Overture: An Object Oriented Framework for Solving PDEs on Composite Grids

Introduction

This document contains the Overture source code documentation. Overture is a framework for grid generation and solving partial differential equations (PDEs) on composite overlapping grids.

Overview

Here is a summary of the various capabilities of Overture.

• Mapping's such as AnnulusMapping, NurbsMapping and HyperbolicMapping represent geometry and continuous representation of grids.
• Grids and GridCollections such as MappedGrid, GridCollection and CompositeGrid represent discrete forms of the domain.
• GridFunctions such as doubleMappedGridFunction, intGridCollectionFunction and floatCompositeGridFunction hold solutions (fields) on grids.
• Ogen is the overlapping grid generator from constructing overlapping grids from Mapping's.
• Interactive graphics is provided through classes such as PlotStuff and PlotIt.
• Graphics postprocessing is done with classes such as plotStuff, Ogshow and ShowFileReader.
• Database support using HDF is managed through the HDF_DataBase class.
• Operators such as MappedGridOperators and CompositeGridOperators define discrete approximations to differential operators and boundary conditions.
• Ogmg is the overlapping grid multigrid solver.
• Oges can be used to solve sparse systems with e.g. PETSc.
• Ugen is the hybrid (structured/unstructured) grid generator.
• There are a variety of utility routines such as Integrate (for integration on overlapping grids), OGFunction (for manufactured solutions), TridiagonalSolver (for solving tri- and penta-diagonal systems).