OVERTURE: An Object-Oriented Software System for Solving Partial Differential Equations in Serial and Parallel Environments

The OVERTURE Framework is an ob ject-oriented environment for solving PDEs on serial and parallel architectures. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures, as well its the details of the parallel implementation. It is based on the A++/P++ array class library and is designed for solving problems on a structured grid or a collection of structured grids. In particular, it can use curvilinear grids, adaptive mesh refinement and the composite overlapping grid method to represent problems with complex moving geometry. 1 htroduction The OVERTURE Framework is an object-oriented C++ library for solving partial differential equations (PDEs) on serial and parallel architectures. It supports finite difference and finite volume computations on a structured grid, or on a collection of structured grids. Collections of structured grids are used, for example, in the method of composite overlapping grids, with block-structured adaptive mesh refinement (AMR) algorithms, and for patched-based domain decomposition methods. This paper concentrates on the implementation of support for two of the higher-level application environments, which are the method of composite overlapping grids 17,141 and the AMR method [I, 3,171. A composite overlapping grid consists of a set of logically rectangular (in 2-D) or hexahedral (in 3-D) curvlinear computational grids that overlap where they meet and together are used to describe a computational region of arbitrary complexity. This method has been used successfully over the last decade and a half, primarily to solve problems involving fluid flow in complex, often dynamically moving, geometries [3, 5, 9, 10, 211. The data structures associated with a flexible overlapping grid solver can be quite complex. Mathematically, each component grid can be described in terms of a transformation from the unit square or cube to the coordinate space of that grid. In order to complete the description of the computational geometry, the overall composite grid also requires information specifying how the component grids communicate with each other e.g. through interpolation formulas. It is also possible for component grids to move with respect to each other as part of a time-dependent simulation. Thus, tools are required to efficiently 'This work supported by the U.S. Department of Energy through Contract W-7405-ENG-36. +Computing, Information and Communications Division, Los Aiamos National Laboratory, Los Aiamos, NM. Web site: http://wv.c3.lanl.gov/cicl9/teams/napc/