Design and usability of a PDE solver framework for curvilinear coordinates

Abstract An object-oriented PDE solver framework is a library of software components for numerical solution of partial differential equations, where each component is an object or a group of objects. Given such a framework, the construction of a particular PDE solver consists in selecting and combining suitable components. The present paper is focused on tengo [Ahlander K, Otto K. Software design for finite difference schemes based on index notation. Future Generation Comput Syst 2006;22:102–9], an object-oriented PDE solver framework for finite difference methods on structured grids, using tensor abstractions for convenient representation of numerical operators. Here, the design of tengo is extended to address curvilinear coordinates. These extensions to the tengo object model are the result of applying object-oriented analysis and design combined with feature modeling. The framework was implemented in Fortran 90/95, using standard techniques for emulating object-oriented constructs in that language. The new parts of the framework were assessed with respect to programming effort and execution time. It is shown that the programming effort required for construction and modification of PDE solvers on curvilinear grids is significantly reduced through the introduction of the new framework components. Moreover, for the test case of an underwater acoustics computation, there was no significant difference in execution time between the framework based code and a special purpose Fortran 90 code for the same application.