite Element Computing