Using Queries with Multi-Directional Functions for Numerical Database Applications

Object-oriented database management systems are often motivated by their support for new emerging application areas such as computer-aided design and analysis systems. The object-oriented data model is well suited for managing the data complexity and representation needs of such applications. We have built a system for finite element analysis using an object-relational database management system. Our application domain needs customized numerical data representations and an object-oriented data model extended with multi-methods where several arguments are used in type resolution. To efficiently process queries involving domain functions in this environment without having to copy data to the application, support is needed for queries calling multi-methods with any configuration of bound or unbound arguments, called multi-directional functions. We show how to model multi-directional functions views containing matrix algebra operators, how to process queries to these views, and how to execute these queries in presence of late binding.