Overture: An Object-Oriented Framework for Solving Partial Differential Equations

Abst rac t . The Over tu re framework is a collection of C++ classes that can be used to solve partial differential equations (PDEs). These classes were designed to support applications in one, two and three space dimensions on geometries ranging from simple rectangular regions to complicated three dimensional domains, and to support adaptive mesh refinement and moving grids. Over tu re is designed to run on serial and parallel machines through the use of the A + + / P + + serial/parallel array class library. The Over tu re classes hide the details of the underlying data-structures and hide the details of features common to many PDE solvers such as the implementation of finite-difference and finite-volume operators and boundary conditions. In addition to the Mapping and Grid classes that represent geometry, the GridFunction classes that represent solutions, and the operator classes, there are classes for high-level interactive plotting, and data-base management. Over tu re also includes sophisticated grid generation capabilities for creating overlapping grids.