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706 results on '"Langtangen, Hans Petter"'

1. Programming for Computations - Python

Author

Linge, Svein and Langtangen, Hans Petter

Subjects
Mathematics, Computer mathematics, Numerical analysis, Computer software, thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysis, thema EDItEUR::P Mathematics and Science::PD Science: general issues::PDE Maths for scientists, thema EDItEUR::U Computing and Information Technology::UF Business applications::UFM Mathematical and statistical software, thema EDItEUR::U Computing and Information Technology::UY Computer science::UYA Mathematical theory of computation
Abstract

Mathematics; Computer mathematics; Numerical analysis; Computer software; Numerical analysis

Published
2020
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3. Programming for Computations - MATLAB/Octave

Author

Linge, Svein and Langtangen, Hans Petter

Subjects
Computational Science and Engineering, Numerical Analysis, bic Book Industry Communication::U Computing & information technology::UY Computer science
Abstract

Computational Science and Engineering; Numerical Analysis

Published
2016
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4. Solving PDEs in Python

Author

Langtangen, Hans Petter and Logg, Anders

Subjects
Computational Science and Engineering, Algorithms, Visualization, Mathematical Software, Numerical Analysis, Software Engineering/Programming and Operating Systems, Data and Information Visualization, Software Engineering, Finite element, FEniCS, Partial Differential Equations, Python, Simulation, Open access, Maths for scientists, Combinatorics & graph theory, Mathematical & statistical software, Operating systems, bic Book Industry Communication::P Mathematics & science::PD Science: general issues::PDE Maths for scientists, bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBK Calculus & mathematical analysis::PBKS Numerical analysis, bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBV Combinatorics & graph theory, bic Book Industry Communication::U Computing & information technology::UF Business applications::UFM Mathematical & statistical software, bic Book Industry Communication::U Computing & information technology::UM Computer programming / software development::UMZ Software Engineering
Abstract

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.

Published
2016
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5. Scaling of Differential Equations

Author

Langtangen, Hans Petter and Pedersen, Geir K.

Subjects
Ordinary Differential Equations, Partial Differential Equations, Mathematical Modeling and Industrial Mathematics, Computational Science and Engineering, Simulation and Modeling, Analysis, Computer Science, scaling, non-dimensionalization, dimensionless numbers, fluid mechanics, multiphysics models, Differential calculus & equations, Mathematical modelling, Maths for engineers, Maths for scientists, Computer modelling & simulation, bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBK Calculus & mathematical analysis::PBKJ Differential calculus & equations, bic Book Industry Communication::P Mathematics & science::PB Mathematics::PBW Applied mathematics::PBWH Mathematical modelling, bic Book Industry Communication::P Mathematics & science::PD Science: general issues::PDE Maths for scientists, bic Book Industry Communication::U Computing & information technology::UY Computer science::UYM Computer modelling & simulation
Abstract

The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.

Published
2016
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6. Functions and the Writing of Code

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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7. Some More Python Essentials

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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8. Solving Partial Differential Equations

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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9. Computing Integrals and Testing Code

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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10. Solving Ordinary Differential Equations

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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11. Solving Nonlinear Algebraic Equations

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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12. Loops and Branching

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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13. The First Few Steps

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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14. A Few More Steps

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Linge, Svein, and Langtangen, Hans Petter

Published
2020
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15. Variational Forms for Systems of PDEs

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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16. Variational Formulations with Finite Elements

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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17. Nonlinear Problems

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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18. Flexible Implementations of Boundary Conditions

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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19. Time-Dependent Variational Forms

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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20. Function Approximation by Finite Elements

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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21. Quick Overview of the Finite Element Method

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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22. Variational Formulations with Global Basis Functions

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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23. Function Approximation by Global Functions

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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24. Variational Methods for Linear Systems

Author

Langtangen, Hans Petter, Mardal, Kent-Andre, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, Langtangen, Hans Petter, and Mardal, Kent-Andre

Published
2019
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25. High performance Python for direct numerical simulations of turbulent flows

Author

Mortensen, Mikael and Langtangen, Hans Petter

Subjects
Computer Science - Mathematical Software, Computer Science - Distributed, Parallel, and Cluster Computing
Abstract

Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are usually written in low-level languages such as C/C++ or Fortran. In this paper we describe a pure scientific Python pseudo-spectral DNS code that nearly matches the performance of C++ for thousands of processors and billions of unknowns. We also describe a version optimized through Cython, that is found to match the speed of C++. The solvers are written from scratch in Python, both the mesh, the MPI domain decomposition, and the temporal integrators. The solvers have been verified and benchmarked on the Shaheen supercomputer at the KAUST supercomputing laboratory, and we are able to show very good scaling up to several thousand cores. A very important part of the implementation is the mesh decomposition (we implement both slab and pencil decompositions) and 3D parallel Fast Fourier Transforms (FFT). The mesh decomposition and FFT routines have been implemented in Python using serial FFT routines (either NumPy, pyFFTW or any other serial FFT module), NumPy array manipulations and with MPI communications handled by MPI for Python (mpi4py). We show how we are able to execute a 3D parallel FFT in Python for a slab mesh decomposition using 4 lines of compact Python code, for which the parallel performance on Shaheen is found to be slightly better than similar routines provided through the FFTW library. For a pencil mesh decomposition 7 lines of code is required to execute a transform.

Published
2016
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26. Advection-Dominated Equations

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Langtangen, Hans Petter, and Linge, Svein

Published
2017
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27. Nonlinear Problems

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Langtangen, Hans Petter, and Linge, Svein

Published
2017
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28. Diffusion Equations

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Langtangen, Hans Petter, and Linge, Svein

Published
2017
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29. Wave Equations

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Langtangen, Hans Petter, and Linge, Svein

Published
2017
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30. Vibration ODEs

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Langtangen, Hans Petter, and Linge, Svein

Published
2017
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31. Finite Difference Computing with PDEs: A Modern Software Approach

Author

Langtangen, Hans Petter and Linge, Svein

Subjects
finite difference methods, programming, python, verification, numerical methods, differential equations, thema EDItEUR::U Computing and Information Technology::UY Computer science
Abstract

finite difference methods; programming; python; verification; numerical methods; differential equations

Published
2017
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32. Solving PDEs in Python: The FEniCS Tutorial I

Author

Langtangen, Hans Petter and Logg, Anders

Subjects
computer science, algorithms, visualization, software, programming, thema EDItEUR::U Computing and Information Technology::UY Computer science
Abstract

computer science; algorithms; visualization; software; programming

Published
2017
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33. Unified Framework for Finite Element Assembly

Author

Alnæs, Martin Sandve, Logg, Anders, Mardal, Kent-Andre, Skavhaug, Ola, and Langtangen, Hans Petter

Subjects
Mathematics - Numerical Analysis
Abstract

At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.

Published
2012
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34. A FEniCS-Based Programming Framework for Modeling Turbulent Flow by the Reynolds-Averaged Navier-Stokes Equations

Author

Mortensen, Mikael, Langtangen, Hans Petter, and Wells, Garth N.

Subjects
Computer Science - Computational Engineering, Finance, and Science, Physics - Computational Physics, Physics - Fluid Dynamics
Abstract

Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model., Comment: To appear in Advances in Water Resources

Published
2011
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35. Simplifying Parallelization of Scientific Codes by a Function-Centric Approach in Python

Author

Nilsen, Jon K., Cai, Xing, Hoyland, Bjorn, and Langtangen, Hans Petter

Subjects
Computer Science - Distributed, Parallel, and Cluster Computing, Computer Science - Programming Languages
Abstract

The purpose of this paper is to show how existing scientific software can be parallelized using a separate thin layer of Python code where all parallel communication is implemented. We provide specific examples on such layers of code, and these examples may act as templates for parallelizing a wide set of serial scientific codes. The use of Python for parallelization is motivated by the fact that the language is well suited for reusing existing serial codes programmed in other languages. The extreme flexibility of Python with regard to handling functions makes it very easy to wrap up decomposed computational tasks of a serial scientific application as Python functions. Many parallelization-specific components can be implemented as generic Python functions, which may take as input those functions that perform concrete computational tasks. The overall programming effort needed by this parallelization approach is rather limited, and the resulting parallel Python scripts have a compact and clean structure. The usefulness of the parallelization approach is exemplified by three different classes of applications in natural and social sciences., Comment: 29 pages, submitted to Computational Science and Discovery

Published
2010
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36. Analysis

Author

Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, and Langtangen, Hans Petter

Published
2016
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37. Models

Author

Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, and Langtangen, Hans Petter

Published
2016
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38. Scientific Software Engineering

Author

Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, and Langtangen, Hans Petter

Published
2016
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39. Generalizations

Author

Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, and Langtangen, Hans Petter

Published
2016
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40. Algorithms and Implementations

Author

Langtangen, Hans Petter, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, and Langtangen, Hans Petter

Published
2016
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50. Computing Integrals

Author

Linge, Svein, Langtangen, Hans Petter, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Linge, Svein, and Langtangen, Hans Petter

Published
2016
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