June 20^th – 24^th

Department of Mathematics, Warwick University

Organizers: Andreas Dedner (University of Warwick, UK), Robert Klöfkorn and Martin Nolte (University of Freiburg, Germany).

 

The Distributed and Unified Numerics Environment (DUNE) is a modular toolbox for solving partial differential equations using grid-based methods with special emphasise on parallel computing using distributed grids. This one week course will give an introduction to the DUNE core modules including the DUNE grid interface library, and the DUNE-FEM module. The school consists of lectures providing required background information but consists to a large part of hands on practical session.

The course will focus on the numerical treatment of evolution equations of the form

using continuous and discontinuous Galerkin methods. These schemes will be implemented with the DUNE-FEM module. We will introduce the dune core modules focusing on the parallel grid interface. Then the DUNE-FEM module will be introduced which provides interfaces for implementing higher order numerical methods. The emphasis will be on solving evolution equation on complex domains included surfaces using local adaptivity, parallelization and load balancing to obtain highly efficient numerical methods.

 

Support

This event is made possible by funding from the EPSRC's S\&I Centre for Numerical Algorithms and Intelligent Software (NAIS), the EPSRC's Mathematics and Statistics Centre for Doctoral Training (MASDOC), and the UK & Republic of Ireland SIAM section (SIAM UKIE).

 

Topics

Introduction to DUNE and the DUNE grid interface  (June 20^th – 21^th)

Overview of required C++ and template programming techniques Installing and building the core DUNE modules Introduction to the DUNE grid interface Efficient use of local grid adaptivity Performing parallel computations with dynamic load balancing (see movie)

Density and locally adapted and partitioned grid of the compressible Euler equations in a tunnel with a step.

Discretization of Partial Differential Equations with DUNE-FEM  (June 22^th – 23^th)

• Introduction to DUNE-FEM
• Higher Order discretization schemes (Lagrange Finite Element, Discontinuous Galerkin methods)
• Evolution equations (Explicit, implicit and IMEX Runge-Kutta methods)
• Checkpointing and Data I/O

Advanced Concepts (June 24^th)

More on local adaptivity and parallelization Introduction to Partial Differential Equations on surfaces Handling evolving domains with GeometryGrid Visualization

Front and rear view on the numerical solution to a burgers type equation on the sphere.

Prerequisites

Participants are expected to have a basic knowledge of numerical methods for PDEs, Unix, and C++ as can be obtained from online tutorials, e.g. here.

If you have any problems please send me an email.

Registration and Accommodation

Please register in advance since there is only a limited number of spaces available ( register ).

There are also a limited number of rooms available on campus

• MRC houses: there are a few 3 bedroom houses available for 12 GBP per night per room.
  
• There are a number of B&Bs off campus, e.g., in Kenilworth

  Abbey G H, Ferndall, Hollyhurst, Enderley, Westwood Cottage. Links to these and others can be found here.

The Maths Research Center (MRC) can help with booking accommodation after registration.

See also:
Mathematics Research Centre
Mathematical Interdisciplinary Research at Warwick (MIR@W)
Past Events 
Past Symposia